High resolution schemes for hyperbolic conservation laws

DOI10.1016/0021-9991(83)90136-5zbMath0565.65050OpenAlexW1998830482MaRDI QIDQ1058830

Amiram Harten

Publication date: 1983

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2060/19830002586

zbMATH Keywords

weak solutionsNumerical experimentssecond orderflux functionnonoscillatorynonlinear schemes

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

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II: A multidimensional extension, A continuously differentiable upwinding scheme for the simulation of fluid flow problems, A localized collocation meshless method (LCMM) for incompressible flows CFD modeling with applications to transient hemodynamics, Node-pair finite volume/finite element schemes for the Euler equation in cylindrical and spherical coordinates, The multi-dimensional limiters for solving hyperbolic conservation laws on unstructured grids, A high-resolution Petrov-Galerkin method for the 1D convection-diffusion-reaction problem, A finite volume formulation for transient convection and diffusion equations with unstructured distorted grids and its applications in fluid flow simulations with a collocated variable arrangement, A class of large time step Godunov schemes for hyperbolic conservation laws and applications, Simulation of shock wave diffraction over \(90^\circ \) sharp corner in gases of arbitrary statistics, Optimal strong-stability-preserving Runge-Kutta time discretizations for discontinuous Galerkin methods, A new shock-capturing technique based on moving least squares for higher-order numerical schemes on unstructured grids, An oscillation-free high order TVD/CBC-based upwind scheme for convection discretization, Modification of the CABARET scheme ensuring its strong monotonicity and high accuracy on local extrema, Two-dimensional interaction between an incident shock and a turbulent boundary layer in the presence of an entropy layer, Roe-type schemes for shallow water magnetohydrodynamics with hyperbolic divergence cleaning, An approximate Riemann solver for shallow water equations and heat advection in horizontal centrifugal casting, Preconditioning of gas dynamics equations in compressible gas flow computations at low Mach numbers, Uniformly high order accurate essentially non-oscillatory schemes. III. (Reprint), Explicit time marching methods for the time-dependent Euler computations, An implicit scheme for nonideal magnetohydrodynamics, Moving mesh methods with upwinding schemes for time-dependent PDEs, A phenomenon of artificial odd-even grid oscillation and its presence in domain decomposition computation: algebraic analysis and numerical illustration, Harten solution for one-dimensional unsteady equation, TVD scheme for stiff problems of wave dynamics of heterogeneous media of nonhyperbolic nonconservative type, On the convergence of a local third order shock capturing method for hyperbolic conservation laws, Numerical experiments with nonoscillatory schemes using Eulerian and new Lagrangian formulations, Higher-order-accurate upwind schemes for solving the compressible Euler and Navier--Stokes equations, Quantification of numerically induced mixing and dissipation in discretisations of shallow water equations, Comparative study of different numerical approaches in space-time CESE framework for high-fidelity flow simulations, Simulation and visualization of the Saint-Venant system using GPUs, Shock calculation based on second viscosity using local differential quadrature method, A pressure-based method for turbulent cavitating flow computations, On the linear stability of the fifth-order WENO discretization, Improvement of convergence to steady state solutions of Euler equations with the WENO Schemes, A positivity-preserving ALE finite element scheme for convection-diffusion equations in moving domains, An unstaggered constrained transport method for the 3D ideal magnetohydrodynamic equations, On the sonic point glitch, A numerical scheme based on a solution of nonlinear advection--diffusion equations, On the spectral and conservation properties of nonlinear discretization operators, Well-balanced and energy stable schemes for the shallow water equations with discontinuous topography, Operator splitting implicit integration factor methods for stiff reaction-diffusion-advection systems, Adaptive mesh refinement for conservative systems: multi-dimensional efficiency evaluation, Second-order schemes for conservation laws with discontinuous flux modelling clarifier-thickener units, Two-dimensional central-upwind schemes for curvilinear grids and application to gas dynamics with angular momentum, Grid adaptive algorithms for the solution of the Euler equations on irregular grids, Reprint of: ``Residual equilibrium schemes for time dependent partial differential equations, Decoupling schemes for predicting compressible fluid flows, A discontinuous Galerkin material point method for the solution of impact problems in solid dynamics, A new fifth order finite difference WENO scheme for solving hyperbolic conservation laws, Hybrid discrete/continuum algorithms for stochastic reaction networks, Finite difference Hermite WENO schemes for conservation laws. II: An alternative approach, A bounded upwinding scheme for computing convection-dominated transport problems, A penalty formulation for the throughflow modeling of turbomachinery, Multi-dimensional limiting process for finite volume methods on unstructured grids, Two-dimensional simulation of shallow-water waves by Lagrangian block advection, A modified TENO scheme with improved efficiency, GPU implementation of explicit and implicit Eulerian methods with TVD schemes for solving 2D solute transport in heterogeneous flows, A new Eulerian model for viscous and heat conducting compressible flows, A new paradigm of dissipation-adjustable, multi-scale resolving schemes for compressible flows, A class of high-order weighted compact central schemes for solving hyperbolic conservation laws, Mitigation of post-shock oscillations induced by artificial viscosity in discontinuous finite element methods, A sixth order entropy condition scheme for compressible flow, A fifth-order low-dissipation discontinuity-resolving TENO scheme for compressible flow simulation, New mapped unequal-sized trigonometric WENO scheme for hyperbolic conservation laws, On the supremum of the steepness parameter in self-adjusting discontinuity-preserving schemes, Continuum modeling of cell sorting within a plane layer with account for the possible separation of the boundaries of the regions occupied by cells of two different types, A theoretical framework for discontinuity capturing: joining variational multiscale analysis and variation entropy theory, Bound-preserving flux limiting schemes for DG discretizations of conservation laws with applications to the Cahn-Hilliard equation, Constructing higher order discontinuity-capturing schemes with upwind-biased interpolations and boundary variation diminishing algorithm, A new type of increasingly high-order multi-resolution trigonometric WENO schemes for hyperbolic conservation laws and highly oscillatory problems, A new method towards high-order weno schemes on structured and unstructured grids, The discontinuous Galerkin material point method for variational hyperelastic-plastic solids, An edge detector based on artificial neural network with application to hybrid compact-WENO finite difference scheme, A low-diffusion self-adaptive flux-vector splitting approach for compressible flows, Solution property preserving reconstruction BVD+MOOD scheme for compressible Euler equations with source terms and detonations, An improved Roe solver for high order reconstruction schemes, Well-balanced central schemes for the one and two-dimensional Euler systems with gravity, Behaviour of the Serre equations in the presence of steep gradients revisited, Combined DG scheme that maintains increased accuracy in shock wave areas, Low shear diffusion central schemes for particle methods, On the range diminishing property of numerical schemes for scalar conservation laws, Direction-aware slope limiter for three-dimensional cubic grids with adaptive mesh refinement, A fast, robust, and simple Lagrangian-Eulerian solver for balance laws and applications, On the accuracy of bicompact schemes as applied to computation of unsteady shock waves, A modified fifth order finite difference Hermite WENO scheme for hyperbolic conservation laws, Adaptive mapping for high order WENO methods, FLEXI: a high order discontinuous Galerkin framework for hyperbolic-parabolic conservation laws, A fifth-order shock capturing scheme with two-stage boundary variation diminishing algorithm, Local discontinuous Galerkin methods to a dispersive system of KdV-type equations, A class of Lagrangian-Eulerian shock-capturing schemes for first-order hyperbolic problems with forcing terms, A new type of multi-resolution WENO schemes with increasingly higher order of accuracy on triangular meshes, Entropy stable artificial dissipation based on Brenner regularization of the Navier-Stokes equations, Bounded and compact weighted essentially nonoscillatory limiters for discontinuous Galerkin schemes: triangular elements, A volume of fluid framework for interface-resolved simulations of vaporizing liquid-gas flows, An efficient and accurate MPI-based parallel simulator for streamer discharges in three dimensions, A comparison of two- and three-dimensional single-mode reshocked Richtmyer-Meshkov instability growth, WENO interpolation for Lagrangian particles in highly compressible flow regimes, Numerical issues in gas flow dynamics with hydraulic shocks using high order finite volume WENO schemes, A hybrid Hermite WENO scheme for hyperbolic conservation laws, A comparative analysis of explicit, IMEX and implicit strong stability preserving Runge-Kutta schemes, On the performance of high resolution non-oscillating advection schemes in the context of the flow generated by a mixed region in a stratified fluid, A semi-discrete central scheme for incompressible multiphase flow in porous media in several space dimensions, Entropy inequalities for fully-discrete E-schemes: a sequel, A class of non-oscillatory direct-space-time schemes for hyperbolic conservation laws, Numerical schemes for quasi-1D steady nozzle flows, Accuracy of MUSCL-type schemes in shock wave calculations, An L2-norm regularized incremental-stencil WENO scheme for compressible flows, Construction and application of several new symmetrical flux limiters for hyperbolic conservation law, Simplified artificial viscosity approach for curing the shock instability, High-order mapped WENO methods with improved efficiency, Fourth-order gas-kinetic scheme for turbulence simulation with multi-dimensional WENO reconstruction, Large-eddy simulations of the flow over a semi-circular cylinder at Re = 50000, A suitability analysis of transient one-dimensional two-fluid numerical models for simulating two-phase gas-liquid flows based on benchmark problems, High resolution central scheme using a new upwind slope limiter for hyperbolic conservation laws, Very-high-order TENO schemes with adaptive accuracy order and adaptive dissipation control, Strong-stability-preserving, Hermite-Birkhoff time-discretization based on \(k\) step methods and 8-stage explicit Runge-Kutta methods of order 5 and 4, A finite volume method parallelization for the simulation of free surface shallow water flows, A convergent finite difference scheme for the Ostrovsky-Hunter equation with Dirichlet boundary conditions, Second-order formulation of a multigrid method for steady Euler equations through defect-correction, A modified monotonicity-preserving high-order scheme with application to computation of multi-phase flows, A new very high-order upwind directional multi-layer compact (DMLC) scheme for multi-dimensional flows, A strong stability preserving analysis for explicit multistage two-derivative time-stepping schemes based on Taylor series conditions, Entropy inequalities for fully-discrete E-schemes, A central scheme for advecting scalars by velocity fields obtained from finite volume multiphase incompressible solvers, Numerical solution of the fully non-linear weakly dispersive Serre equations for steep gradient flows, A probabilistic model for track random irregularities in vehicle/track coupled dynamics, Hybrid flux method in monotonicity-preserving scheme for accurate and robust simulation in supersonic flow, Entropy-stable schemes for relativistic hydrodynamics equations, Strong stability preserving second derivative diagonally implicit multistage integration methods, A Lagrangian finite element method for 3D compressible flow applications, Analysis of slope limiters on unstructured triangular meshes, A new class of adaptive high-order targeted ENO schemes for hyperbolic conservation laws, Progress in the development of a new lattice Boltzmann method, New very high-order upwind multi-layer compact (MLC) schemes with spectral-like resolution for flow simulations, High-order well-balanced finite volume schemes for the Euler equations with gravitation, IB-WENO method for incompressible flow with elastic boundaries, Multiscale polynomial-based high-order central high resolution schemes, Investigation of the spectral composition of the gas pressure and thrust pulsations in nozzles equipped with a deflector, Multiresolution-based adaptive central high resolution schemes for modeling of nonlinear propagating fronts, Discrete regularization, High-order accurate large-eddy simulations of compressible viscous flow in cylindrical coordinates, An accuracy preserving limiter for the high-order discontinuous Galerkin method on unstructured grids, Implicitly coupled phase fraction equations for the Eulerian multi-fluid model, A group of CFL-dependent flux-limiters to control the numerical dissipation in multi-stage unsteady calculation, Strong stability preserving second derivative general linear methods, An efficient hybrid method for solving Euler equations, Multi-element SIAC filter for shock capturing applied to high-order discontinuous Galerkin spectral element methods, Modified stencil approximations for fifth-order weighted essentially non-oscillatory schemes, A shock-capturing meshless scheme using RBF blended interpolation and moving least squares, Recent advances on the numerical modelling of turbulent flows, Finite difference Hermite WENO schemes for hyperbolic conservation laws, Exponential stability of a general slope limiter scheme for scalar conservation laws subject to a dissipative boundary condition, Shock capturing, level sets, and PDE based methods in computer vision and image processing: A review of Osher's contributions, A high-order moment limiter for the discontinuous Galerkin method on triangular meshes, Resolution of high order WENO schemes for complicated flow structures., Hybrid grid-characteristic schemes for arctic seismic problems, On derivation and verification of a kinetic model for quantum vibrational energy of polyatomic gases in the gas-kinetic unified algorithm, Entropy stable discontinuous Galerkin schemes for the special relativistic hydrodynamics equations, Robust numerical fluxes for unrealizable states, Flux-corrected transport for scalar hyperbolic conservation laws and convection-diffusion equations by using linear programming, An efficient targeted ENO scheme with local adaptive dissipation for compressible flow simulation, A locally implicit time-reversible sonic point processing algorithm for one-dimensional shallow-water equations, A new fifth order finite difference WENO scheme to improve convergence rate at critical points, A domain decomposition technique for small amplitude wave interactions with shock waves, Compressible multiphase particle-in-cell method (CMP-PIC) for full pattern flows of gas-particle system, A conservative diffuse-interface method for compressible two-phase flows, Overcoming shock instability of the HLLE-type Riemann solvers, High-resolution FEM-TVD schemes based on a fully multidimensional flux limiter, A low-dissipation shock-capturing framework with flexible nonlinear dissipation control, Low-dissipation BVD schemes for single and multi-phase compressible flows on unstructured grids, Very high order WENO schemes using efficient smoothness indicators, Feature-based and goal-oriented anisotropic mesh adaptation for RANS applications in aeronautics and aerospace, An alternative formulation of targeted ENO scheme for hyperbolic conservation laws, Monotone schemes of conditional approximation and arbitrary order of accuracy for the transport equation, Gas-liquid two-phase flows simulation based on weakly compressible scheme with interface-adapted AMR method, Multi-resolution HWENO schemes for hyperbolic conservation laws, A novel high-order low-dissipation TENO-THINC scheme for hyperbolic conservation laws, Periodic adjoints and anisotropic mesh adaptation in rotating frame for high-fidelity RANS turbomachinery applications, High order residual distribution conservative finite difference HWENO scheme for steady state problems, A compact high-order gas-kinetic scheme on unstructured mesh for acoustic and shock wave computations, Numerical benchmark for the charge cycle in a combustion engine, Godunov scheme for the scalar nonlinear conservation laws with flux depending on the space variable, An approximate solution of one-dimensional piston problem, A note on the effect of artificial viscosity on solutions of conservation laws, High order weighted essentially non-oscillation schemes for two-dimensional detonation wave simulations, A critical study of the compressible lattice Boltzmann methods for Riemann problem, The VOLNA code for the numerical modeling of tsunami waves: generation, propagation and inundation, On the monotonicity of multidimensional difference schemes, A non-oscillatory central scheme for one-dimensional two-layer shallow water flows along channels with varying width, WENO schemes and their application as limiters for RKDG methods based on trigonometric approximation spaces, Roe solver with entropy corrector for uncertain hyperbolic systems, Application of an element-by-element BiCGSTAB iterative solver to a monotonic finite element model, The space-time conservation element and solution element method: A new high-resolution and genuinely multidimensional paradigm for solving conservation laws, MAG -- two-dimensional resistive MHD code using an arbitrary moving coordinate system, On an adaptive monotonic convection-diffusion flux discretization scheme, Numerical simulations for radiation hydrodynamics. II: Transport limit, A symmetric formulation for computing transient shallow water flows, An approximate Riemann solver for a two-phase flow model with numerically given slip relation, Numerical investigation of 3D shock focusing effects on the basis of the Euler equation, An improvement of AUSM schemes by introducing the pressure-based weight functions, Efficient time integration of Navier-Stokes equations, Flux-limiter schemes for oceanic tracers: Application to the English Channel tidal model, New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations, A meshless generalized finite difference method for solving shallow water equations with the flux limiter technique, Variation entropy: a continuous local generalization of the TVD property using entropy principles, Implicit large eddy simulation of compressible turbulence flow with \(\mathrm{P}_n\mathrm{T}_m-\mathrm{BVD}\) scheme, High-order filtered schemes for first order time dependent linear and non-linear partial differential equations, An improved flux limiter using fuzzy modifiers for hyperbolic conservation laws, A compact fourth-order gas-kinetic scheme for the Euler and Navier-Stokes equations, Suitable diffusion for constructing non-oscillatory entropy stable schemes, Linear hybrid-variable methods for advection equations, A new type of multi-resolution WENO schemes with increasingly higher order of accuracy, Numerical error control for second-order explicit TVD scheme with limiters in advection simulation, Numerical homogenization of a second order discrete model for traffic flow, Numerical model of compression plasma flows in channels under a longitudinal magnetic field, Numerical solution of multidimensional hyperbolic PDEs using defect correction on adaptive grids, An explicit implicit scheme for cut cells in embedded boundary meshes, Cartesian grid method for the compressible Euler equations using simplified ghost point treatments at embedded boundaries, Kinetic numerical methods for solving the semiclassical Boltzmann-BGK equation, A new perspective on flux and slope limiting in discontinuous Galerkin methods for hyperbolic conservation laws, Algebraic entropy fixes and convex limiting for continuous finite element discretizations of scalar hyperbolic conservation laws, A new sixth-order finite difference WENO scheme for fractional differential equations, High-order Runge-Kutta discontinuous Galerkin methods with multi-resolution WENO limiters for solving steady-state problems, A method to solve Hamilton-Jacobi type equation on unstructured meshes, Stable time step estimation for multi-material Eulerian hydrocodes, Hybrid upwind methods for the simulation of unsteady shock-wave diffraction over a cylinder, Maximum principle and positivity-preserving high order spectral volume schemes with parametrized flux limiters for solving hyperbolic conservation laws, Multi-stencils fast marching method for factored eikonal equations with quadratic anisotropy, On the use of nonlinear filtering, artificial viscosity, and artificial heat transfer for strong shock computations, Multiresolution schemes for the reactive Euler equations, A solution-adaptive upwind scheme for ideal magnetohydrodynamics, A class of positive semi-discrete Lagrangian-Eulerian schemes for multidimensional systems of hyperbolic conservation laws, An efficient low-dissipation high-order TENO scheme for MHD flows, Enhanced fifth order WENO shock-capturing schemes with deep learning, Three-level order-adaptive weighted essentially non-oscillatory schemes, A high-order weighted compact nonlinear scheme for compressible Flows, A semi-discrete Lagrangian-Eulerian scheme for hyperbolic-transport models, Progress in computational physics, An efficient smoothness indicator mapped WENO scheme for hyperbolic conservation laws, Parallel high-order resolution of the shallow-water equations on real large-scale meshes with complex bathymetries, Using a combination of Godunov and Rusanov solvers based on the piecewise parabolic reconstruction of primitive variables for numerical simulation of supernovae Ia type explosion, Accuracy and nonoscillatory properties of enslaved difference schemes, High-order variable index weighted essentially non-oscillatory scheme for hyperbolic conservation law, Finite element analysis of contaminant transport in groundwater., Combined numerical schemes, A finite difference mapped WENO scheme with unequal-size stencils for hyperbolic conservation laws, Adaptive multiresolution approach for solution of hyperbolic PDEs, Improvements of the fifth-order WENO-JS-type scheme with normalized smoothing factor for gas dynamic Euler equations, Simulation of the sorting of two types of cells in a cell spheroid with account for the movement of the boundaries of regions occupied by cells of different types, Error estimates on the random projection methods for hyperbolic conservation laws with stiff reaction terms, Bound-preserving flux limiting for high-order explicit Runge-Kutta time discretizations of hyperbolic conservation laws, Construction of approximate entropy measure-valued solutions for hyperbolic systems of conservation laws, The application of the locally implicit method to upwind TVD schemes, A new Lagrangian method for steady supercritical shallow water flow computation, A discontinuous Galerkin scheme for the numerical solution of flow problems with discontinuities, On the convergence of finite difference methods for PDE under temporal refinement, TVD differencing on three-dimensional unstructured meshes with monotonicity-preserving correction of mesh skewness, An optimized dispersion-relation-preserving combined compact difference scheme to solve advection equations, A review on TVD schemes and a refined flux-limiter for steady-state calculations, A family of high-order targeted ENO schemes for compressible-fluid simulations, Exploring various flux vector splittings for the magnetohydrodynamic system, Compact high order finite volume method on unstructured grids I: Basic formulations and one-dimensional schemes, A roe-like numerical method for weakly hyperbolic systems of equations in conservation and non-conservation form, Well-posedness of a conservation law with non-local flux arising in traffic flow modeling, Selected Topics in Approximate Solutions of Nonlinear Conservation Laws. High-Resolution Central Schemes, Accurate monotonicity- and extrema-preserving methods through adaptive nonlinear hybridizations, A hybrid Godunov method for radiation hydrodynamics, A new approach of a limiting process for multi-dimensional flows, An interface capturing method for the simulation of multi-phase compressible flows, Spectral difference method for unstructured grids. II. Extension to the Euler equations, A new smoothness indicator for the WENO schemes and its effect on the convergence to steady state solutions, 1D gas dynamic modelling of mass conservation in engine duct systems with thermal contact discontinuities, A single-stage flux-corrected transport algorithm for high-order finite-volume methods, Multi-dimensional limiting process for hyperbolic conservation laws on unstructured grids, Numerical investigations of turbulent free surface flows using TOPUS scheme, A new adaptive weighted essentially non-oscillatory WENO-\(\theta\) scheme for hyperbolic conservation laws, A review of the XFEM-based approximation of flow in fractured porous media, Finite volume schemes for the numerical simulation of tracer transport in plants, Convergence to steady-state solutions of the new type of high-order multi-resolution WENO schemes: a numerical study, An essential seventh-order weighted compact adaptive scheme for hyperbolic conservation laws, A \(2\times 2\) hyperbolic system modelling incompressible two phase flows: theory and numerics, Positivity preserving pointwise implicit schemes with application to turbulent compressible flat plate flow, Adaptive total variation stable local timestepping for conservation laws, Self-adjusting steepness-based schemes that preserve discontinuous structures in compressible flows, An implicit large eddy simulation method based on all-speed schemes, On alternative setups of the double Mach reflection problem, On the numerical simulation of non-classical quasi-1D steady nozzle flows: capturing sonic shocks, Comparison among unstructured TVD, ENO and UNO schemes in two- and three-dimensions, Compact third-order accurate, positive preserving and divergence-free scheme, Numerical investigation of Mach number consistent Roe solvers for the Euler equations of gas dynamics, Pressure-based algorithm for compressible interfacial flows with acoustically-conservative interface discretisation, Derivation and numerical comparison of Shakhov and ellipsoidal statistical kinetic models for a monoatomic gas mixture, Flux-limiting techniques for simulation of pollutant transport in porous media: application to groundwater management, Wavenumber-extended high-order oscillation control finite volume schemes for multi-dimensional aeroacoustic computations, New finite difference mapped WENO schemes with increasingly high order of accuracy, Quinpi: integrating conservation laws with CWENO implicit methods, Adaptive edge detectors for piecewise smooth data based on the minmod limiter, Simulation of space plasma allowing for the Hall effect: Kelvin-Helmholtz and Rayleigh-Taylor instabilities, GPU-accelerated DNS of compressible turbulent flows, A unified framework for non-linear reconstruction schemes in a compact stencil. I: Beyond second order, Central schemes and contact discontinuities, Phase appearance or disappearance in two-phase flows, Modeling of III-D problems of gas dynamics on multiprocessing computers and GPU, 3DFLUX: a high-order fully three-dimensional flux integral solver for the scalar transport equation, New adaptive artificial viscosity method for hyperbolic systems of conservation laws, A finite volume method with a modified ENO scheme using a Hermite interpolation to solve advection diffusion equations, Improved ninth order WENO scheme for hyperbolic conservation laws, A class of high order TVD schemes for systems of conservation laws, An arbitrary Lagrangian-Eulerian discretization of MHD on 3D unstructured grids, Limiters for high-order discontinuous Galerkin methods, Hybrid block-AMR in Cartesian and curvilinear coordinates: MHD applications, Modeling of industrial problems on high-performance polyprocessor computing systems, Multirate timestepping methods for hyperbolic conservation laws, A class of high resolution shock capturing schemes for hyperbolic conservation laws, A shock-capturing model based on flux-vector splitting method in boundary-fitted curvilinear coordinates, An improved \(r\)-factor algorithm for TVD schemes, Effect of discretization order on preconditioning and convergence of a high-order unstructured Newton-GMRES solver for the Euler equations, Very simple, carbuncle-free, boundary-layer-resolving, rotated-hybrid Riemann solvers, A high-order accurate unstructured finite volume Newton-Krylov algorithm for inviscid compressible flows, The construction of discretely conservative finite volume schemes that also globally conserve energy or entropy, Formulation of kinetic energy preserving conservative schemes for gas dynamics and direct numerical simulation of one-dimensional viscous compressible flow in a shock tube using entropy and kinetic energy preserving schemes, A family of numerical schemes for kinematic flows with discontinuous flux, Fully adaptive multiresolution schemes for strongly degenerate parabolic equations with discontinuous flux, On the link between weighted least-squares and limiters used in higher-order reconstructions for finite volume computations of hyperbolic equations, Accurate, efficient and monotonic numerical methods for multi-dimensional compressible flows. I: Spatial discretization, Accurate, efficient and monotonic numerical methods for multi-dimensional compressible flows. II: Multi-dimensional limiting process, High order residual distribution conservative finite difference WENO schemes for steady state problems on nonsmooth meshes, A high resolution total variation diminishing scheme for hyperbolic conservation law and related problems, High-resolution finite compact difference schemes for hyperbolic conservation laws, Generalized Harten Formalism and Longitudinal Variation Diminishing schemes for Linear Advection on Arbitrary Grids, A high resolution scheme for Eulerian gas--solid two-phase isentropic flow, Hybrid Compact-WENO Finite Difference Scheme with Conjugate Fourier Shock Detection Algorithm for Hyperbolic Conservation Laws, High-resolution schemes for bubbling flow computations, MUSTA: a multi-stage numerical flux, A General Approach to Enhance Slope Limiters in MUSCL Schemes on Nonuniform Rectilinear Grids, A structured model for the spread of \textit{Mycobacterium marinum}: foundations for a numerical approximation scheme, The reservoir technique: a way to make Godunov-type schemes zero or very low diffuse. Application to Colella-Glaz solver, A class of the fourth order finite volume Hermite weighted essentially non-oscillatory schemes, Large Time Step TVD Schemes for Hyperbolic Conservation Laws, Stable Simulation of Shallow-Water Waves by Block Advection, Hybrid Compact-WENO Finite Difference Scheme For Detonation Waves Simulations, A Second-Order High-Resolution Scheme for a Juvenile-Adult Model of Amphibians, Computer evaluation of high order numerical schemes to solve advective transport problems, A hybrid scheme for the numerical simulation of shock/discontinuity problems, Multi-level lattice Boltzmann model on square lattice for compressible flows, Simulation of transition and turbulence decay in the Taylor–Green vortex, Numerical modeling of seismic triggering, evolution, and deposition of rapid landslides: Application to Higashi-Takezawa (2004), Numerical experiments using high-resolution schemes for unsteady, inviscid, compressible flows, High-resolution FEM--FCT schemes for multidimensional conservation laws, A second-order finite difference approximation for a mathematical model of erythropoiesis, High-order mixed weighted compact and non-compact scheme for shock and small length scale interaction, Unnamed Item, Boundedness and strong stability of Runge-Kutta methods, Adaptive methods for multi‐material ALE hydrodynamics, Slope limiting for vectors: A novel vector limiting algorithm, Error estimates for forward Euler shock capturing finite element approximations of the one-dimensional Burgers' equation, Sergei Konstantinovich Godunov has turned 85 years old, Unnamed Item, A high resolution upwind scheme for multi-component flows, Front tracking for two-phase flow in reservoir simulation by adaptive mesh, Software package for solving hyperbolic-type equations, Composite high resolution localized relaxation scheme based on upwinding for hyperbolic conservation laws, Error Estimates of a First-order Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations, An Efficient Filtered Scheme for Some First Order Time-Dependent Hamilton--Jacobi Equations, Linearized form of implicit TVD schemes for the multidimensional Euler and Navier-Stokes equations, Parametrized maximum principle preserving flux limiters for high order schemes solving hyperbolic conservation laws: one-dimensional scalar problem, Hybrid Compact-WENO Finite Difference Scheme with Radial Basis Function Based Shock Detection Method for Hyperbolic Conservation Laws, Strong Stability Preserving Integrating Factor Runge--Kutta Methods, Shock waves and phase changes in a large-heat-capacity fluid emerging from a tube, Total variation bounded flux limiters for high order finite difference schemes solving one-dimensional scalar conservation laws, On the shock enhancement of confined supersonic mixing flows, Numerical investigation on the structure of a confined supersonic mixing layer, Numerical Simulations Using TVD Schemes of Two-Dimensional Supersonic Flow in Chemical Equilibrium, The Lattice-Boltzmann Method for Multiphase Fluid Flow Simulations and Euler-Lagrange Large-Eddy Simulations, A Riemann solver for RANS, A new, high-resolution shock-capturing hybrid scheme of flux vector splitting-Harten's TVD, Application of Finite Difference TVD Methods in Hypersonic Aerodynamics, Nonlocal Conservation Laws. A New Class of Monotonicity-Preserving Models, Analysis and Design of a Class of Limiter Schemes in Presence of Physical Diffusion, Simulation of aeroacoustic resonance in a deep cavity with grazing flow using a pressure-based solver, On high-order accurate weighted essentially non-oscillatory and discontinuous Galerkin schemes for compressible turbulence simulations, On the practical accuracy of shock-capturing schemes, Discontinuous Galerkin Methods for Time-Dependent Convection Dominated Problems: Basics, Recent Developments and Comparison with Other Methods, Comparisons of numerical methods with respect to convectively dominated problems, Entropy Stability and the No-Slip Wall Boundary Condition, Simulation of multiphase flows in porous media with gravitational effects using dominant wave method, Numerical simulation of two-phase reactive flow with moving boundary, High-order interpolation schemes for shear instability simulations, An accurate shock-capturing scheme based on rotated-hybrid Riemann solver, Arbitrary Lagrangian-Eulerian discontinuous Galerkin method for conservation laws: Analysis and application in one dimension, Entropic sub-cell shock capturing schemes via Jin-Xin relaxation and Glimm front sampling for scalar conservation laws, AN ALTERNATING EVOLUTION APPROXIMATION TO SYSTEMS OF HYPERBOLIC CONSERVATION LAWS, Error estimates to smooth solutions of semi‐discrete discontinuous Galerkin methods with quadrature rules for scalar conservation laws, Hamilton–Jacobi–Bellman Equations, Unnamed Item, A fast, high resolution, second-order central scheme for incompressible flows, Large time step HLL and HLLC schemes, Numerical experiments with several variant WENO schemes for the Euler equations, A Moment Limiter for the Discontinuous Galerkin Method on Unstructured Triangular Meshes, Numerical investigation of the propagation of shock waves in rigid porous materials: development of the computer code and comparison with experimental results, An accurate numerical algorithm for solving compressible three-phase flows in porous media, An adaptive wavelet-collocation method for shock computations, A computational framework for predicting laminar reactive flows with soot formation, Finite difference approximations for a size-structured population model with distributed states in the recruitment, A second-order high-resolution finite difference scheme for a size-structured model for the spread ofMycobacterium marinum, Temperature-dependent viscous gravity currents with shear heating, Total variation diminishing Runge-Kutta schemes, A new finite variable difference method with application to nonlinear Burgers' equation, Conservative Upwind Correction Method for Scalar Linear Hyperbolic Equations, Finite volume simulation of waves formed by sliding masses, On the approximation of local efflux/influx bed discharge in the shallow water equations based on a wave propagation algorithm, Why Nonconservative Schemes Converge to Wrong Solutions: Error Analysis, CENTERED DIFFERENCE SCHEMES FOR NONLINEAR HYPERBOLIC EQUATIONS, Computational method for turbulent supersonic flows, Higher-Order Flux-Limiting Schemes for the Finite Volume Computation of Incompressible Flow, Data assimilation and inverse problem for fluid traffic flow models and algorithms, Healing of shock instability for Roe's flux-difference splitting scheme on triangular meshes, An improvement of classical slope limiters for high-order discontinuous Galerkin method, Discretization methods with analytical solutions for a convection–reaction equation with higher-order discretizations, Evaluation of linear and nonlinear convection schemes on multidimensional non-orthogonal grids with applications to KVLCC2 tanker, Simplified Energy Landscape for Modularity Using Total Variation, A new shock/discontinuity detector, Shock-Capturing Schemes in Computational MHD, A Third-Order Accurate Variation Nonexpansive Difference Scheme for Single Nonlinear Conservation Laws, Construction of monotonic schemes by the differential approximation method, Flux-corrected transport technique for open channel flow, Multigrid solutions of the Euler and Navier-Stokes equations on unstructured grids, A practical implementation of high-order RKDG models for the 1D open-channel flow equations, A central scheme for shallow water flows along channels with irregular geometry, Modified Multidimensional Dissipation Scheme on Unstructured Meshes for High-speed Compressible Flow Analysis, On the Convergence of Difference Approximations to Scalar Conservation Laws, On the propagation of a normal shock wave through a layer of incompressible porous material, Multi-dimensional wave-oriented upwind schemes with reduced cross-wind diffusion for flow in porous media, An efficient TVD-WENO method for conservation laws, High-Order Schemes and Entropy Condition for Nonlinear Hyperbolic Systems of Conservation Laws, Insights on a sign-preserving numerical method for the advection-diffusion equation, A comparative study of TVD-limiters-well-known limiters and an introduction of new ones, A flow solver for the Euler and Navier‐Stokes equations for multi‐phase flows with a stiffened gas equation of state, The approximate Riemann solver of Roe applied to a drift-flux two-phase flow model, Nonlinear Filters for Efficient Shock Computation, On the Accuracy of Upwind and Symmetric TVD Schemes in Simulating Low Mach Number Flow, A Cure for the Sonic Point Glitch, Flux limiters fourth and sixth order high resolution method for hyperbolic conservation laws, Predictor–corrector scheme for the solution of shallow water equations, A comparison of TVD Lax-Wendroff methods, Numerical investigation of the propagation of shock waves in rigid porous materials, Multi‐dimensional monotone flux discretization scheme for convection dominated flows, On Some Numerical Schemes for Transonic Flow Problems, Unnamed Item, Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions, Numerical investigation of a gas dynamic model for charge transport in semiconductors, A level set approach for computing discontinuous solutions of Hamilton-Jacobi equations, A localised dynamic closure model for Euler turbulence, An Acoustic and Shock Wave Capturing Compact High-Order Gas-Kinetic Scheme with Spectral-Like Resolution, On the Behaviour of High-Order One-Step Monotonicity-Preserving Scheme for Direct Numerical Simulation of Shocked Turbulent Flows, A Fifth Order Alternative Mapped WENO Scheme for Nonlinear Hyperbolic Conservation Laws, Multiderivative Combined Dissipative Compact Scheme Satisfying Geometric Conservation Law III: Characteristic-Wise Hybrid Method, Essentially non-oscillatory and weighted essentially non-oscillatory schemes, THE FINITE-DIFFERENCE SCHEME FOR THE UNSTEADY CONVECTION-DIFFUSION EQUATION BASED ON WEIGHTED LOCAL CUBIC SPLINE INTERPOLATION, Invariant-Domain-Preserving High-Order Time Stepping: I. Explicit Runge--Kutta Schemes, Сравнительный анализ точности трех различных схем при сквозном расчете ударных волн, Discrete filtering of numerical solutions to hyperbolic conservation laws, NUMERICAL MODELLING OF POLLUTION TRANSPORT IN TOM RIVER, Conjugate filter approach for shock capturing, BEHAVIOR OF TVD LIMITERS ON THE SOLUTION OF NON-LINEAR HYPERBOLIC EQUATION, HIGH ORDER LOCALIZED ENO SCHEMES ON UNSTRUCTURED MESHES FOR CONSERVATION LAWS, Adaptive Solution of Initial Value Problems by a Dynamical Galerkin Scheme, A Second Order Time Homogenized Model for Sediment Transport, On the convergence of high resolution methods with multiple time scales for hyperbolic conservation laws, A high resolution NV/TVD Hermite polynomial upwind scheme for convection‐dominated problems, Rapid motions of free-surface avalanches down curved and twisted channels and their numerical simulation, Unnamed Item, A family of efficient high-order hybrid finite difference schemes based on WENO schemes, An extension and analysis of the Shu-Osher representation of Runge-Kutta methods, A note on (2K+1)-point conservative monotone schemes, A CELL-CENTERED SECOND-ORDER ACCURATE FINITE VOLUME METHOD FOR CONVECTION–DIFFUSION PROBLEMS ON UNSTRUCTURED MESHES, Derivative artificial compression method for conservation laws with multi-dimensional extension, A locally modified second order upwind scheme for convection terms discretization, Эффективная реализация гибридного метода крупных частиц, Numerical Solution of Partial Differential Equations in Arbitrary Shaped Domains Using Cartesian Cut-Stencil Finite Difference Method. Part II: Higher-Order Schemes, A New Fifth-Order Finite Volume Central WENO Scheme for Hyperbolic Conservation Laws on Staggered Meshes, Simulation of shock wave diffraction by a square cylinder in gases of arbitrary statistics using a semiclassical Boltzmann–Bhatnagar–Gross–Krook equation solver, A family of fast multi-resolution ENO schemes for compressible flows, Quadratic stability of flux limiters, An implicit-explicit upwind algorithm for the parabolized Navier-Stokes equations, A SOLUTION OF THE CONSERVATION LAW FORM OF THE SERRE EQUATIONS, Direct numerical simulations of hypersonic boundary-layer transition for a flared cone: fundamental breakdown, Existence and Computation of Solutions of a Model of Traffic Involving Hysteresis, Error self-canceling of a difference scheme maintaining two conservation laws for linear advection equation, A parallel solution-adaptive scheme for multi-phase core flows in solid propellant rocket motors, New two‐dimensional slope limiters for discontinuous Galerkin methods on arbitrary meshes, О точности схемы типа MUSCL при расчете разрывных решений, COMPENSATED COMPACTNESS FOR 2D CONSERVATION LAWS, Improving Accuracy of the Fifth-Order WENO Scheme by Using the Exponential Approximation Space, A review of numerical methods for nonlinear partial differential equations, Numerical Simulations of Two Coaxial Vortex Rings Head-on Collision, Towards an Accurate and Robust Roe-Type Scheme for All Mach Number Flows, Fundamentals of Lax-Wendroff Type Approach to Hyperbolic Problems with Discontinuities, A New Fifth-Order Trigonometric WENO Scheme for Hyperbolic Conservation Laws and Highly Oscillatory Problems, A New Fifth-Order Finite Difference WENO Scheme for Dam-Break Simulations, A Novel Multi-Dimensional Limiter for High-Order Finite Volume Methods on Unstructured Grids, A Hybrid Numerical Simulation of Supersonic Isotropic Turbulence, Troubled-Cell Indicator based on Mean Value Property for Hybrid WENO schemes, A Higher Order Interpolation Scheme of Finite Volume Method for Compressible Flow on Curvilinear Grids, Solution of a kinetic equation for diatomic gas with the use of differential scattering cross sections computed by the method of classical trajectories, Evaluation of TVD high-resolution schemes for unsteady viscous shocked flows, Sufficient stability criteria and uniform stability of difference schemes, High resolution finite element analysis of shallow water equations in two dimensions, A summary of numerical methods for time-dependent advection-dominated partial differential equations, Simulation of free surface flows using a Runge-Kutta technique, Application of a generalized total variation diminishing algorithm to cosmic ray transport and acceleration., A review and comparative study of upwind biased schemes for compressible flow computation. II: 1-D higher-order schemes, Sixth-order Weighted Essentially Nonoscillatory Schemes Based on Exponential Polynomials, A theory for particle size segregation in shallow granular free-surface flows, A high-resolution pressure-based algorithm for fluid flow at all speeds, On consistent time-integration methods for radiation hydrodynamics in the equilibrium diffusion limit: Low-energy-density regime, Numerical Schemes for Conservation Laws via Hamilton-Jacobi Equations, On the optimization of flux limiter schemes for hyperbolic conservation laws, Numerical computation of wave propagation in dynamic materials, The Koren upwind scheme for variable grid size, A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method, Construction of second-order TVD schemes for nonhomogeneous hyperbolic conservation laws, WENO-TVD schemes for hyperbolic conservation laws, An overview and generalization of implicit Navier-Stokes algorithms and approximate factoriza\-tion., A second-order accurate, component-wise TVD scheme for nonlinear, hyperbolic conservation laws, Some numerical schemes using curvilinear coordinate grids for incompressible and compressible Navier-Stokes equations., Optimized weighted essentially nonoscillatory schemes for linear waves with discontinuity, Divergence-free adaptive mesh refinement for magnetohydrodynamics., Shock-capturing and front-tracking methods for granular avalanches., The third-order relaxation schemes for hyperbolic conservation laws, L²-stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes, Multimesh and multiresolution analysis for mesh adaptive interpolation, Numerical Tracking of Shallow Water Waves by the Unstructured Finite Volume WAF Approximation, Structural Properties of the Stability of Jamitons, Aerodynamic Analysis of Rotor Blades using Overset Grid with Parallel Computation, Unnamed Item, A finite volume scheme for two‐dimensional chemically reactive hypersonic flow, Unnamed Item, Unnamed Item, A New TVD Scheme for Gradient Smoothing Method Using Unstructured Grids, К обоснованию метода интегральной сходимости исследования точности разностных схем сквозного счета, О повышении устойчивости комбинированной схемы разрывного метода Галеркина, Second-Order Accurate TVD Numerical Methods for Nonlocal Nonlinear Conservation Laws, An Oscillation-free Discontinuous Galerkin Method for Scalar Hyperbolic Conservation Laws, Truncation error, dissipation and dispersion terms of fifth order WENO and of WCS for 1D conservation law, Сравнение гибридных схем DDAD/ST и DDAD-TVDR при решении двумерного уравнения переноса теплового излучения, Unnamed Item, A New Type of Modified WENO Schemes for Solving Hyperbolic Conservation Laws, Stability and boundedness in the numerical solution of initial value problems, An improved weighted essentially non-oscillatory scheme with modified smoothness indicator τ and adaptive index p, On Construction of Combined Shock-Capturing Finite-Difference Schemes of High Accuracy

Uses Software

• HLLE

Cites Work

• Approximate Riemann solvers, parameter vectors, and difference schemes
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• The entropy condition and the admissibility of shocks
• A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
• Towards the ultimate conservative difference scheme. II: Monotonicity and conservation combined in a second-order scheme
• On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws
• Monotone Difference Approximations for Scalar Conservation Laws
• A Random Choice Finite Difference Scheme for Hyperbolic Conservation Laws
• The artificial compression method for computation of shocks and contact discontinuities. I. Single conservation laws
• On finite-difference approximations and entropy conditions for shocks
• The Artificial Compression Method for Computation of Shocks and Contact Discontinuities: III. Self-Adjusting Hybrid Schemes
• Solutions in the large for nonlinear hyperbolic systems of equations
• Flux-corrected transport. I: SHASTA, a fluid transport algorithm that works