Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems

From MaRDI portal

Publication:870579

Jump to:navigation, search

DOI10.1016/j.jcp.2006.06.043zbMath1110.65077OpenAlexW2008182598MaRDI QIDQ870579

Martin Käser, Michael Dumbser

Publication date: 13 March 2007

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2006.06.043

zbMATH Keywords

convergence numerical examples unstructured meshes finite volume schemes linear hyperbolic systems ADER approach WENO reconstruction arbitrary high order schemes using derivatives (ADER)discontinuous Galerkin finite element weighted essential nonoscillatory (WENO)

Mathematics Subject Classification ID

Finite volume methods applied to problems in fluid mechanics (76M12) 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) Initial value problems for first-order hyperbolic systems (35L45)

Related Items

High order direct arbitrary-Lagrangian-Eulerian schemes on moving Voronoi meshes with topology changes, A \(p\)-weighted limiter for the discontinuous Galerkin method on one-dimensional and two-dimensional triangular grids, Space-time adaptive ADER discontinuous Galerkin schemes for nonlinear hyperelasticity with material failure, High order central WENO-implicit-explicit Runge Kutta schemes for the BGK model on general polygonal meshes, High order pressure-based semi-implicit IMEX schemes for the 3D Navier-Stokes equations at all Mach numbers, Discontinuous Galerkin schemes with defect corrections based on reconstruction, Improved detection criteria for the multi-dimensional optimal order detection (MOOD) on unstructured meshes with very high-order polynomials, High order ADER schemes and GLM curl cleaning for a first order hyperbolic formulation of compressible flow with surface tension, A third-order subcell finite volume gas-kinetic scheme for the Euler and Navier-Stokes equations on triangular meshes, Absolutely convergent fixed-point fast sweeping WENO methods for steady state of hyperbolic conservation laws, A universal centred high-order method based on implicit Taylor series expansion with fast second order evolution of spatial derivatives, A novel numerical method of high-order accuracy for flow in unsaturated porous media, An implicit high-order \(k\)-exact finite-volume approach on vertex-centered unstructured grids for incompressible flows, A cell-centered implicit-explicit Lagrangian scheme for a unified model of nonlinear continuum mechanics on unstructured meshes, On the properties of high-order least-squares finite-volume schemes, A 3D cell-centered ADER MOOD finite volume method for solving updated Lagrangian hyperelasticity on unstructured grids, A high order approximation of hyperbolic conservation laws in networks: application to one-dimensional blood flow, A novel numerical flux for the 3D Euler equations with general equation of state, Implicit, semi-analytical solution of the generalized Riemann problem for stiff hyperbolic balance laws, A two-dimensional Riemann solver with self-similar sub-structure - alternative formulation based on least squares projection, Multi-dimensional Optimal Order Detection (MOOD) — a Very High-Order Finite Volume Scheme for Conservation Laws on Unstructured Meshes, Consistent treatment of viscoelastic effects at junctions in one-dimensional blood flow models, High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: viscous heat-conducting fluids and elastic solids, Compact high order finite volume method on unstructured grids I: Basic formulations and one-dimensional schemes, Compact high order finite volume method on unstructured grids II: extension to two-dimensional Euler equations, Junction-generalized Riemann problem for stiff hyperbolic balance laws in networks: an implicit solver and ADER schemes, High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments, Comparison of structured- and unstructured-grid, compressible and incompressible methods using the vortex pairing problem, Nonuniform time-step Runge-Kutta discontinuous Galerkin method for computational aeroacoustics, A class of high-order weighted compact central schemes for solving hyperbolic conservation laws, A physical-constraint-preserving finite volume WENO method for special relativistic hydrodynamics on unstructured meshes, A new finite difference mapped unequal-sized WENO scheme for Hamilton-Jacobi equations, A class of new high-order finite-volume TENO schemes for hyperbolic conservation laws with unstructured meshes, New mapped unequal-sized trigonometric WENO scheme for hyperbolic conservation laws, A simple WENO-AO method for solving hyperbolic conservation laws, High-accurate and robust conservative remapping combining polynomial and hyperbolic tangent reconstructions, A staggered semi-implicit discontinuous Galerkin scheme with a posteriori subcell finite volume limiter for the Euler equations of gasdynamics, 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, Convergence to steady-state solutions of the new type of high-order multi-resolution WENO schemes: a numerical study, An approximate Riemann solver for advection-diffusion based on the generalized Riemann problem, High-fidelity solver on polyhedral unstructured grids for low-Mach number compressible viscous flow, A simplified Cauchy-Kowalewskaya procedure for the local implicit solution of generalized Riemann problems of hyperbolic balance laws, New central and central discontinuous Galerkin schemes on overlapping cells of unstructured grids for solving ideal magnetohydrodynamic equations with globally divergence-free magnetic field, Arbitrary Lagrangian-Eulerian discrete velocity method with application to laser-induced plume expansion, Stencil selection algorithms for WENO schemes on unstructured meshes, Compact high order finite volume method on unstructured grids. III: Variational reconstruction, High order sub-cell finite volume schemes for solving hyperbolic conservation laws. II: Extension to two-dimensional systems on unstructured grids, Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws, A fourth-order unstructured NURBS-enhanced finite volume WENO scheme for steady Euler equations in curved geometries, Cosine expansion based differential quadrature algorithm for numerical simulation of two dimensional hyperbolic equations with variable coefficients, Compact schemes for multiscale flows with cell-centered finite difference method, Application of the Nesvetay code for solving three-dimensional high-altitude aerodynamics problems, ENO-ET: a reconstruction scheme based on extended ENO stencil and truncated highest-order term, A new mean preserving moving least squares method for arbitrary order finite volume schemes, High-resolution finite volume methods on unstructured grids for turbulence and aeroacoustics, FLEXI: a high order discontinuous Galerkin framework for hyperbolic-parabolic conservation laws, Modeling and numerical approximation of a 2.5D set of equations for mesoscale atmospheric processes, Comparison of solvers for the generalized Riemann problem for hyperbolic systems with source terms, A reconstructed discontinuous Galerkin method based on a hierarchical WENO reconstruction for compressible flows on tetrahedral grids, A new type of multi-resolution WENO schemes with increasingly higher order of accuracy on triangular meshes, High-order multi-moment finite volume method with smoothness adaptive fitting reconstruction for compressible viscous flow, Compact high order finite volume method on unstructured grids. IV: Explicit multi-step reconstruction schemes on compact stencil, High order direct arbitrary-Lagrangian-Eulerian (ALE) \(P_NP_M\) schemes with WENO adaptive-order reconstruction on unstructured meshes, Finite volume WENO schemes for nonlinear parabolic problems with degenerate diffusion on non-uniform meshes, A new WENO based Chebyshev spectral volume method for solving one- and two-dimensional conservation laws, An efficient class of WENO schemes with adaptive order for unstructured meshes, Hermite WENO-based limiters for high order discontinuous Galerkin method on unstructured grids, A new type of third-order finite volume multi-resolution WENO schemes on tetrahedral meshes, Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems, A new fifth-order alternative finite difference multi-resolution WENO scheme for solving compressible flow, An alternative SPH formulation: ADER-WENO-SPH, Fourth-order gas-kinetic scheme for turbulence simulation with multi-dimensional WENO reconstruction, A hybrid first-order and WENO scheme for the high-resolution and computationally efficient modeling of pollutant transport, Arbitrary high order central non-oscillatory schemes on mixed-element unstructured meshes, Implicit large eddy simulations of turbulent flow around a square cylinder at \(R e = 22 , 000\), A hierarchical reconstruction for DG/FV method with low dispersion: basic formulation and applications, High order finite volume schemes with IMEX time stepping for the Boltzmann model on unstructured meshes, Efficient implementation of ADER schemes for Euler and magnetohydrodynamical flows on structured meshes -- speed comparisons with Runge-Kutta methods, Solvers for the high-order Riemann problem for hyperbolic balance laws, On one-dimensional arbitrary high-order WENO schemes for systems of hyperbolic conservation laws, High-order gas-kinetic scheme with three-dimensional WENO reconstruction for the Euler and Navier-Stokes solutions, CWENO finite-volume interface capturing schemes for multicomponent flows using unstructured meshes, Efficient implementation of adaptive order reconstructions, New finite difference Hermite WENO schemes for Hamilton-Jacobi equations, WENO schemes on unstructured meshes using a relaxed \textit{a posteriori} MOOD limiting approach, A compact subcell WENO limiting strategy using immediate neighbors for Runge-Kutta discontinuous Galerkin methods for unstructured meshes, Three-level order-adaptive weighted essentially non-oscillatory schemes, High order residual distribution for steady state problems for hyperbolic conservation laws, Weighted essentially non-oscillatory scheme on unstructured quadrilateral and triangular meshes for hyperbolic conservation laws, Efficient seventh order WENO schemes of adaptive order for hyperbolic conservation laws, Constrained least-squares based adaptive-order finite-volume WENO scheme for the simulation of viscous compressible flows on unstructured grids, Third order maximum-principle-satisfying and positivity-preserving Lax-Wendroff discontinuous Galerkin methods for hyperbolic conservation laws, High accuracy modeling of sharp wave fronts for hyperbolic problems, A group of CFL-dependent flux-limiters to control the numerical dissipation in multi-stage unsteady calculation, Spatial spread of COVID-19 outbreak in Italy using multiscale kinetic transport equations with uncertainty, High-order finite volume schemes based on defect corrections, A finite difference mapped WENO scheme with unequal-size stencils for hyperbolic conservation laws, A short note on a 3D spectral analysis for turbulent flows on unstructured meshes, Third-order accurate conservative method on a unstructured mesh for gasdynamic simulations, Second Order ADER Scheme for Unsteady Advection-Diffusion on Moving Overset Grids with a Compact Transmission Condition, Essentially non-oscillatory and weighted essentially non-oscillatory schemes, High-resolution algorithms of sharp interface treatment for compressible two-phase flows, Extension of the ENO-ET Reconstruction Scheme to Two Space Dimensions on Cartesian Meshes in Conjunction with the ADER Approach, On a Power WENO Scheme with Improved Accuracy Near Discontinuities, Central Weighted ENO Schemes for Hyperbolic Conservation Laws on Fixed and Moving Unstructured Meshes, An improved fifth-order WENO scheme with symmetry-preserving smoothness indicators for hyperbolic conservation laws, A high-order conservative semi-Lagrangian solver for 3D free surface flows with sediment transport on Voronoi meshes, AENO: a novel reconstruction method in conjunction with ADER schemes for hyperbolic equations, High-order finite-volume TENO schemes with dual ENO-like stencil selection for unstructured meshes, An all Froude high order IMEX scheme for the shallow water equations on unstructured Voronoi meshes, A low-dissipation finite-volume method based on a new TENO shock-capturing scheme, Novel adaptive finite volume method on unstructured meshes for time-domain wave scattering and diffraction, A fault detection method based on partition of unity and kernel approximation, High-Order Multi-Resolution Weno Schemes with Lax-Wendroff Method for Fractional Differential Equations, A finite volume multilevel WENO scheme for multidimensional scalar conservation laws, Three-dimensional third-order gas-kinetic scheme on hybrid unstructured meshes for Euler and Navier-Stokes equations, An improved discontinuity sensor for high-order weighted essentially non-oscillatory scheme on triangular meshes, New Finite Volume Mapped Unequal-Sized WENO Scheme for Hyperbolic Conservation Laws, A New High-Order Compact Scheme of Unstructured Finite Volume Method, New Finite Volume Weighted Essentially Nonoscillatory Schemes on Triangular Meshes, Современные методы математического моделирования развития гидродинамических неустойчивостей и турбулентного перемешивания, An implicit upwinding volume element method based on meshless radial basis function techniques for modelling transport phenomena, CWENO: Uniformly accurate reconstructions for balance laws, A Maximum-Principle-Preserving Third Order Finite Volume SWENO Scheme on Unstructured Triangular Meshes, A New Fifth-Order Trigonometric WENO Scheme for Hyperbolic Conservation Laws and Highly Oscillatory Problems, Runge-Kutta Discontinuous Galerkin Method with a Simple and Compact Hermite WENO Limiter on Unstructured Meshes, The Weak Galerkin Method for Linear Hyperbolic Equation, Central WENO Subcell Finite Volume Limiters for ADER Discontinuous Galerkin Schemes on Fixed and Moving Unstructured Meshes, Construction of the High Order Accurate Generalized Finite Difference Schemes for Inviscid Compressible Flows, A New Type of High-Order WENO Schemes for Hamilton-Jacobi Equations on Triangular Meshes, Performance Enhancement for High-Order Gas-Kinetic Scheme Based on WENO-Adaptive-Order Reconstruction, High-Order Runge-Kutta Discontinuous Galerkin Methods with a New Type of Multi-Resolution WENO Limiters on Tetrahedral Meshes, Modeling and simulating the spatial spread of an epidemic through multiscale kinetic transport equations, Unnamed Item, Space–time adaptive numerical methods for geophysical applications, A high-order discontinuous Galerkin method with time-accurate local time stepping for the Maxwell equations, Computational Methods for Hyperbolic Equations, Discontinuous Galerkin method for wave propagation in elastic media with inhomogeneous inclusions, Stencil selection algorithms for WENO schemes on unstructured meshes, Three-dimensional flow evolution after a dam break, The Picard Integral Formulation of Weighted Essentially Nonoscillatory Schemes, A posteriori sub-cell finite volume limiting of staggered semi-implicit discontinuous Galerkin schemes for the shallow water equations, An efficient quadrature-free formulation for high order arbitrary-Lagrangian-Eulerian ADER-WENO finite volume schemes on unstructured meshes, Divergence-free reconstruction of magnetic fields and WENO schemes for magnetohydrodynamics, Very high order \(P_NP_M\) schemes on unstructured meshes for the resistive relativistic MHD equations, A high-order weighted essentially non-oscillatory (WENO) finite difference scheme for nonlinear degenerate parabolic equations, A high-order symmetrical weighted hybrid ENO-flux limiter scheme for hyperbolic conservation laws, Extended bounds limiter for high-order finite-volume schemes on unstructured meshes, The multi-dimensional limiters for discontinuous Galerkin method on unstructured grids, A high-order vertex-based central ENO finite-volume scheme for three-dimensional compressible flows, An ADER-type scheme for a class of equations arising from the water-wave theory, Cell centered direct arbitrary-Lagrangian-Eulerian ADER-WENO finite volume schemes for nonlinear hyperelasticity, High order accurate direct arbitrary-Lagrangian-Eulerian ADER-WENO finite volume schemes on moving curvilinear unstructured meshes, A strategy to implement Dirichlet boundary conditions in the context of ADER finite volume schemes. One-dimensional conservation laws, Assessment of high-order finite volume methods on unstructured meshes for RANS solutions of aeronautical configurations, Efficient direct re-initialization approach of a level set method for unstructured meshes, A cell-centered polynomial basis for efficient Galerkin predictors in the context of ADER finite volume schemes. the one-dimensional case, EBR-WENO scheme for solving gas dynamics problems with discontinuities on unstructured meshes, Finite volume scheme with local high order discretization of the hydrostatic equilibrium for the Euler equations with external forces, A solution accurate, efficient and stable unsplit staggered mesh scheme for three dimensional magnetohydrodynamics, Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes, ADER-WENO finite volume schemes with space-time adaptive mesh refinement, WENO schemes on arbitrary unstructured meshes for laminar, transitional and turbulent flows, High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows, A gradient augmented level set method for unstructured grids, Multidimensional HLLC Riemann solver for unstructured meshes -- with application to Euler and MHD flows, Lagrangian ADER-WENO finite volume schemes on unstructured triangular meshes based on genuinely multidimensional HLL Riemann solvers, A new smoothness indicator for improving the weighted essentially non-oscillatory scheme, High order weighted essentially nonoscillatory WENO-\(\eta\) schemes for hyperbolic conservation laws, A new class of moving-least-squares WENO-SPH schemes, Reformulations for general advection-diffusion-reaction equations and locally implicit ADER schemes, A direct arbitrary-Lagrangian-Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D, Multidimensional Riemann problem with self-similar internal structure. I: Application to hyperbolic conservation laws on structured meshes, \textit{A posteriori} subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws, High order cell-centered Lagrangian-type finite volume schemes with time-accurate local time stepping on unstructured triangular meshes, Direct arbitrary-Lagrangian-Eulerian ADER-MOOD finite volume schemes for multidimensional hyperbolic conservation laws, Three dimensional HLL Riemann solver for conservation laws on structured meshes; application to Euler and magnetohydrodynamic flows, Space-time generalized Riemann problem solvers of order \(k\) for linear advection with unrestricted time step, Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume schemes with time-accurate local time stepping for hyperbolic conservation laws, An efficient class of WENO schemes with adaptive order, Linearized acoustic perturbation equations for low Mach number flow with variable density and temperature, Third-order accurate conservative method on unstructured meshes for gasdynamic simulations, A new high-order finite volume method for 3D elastic wave simulation on unstructured meshes, A new type of finite volume WENO schemes for hyperbolic conservation laws, Multidimensional Riemann problem with self-similar internal structure. Part III: A multidimensional analogue of the HLLI Riemann solver for conservative hyperbolic systems, Arbitrary-Lagrangian-Eulerian discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes, Numerical study on the convergence to steady state solutions of a new class of high order WENO schemes, A new third order finite volume weighted essentially non-oscillatory scheme on tetrahedral meshes, Computational electrodynamics in material media with constraint-preservation, multidimensional Riemann solvers and sub-cell resolution. I: Second-order FVTD schemes., A class of hybrid DG/FV methods for conservation laws. II: Two-dimensional cases, WENO schemes on arbitrary mixed-element unstructured meshes in three space dimensions, Approximation error of the Lagrange reconstructing polynomial, A second-order cell-centered Lagrangian ADER-MOOD finite volume scheme on multidimensional unstructured meshes for hydrodynamics, Implicit high-order method for calculating rarefied gas flow in a planar microchannel, A robust reconstruction for unstructured WENO schemes, Adaptive-mesh-refinement for hyperbolic systems of conservation laws based on a posteriori stabilized high order polynomial reconstructions, Computational electrodynamics in material media with constraint-preservation, multidimensional Riemann solvers and sub-cell resolution. II: Higher order FVTD schemes, Arbitrary high order \(P_{N}P_{M}\) schemes on unstructured meshes for the compressible Navier-Stokes equations, The multi-dimensional limiters for solving hyperbolic conservation laws on unstructured grids. II: Extension to high order finite volume schemes, The Hermite radial basis function control volume method for multi-zones problems; A non-overlapping domain decomposition algorithm, A simple two-phase method for the simulation of complex free surface flows, FORCE schemes on unstructured meshes. II: Non-conservative hyperbolic systems, Runge-Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes, Two-dimensional sediment transport models in shallow water equations. A second order finite volume approach on unstructured meshes, A high order semi-implicit discontinuous Galerkin method for the two dimensional shallow water equations on staggered unstructured meshes, A new shock-capturing technique based on moving least squares for higher-order numerical schemes on unstructured grids, A new high-order approximation for the solution of two-space-dimensional quasilinear hyperbolic equations, Brain venous haemodynamics, neurological diseases and mathematical modelling. A review, A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes, High-order Runge-Kutta discontinuous Galerkin methods with a new type of multi-resolution WENO limiters on triangular meshes, A third order finite volume WENO scheme for Maxwell's equations on tetrahedral meshes, A compact fourth-order gas-kinetic scheme for the Euler and Navier-Stokes equations, A new type of multi-resolution WENO schemes with increasingly higher order of accuracy, Simple smoothness indicator and multi-level adaptive order WENO scheme for hyperbolic conservation laws, FORCE schemes on moving unstructured meshes for hyperbolic systems, Explicit one-step time discretizations for discontinuous Galerkin and finite volume schemes based on local predictors, Two-dimensional compact third-order polynomial reconstructions. Solving nonconservative hyperbolic systems using GPUs, A novel solver for the generalized Riemann problem based on a simplified LeFloch-Raviart expansion and a local space-time discontinuous Galerkin formulation, Efficient implementation of high order unstructured WENO schemes for cavitating flows, High-order unstructured Lagrangian one-step WENO finite volume schemes for non-conservative hyperbolic systems: applications to compressible multi-phase flows, Dispersive nonlinear shallow-water equations: some preliminary numerical results, Cool WENO schemes, Reprint of: ``EBR-WENO scheme for solving gas dynamics problems with discontinuities on unstructured meshes, A posteriori subcell finite volume limiter for general \(P_NP_M\) schemes: applications from gasdynamics to relativistic magnetohydrodynamics, A new sixth-order finite difference WENO scheme for fractional differential equations, High order direct arbitrary-Lagrangian-Eulerian (ALE) finite volume schemes for hyperbolic systems on unstructured meshes, A new fifth order finite difference WENO scheme for solving hyperbolic conservation laws, A high-order relativistic two-fluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism, A simple robust and accurate \textit{a posteriori} sub-cell finite volume limiter for the discontinuous Galerkin method on unstructured meshes, Efficient high-order discontinuous Galerkin schemes with first-order hyperbolic advection-diffusion system approach, HFVS: an arbitrary high order approach based on flux vector splitting, ADER schemes and high order coupling on networks of hyperbolic conservation laws, High order parametrized maximum-principle-preserving and positivity-preserving WENO schemes on unstructured meshes, Multidimensional Riemann problem with self-similar internal structure. Part II: Application to hyperbolic conservation laws on unstructured meshes, Divergence-free MHD on unstructured meshes using high order finite volume schemes based on multidimensional Riemann solvers, Efficient, high accuracy ADER-WENO schemes for hydrodynamics and divergence-free magneto\-hydrodynamics, High order space-time adaptive ADER-WENO finite volume schemes for non-conservative hyperbolic systems, A rotated characteristic decomposition technique for high-order reconstructions in multi-dimensions, FORCE schemes on unstructured meshes. I: Conservative hyperbolic systems, ADER schemes on unstructured meshes for nonconservative hyperbolic systems: applications to geophysical flows, Adaptive mesh refinement for hyperbolic systems based on third-order compact WENO reconstruction

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:870579&oldid=12817540"