DOI10.1006/jcph.1998.6114zbMath0921.65059OpenAlexW1978362527MaRDI QIDQ1282422
Mark H. Carpenter, Jan Nordström, David Gottlieb
Publication date: 29 September 1999
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/5c40f483b864ab2490fce98d9e21bb633ec9cd41
Convergence of energy stable finite-difference schemes with interfaces,
Shock-wave/boundary-layer interactions in the automatic source-code generation framework OpenSBLI,
An efficient finite difference method for the shallow water equations,
Learning to differentiate,
Neural network enhanced computations on coarse grids,
Stability of finite volume approximations for the Laplacian operator on quadrilateral and triangular grids,
Summation by parts operators for finite difference approximations of second derivatives,
An efficient hybrid method for uncertainty quantification,
Nondissipative and energy-stable high-order finite-difference interface schemes for 2-D patch-refined grids,
Simultaneous approximation terms and functional accuracy for diffusion problems discretized with multidimensional summation-by-parts operators,
Well-posedness, stability and conservation for a discontinuous interface problem,
Efficient computation of Jacobian matrices for entropy stable summation-by-parts schemes,
A stable domain decomposition technique for advection-diffusion problems,
An improved high order finite difference method for non-conforming grid interfaces for the wave equation,
Conservative and stable degree preserving SBP operators for non-conforming meshes,
A dual consistent finite difference method with narrow stencil second derivative operators,
Time-stable overset grid method for hyperbolic problems using summation-by-parts operators,
On pseudo-spectral time discretizations in summation-by-parts form,
A hybrid framework for coupling arbitrary summation-by-parts schemes on general meshes,
Direct numerical simulation of a turbulent flow over an axisymmetric Hill,
Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations,
Stable artificial dissipation operators for finite volume schemes on unstructured grids,
On the order of accuracy for difference approximations of initial-boundary value problems,
Efficient fully discrete summation-by-parts schemes for unsteady flow problems,
High order finite difference methods for the wave equation with non-conforming grid interfaces,
Interior penalties for summation-by-parts discretizations of linear second-order differential equations,
Energy stable flux reconstruction schemes for advection-diffusion problems on triangles,
High order finite difference methods for wave propagation in discontinuous media,
Well-posed and stable transmission problems,
Summation-by-parts in time,
High-order accurate difference schemes for the Hodgkin-Huxley equations,
A solution to the stability issues with block norm summation by parts operators,
Dual consistency and functional accuracy: a finite-difference perspective,
Duality based boundary conditions and dual consistent finite difference discretizations of the Navier-Stokes and Euler equations,
High-fidelity numerical solution of the time-dependent Dirac equation,
Optimal diagonal-norm SBP operators,
Review of summation-by-parts schemes for initial-boundary-value problems,
The SBP-SAT technique for initial value problems,
Fully discrete energy stable high order finite difference methods for hyperbolic problems in deforming domains,
The second order spin-2 system in flat space near space-like and null-infinity,
Conservative finite difference formulations, variable coefficients, energy estimates and artificial dissipation,
A three-dimensional hybrid LES-acoustic analogy method for predicting open-cavity noise,
A fourth order accurate finite difference scheme for the elastic wave equation in second order formulation,
The boundary data immersion method for compressible flows with application to aeroacoustics,
A generalized framework for nodal first derivative summation-by-parts operators,
A fully discrete, stable and conservative summation-by-parts formulation for deforming interfaces,
Summation-by-parts operators with minimal dispersion error for coarse grid flow calculations,
Revisiting and extending interface penalties for multi-domain summation-by-parts operators,
Stability at nonconforming grid interfaces for a high order discretization of the Schrödinger equation,
Corner-corrected diagonal-norm summation-by-parts operators for the first derivative with increased order of accuracy,
On the relation between conservation and dual consistency for summation-by-parts schemes,
Output error estimation for summation-by-parts finite-difference schemes,
Interaction of waves with frictional interfaces using summation-by-parts difference operators: weak enforcement of nonlinear boundary conditions,
Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements,
A hybrid method for unsteady inviscid fluid flow,
A roadmap to well posed and stable problems in computational physics,
A computational study of vortex-airfoil interaction using high-order finite difference methods,
Weak and strong wall boundary procedures and convergence to steady-state of the Navier-Stokes equations,
A new multigrid formulation for high order finite difference methods on summation-by-parts form,
Toward optimally seeded airflow on hypersonic vehicles using control theory,
Spectral analysis of the continuous and discretized heat and advection equation on single and multiple domains,
Energy stable numerical methods for hyperbolic partial differential equations using overlapping domain decomposition,
Interface procedures for finite difference approximations of the advection-diffusion equation,
A stable high-order finite difference scheme for the compressible Navier-Stokes equations: No-slip wall boundary conditions,
Stable Robin solid wall boundary conditions for the Navier-Stokes equations,
Atmospheric sound propagation over large-scale irregular terrain,
Stable and accurate wave-propagation in discontinuous media,
Constructing non-reflecting boundary conditions using summation-by-parts in time,
Simultaneous approximation terms for multi-dimensional summation-by-parts operators,
Mimetic properties of difference operators: product and chain rules as for functions of bounded variation and entropy stability of second derivatives,
Finite difference schemes with transferable interfaces for parabolic problems,
Stable finite difference schemes for the magnetic induction equation with Hall effect,
Boundary closures for fourth-order energy stable weighted essentially non-oscillatory finite-difference schemes,
A stable and conservative method for locally adapting the design order of finite difference schemes,
A kinetic energy preserving DG scheme based on Gauss-Legendre points,
An intrusive hybrid method for discontinuous two-phase flow under uncertainty,
A stable and high-order accurate conjugate heat transfer problem,
Entropy-stable \(p\)-nonconforming discretizations with the summation-by-parts property for the compressible Navier-Stokes equations,
A new class of \(A\) stable summation by parts time integration schemes with strong initial conditions,
Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts,
Hybridized summation-by-parts finite difference methods,
Diagonal-norm summation by parts operators for finite difference approximations of third and fourth derivatives,
Stable and high order accurate difference methods for the elastic wave equation in discontinuous media,
Variance reduction through robust design of boundary conditions for stochastic hyperbolic systems of equations,
A well-posed and stable stochastic Galerkin formulation of the incompressible Navier-Stokes equations with random data,
A Fourier penalty method for solving the time-dependent Maxwell's equations in domains with curved boundaries,
A spectrally accurate method for overlapping grid solution of incompressible Navier-Stokes equations,
Third-order energy stable WENO scheme,
Finite volume methods, unstructured meshes and strict stability for hyperbolic problems,
A systematic methodology for constructing high-order energy stable WENO schemes,
Stability and functional superconvergence of narrow-stencil second-derivative generalized summation-by-parts discretizations,
A stable and conservative high order multi-block method for the compressible Navier-Stokes equations,
Numerical analysis of the Burgers' equation in the presence of uncertainty,
Accurate solution-adaptive finite difference schemes for coarse and fine grids,
Eigenanalysis and non-modal analysis of collocated discontinuous Galerkin discretizations with the summation-by-parts property,
High-order accurate computations for unsteady aerodynamics,
An entropy stable spectral vanishing viscosity for discontinuous Galerkin schemes: application to shock capturing and LES models,
On an eigenvalue property of summation-by-parts operators,
Entropy splitting for high-order numerical simulation of compressible turbulence,
Provably non-stiff implementation of weak coupling conditions for hyperbolic problems,
Conjugate heat transfer for the unsteady compressible Navier-Stokes equations using a multi-block coupling,
High-order accurate finite difference discretisations on fully unstructured dual quadrilateral meshes,
A new high order energy and enstrophy conserving Arakawa-like Jacobian differential operator,
A Legendre-Fourier spectral method with exact conservation laws for the Vlasov-Poisson system,
High-Order Implicit Time-Marching Methods Based on Generalized Summation-By-Parts Operators,
Generalized Summation-by-Parts Operators for the Second Derivative,
Boundary conditions for a divergence-free velocity-pressure formulation of the Navier-Stokes equations,
A stable high-order finite difference scheme for the compressible Navier-Stokes equations, far-field boundary conditions,
Optimized high-order derivative and dissipation operators satisfying summation by parts, and applications in three-dimensional multi-block evolutions,
High order stable finite difference methods for the Schrödinger equation,
Simulation of dynamic earthquake ruptures in complex geometries using high-order finite difference methods,
Large-eddy simulations and modal reconstruction of laminar transonic buffet,
Provably stable flux reconstruction high-order methods on curvilinear elements,
A non-stiff summation-by-parts finite difference method for the scalar wave equation in second order form: characteristic boundary conditions and nonlinear interfaces,
Coupling Requirements for Multiphysics Problems Posed on Two Domains,
The non-linear perturbation of a black hole by gravitational waves. II. Quasinormal modes and the compactification problem,
Robust boundary conditions for stochastic incompletely parabolic systems of equations,
Transition mechanisms in cross-flow-dominated hypersonic flows with free-stream acoustic noise,
The effect of flow confinement on laminar shock-wave/boundary-layer interactions,
Discontinuous Galerkin spectral element method for shock capturing with summation by parts properties,
Direct numerical simulations of forced and unforced separation bubbles on an airfoil at incidence,
Encapsulated high order difference operators on curvilinear non-conforming grids,
Strong interaction of a turbulent spot with a shock-induced separation bubble,
The effect of Mach number on unstable disturbances in shock/boundary-layer interactions,
Entropy stable \(h/p\)-nonconforming discretization with the summation-by-parts property for the compressible Euler and Navier-Stokes equations,
Superconvergent functional output for time-dependent problems using finite differences on summation-by-parts form,
On the impact of boundary conditions on dual consistent finite difference discretizations,
Staggered-grid entropy-stable multidimensional summation-by-parts discretizations on curvilinear coordinates,
On stability and monotonicity requirements of finite difference approximations of stochastic conservation laws with random viscosity,
An energy stable coupling procedure for the compressible and incompressible Navier-Stokes equations,
On the convergence rates of energy-stable finite-difference schemes,
Entropy stable spectral collocation schemes for the 3-D Navier-Stokes equations on dynamic unstructured grids,
A stable and efficient hybrid scheme for viscous problems in complex geometries,
A methodology for the development of discrete adjoint solvers using automatic differentiation tools,
Inverses of SBP-SAT finite difference operators approximating the first and second derivative,
On the order of Accuracy of Finite Difference Operators on Diagonal Norm Based Summation-by-Parts Form,
Performance of very-high-order upwind schemes for DNS of compressible wall-turbulence,
A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations,
Summation-by-Parts Approximations of the Second Derivative: Pseudoinverse and Revisitation of a High Order Accurate Operator,
Linear and Nonlinear Boundary Conditions for Wave Propagation Problems,
Stability and receptivity characteristics of a laminar separation bubble on an aerofoil,
Multidimensional Summation-by-Parts Operators: General Theory and Application to Simplex Elements,
Effects of pressure gradient on the evolution of velocity-gradient tensor invariant dynamics on a controlled-diffusion aerofoil at,
A high-order Padé ADI method for unsteady convection-diffusion equations,
Finite volume approximations and strict stability for hyperbolic problems,
Analysis of the order of accuracy for node-centered finite volume schemes,
High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates,
Direct numerical simulation of turbulent flow past a trailing edge and the associated noise generation,
Stable, high order accurate adaptive schemes for long time, highly intermittent geophysics problems,
Compressibility and variable inertia effects on heat transfer in turbulent impinging jets,
Summation-By-Parts in Time: The Second Derivative,
Numerical investigation of the flow over a model transonic turbine blade tip,
Development and stability analysis of the inverse Lax−Wendroff boundary treatment for central compact schemes,
Well-Posedness, Stability and Conservation for a Discontinuous Interface Problem: An Initial Investigation,
Higher Order Accurate Solutions for Flow in a Cavity: Experiences and Lessons Learned,
Error boundedness of discontinuous Galerkin methods with variable coefficients,
Analytical models of the wall-pressure spectrum under a turbulent boundary layer with adverse pressure gradient,
Extension of tensor-product generalized and dense-norm summation-by-parts operators to curvilinear coordinates,
Steady-state computations using summation-by-parts operators,
Acoustic and hydrodynamic analysis of the flow around an aerofoil with trailing-edge serrations,
Energy decay of vortices in viscous fluids: an applied mathematics view,
A stable hybrid method for hyperbolic problems,
Direct numerical simulation of jets in cross-flow,
Continuum and discrete initial-boundary value problems and Einstein's field equations,
Numerical treatment of interfaces for second-order wave equations