GRP -- a direct Godunov extension
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Publication:6639306
DOI10.1016/j.jcp.2024.113388MaRDI QIDQ6639306
Publication date: 15 November 2024
Published in: Journal of Computational Physics (Search for Journal in Brave)
convergenceconservation lawsfinite volume schemesRiemann problemdiscontinuous solutionsgeneralized Riemann problemGodunov schemenumerical fluxhigh order schemeshyperbolic balance lawsLax-Wendroff theorem
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)
Cites Work
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- The generalized Riemann problems for compressible fluid flows: towards high order
- A third-order accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics
- A direct Eulerian GRP scheme for relativistic hydrodynamics: two-dimensional case
- Comparison of the generalized Riemann solver and the gas-kinetic scheme for inviscid compressible flow simulations
- Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for the isentropic system of gas dynamics
- A direct Eulerian GRP scheme for relativistic hydrodynamics: One-dimensional case
- The piecewise parabolic method (PPM) for gas-dynamical simulations
- A second-order Godunov-type scheme for compressible fluid dynamics
- Hyperbolic conservation laws on the sphere. A geometry-compatible finite volume scheme
- Implementation of the GRP scheme for computing radially symmetric compressible fluid flows
- A high-order cell-centered Lagrangian scheme for compressible fluid flows in two-dimensional cylindrical geometry
- An adaptive GRP scheme for compressible fluid flows
- A direct Eulerian GRP scheme for compressible fluid flows
- An asymptotic expansion for the solution of the generalized Riemann problem. II: Application to the equation of gas dynamics
- The convergence of the GRP scheme
- A high-order cell-centered Lagrangian scheme for two-dimensional compressible fluid flows on unstructured meshes
- Convergence of approximate solutions to conservation laws
- Application of the generalized Riemann problem method to 1-D compressible flows with material interfaces
- The generalized Riemann problem for reactive flows
- Higher order Godunov methods for general systems of hyperbolic conservation laws
- Approximate Riemann solvers, parameter vectors, and difference schemes
- Random choice solution of hyperbolic systems
- A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
- Weighted essentially non-oscillatory schemes
- Convergence of MUSCL and filtered schemes for scalar conservation laws and Hamilton-Jacobi equations
- High resolution schemes for hyperbolic conservation laws. (Reprint)
- The numerical interface coupling of nonlinear hyperbolic systems of conservation laws. I: The scalar case
- Thermodynamical effects and high resolution methods for compressible fluid flows
- A Hermite WENO reconstruction for fourth order temporal accurate schemes based on the GRP solver for hyperbolic conservation laws
- Computation of reactive duct flows in external fields
- Uniqueness of weak solutions of the Cauchy problem for general 2 x 2 conservation laws
- The unique limit of the Glimm scheme
- New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations
- An efficient, second order accurate, universal generalized Riemann problem solver based on the HLLI Riemann solver
- A novel solver for the generalized Riemann problem based on a simplified LeFloch-Raviart expansion and a local space-time discontinuous Galerkin formulation
- One-sided GRP solver and numerical boundary conditions for compressible fluid flows
- On the weak consistency of finite volumes schemes for conservation laws on general meshes
- Transversal effects of high order numerical schemes for compressible fluid flows
- Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
- Hyperbolic balance laws: Riemann invariants and the generalized Riemann problem
- Arbitrary high order discontinuous Galerkin schemes based on the GRP method for compressible Euler equations
- High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments
- Derivative Riemann solvers for systems of conservation laws and ader methods
- A Two-Stage Fourth Order Time-Accurate Discretization for Lax--Wendroff Type Flow Solvers I. Hyperbolic Conservation Laws
- ANALYSIS AND APPROXIMATION OF A SCALAR CONSERVATION LAW WITH A FLUX FUNCTION WITH DISCONTINUOUS COEFFICIENTS
- A Lax--Wendroff type theorem for unstructured quasi-uniform grids
- The generalized Riemann problem method for the shallow water equations with bottom topography
- Riemann Solvers and Numerical Methods for Fluid Dynamics
- On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws
- Riemann Solvers, the Entropy Condition, and Difference
- An Upwind Second-Order Scheme for Compressible Duct Flows
- Approximate Riemann Solvers and Numerical Flux Functions
- Convergence of Generalized MUSCL Schemes
- On the Convergence of Difference Approximations to Scalar Conservation Laws
- A Geometric Approach to High Resolution TVD Schemes
- Convergence of Finite Difference Schemes for Conservation Laws in Several Space Dimensions: A General Theory
- Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions
- Remarks on High-Resolution Split Schemes Computation
- Numerical Solution of Partial Differential Equations
- Increasing the order of approximation of Godunov's scheme using solutions of the generalized riemann problem
- A MUSCL method satisfying all the numerical entropy inequalities
- An Analysis of a Class of Second-Order Accurate Godunov-Type Schemes
- Generalized Riemann Problems in Computational Fluid Dynamics
- Lax theorem and finite volume schemes
- A review of numerical methods for nonlinear partial differential equations
- Accelerated Piston Problem and High Order Moving Boundary Tracking Method for Compressible Fluid Flows
- Consistency of finite volume approximations to nonlinear hyperbolic balance laws
- Gauss‐Green theorem for weakly differentiable vector fields, sets of finite perimeter, and balance laws
- Systems of conservation laws
- FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES
- Hyperbolic Conservation Laws in Continuum Physics
- Regularity of fluxes in nonlinear hyperbolic balance laws
- Stiffened gas approximation and GRP resolution for compressible fluid flows of real materials
- The generalized Riemann problem scheme for a laminar two-phase flow model with two-velocities
- Convergence of a generalized Riemann problem scheme for the Burgers equation
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