Numerical path preserving Godunov schemes for hyperbolic systems

DOI10.1016/j.jcp.2023.112297OpenAlexW4380758600MaRDI QIDQ6173326

Chun Hian Lee, Zhansen Qian, Ke Xu, Chongwen Jiang, ZhenXun Gao

Publication date: 21 July 2023

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2023.112297

zbMATH Keywords

conservation lawshyperbolic systemsnonconservative systemsGodunov schemesnonconvex flux

Mathematics Subject Classification ID

Basic methods in fluid mechanics (76Mxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Hyperbolic equations and hyperbolic systems (35Lxx)

Cites Work

• Unnamed Item
• High-order WENO schemes: Investigations on non-uniform convergence for MHD Riemann problems
• A high-order nonconservative approach for hyperbolic equations in fluid dynamics
• Removal of pseudo-convergence in coplanar and near-coplanar Riemann problems of ideal magnetohydrodynamics solved using finite volume schemes
• Why many theories of shock waves are necessary: convergence error in formally path-consistent schemes
• A comment on the computation of non-conservative products
• Non-uniform convergence of finite volume schemes for Riemann problems of ideal magnetohydrodynamics
• A new comment on the computation of non-conservative products using Roe-type path conservative schemes
• Definition and weak stability of nonconservative products
• Path-conservative in-cell discontinuous reconstruction schemes for non conservative hyperbolic systems
• In-cell discontinuous reconstruction path-conservative methods for non conservative hyperbolic systems -- second-order extension
• Accurate numerical discretizations of non-conservative hyperbolic systems
• Entropy Conservative and Entropy Stable Schemes for Nonconservative Hyperbolic Systems
• Well-Balanced Schemes and Path-Conservative Numerical Methods
• Why many theories of shock waves are necessary: kinetic relations for non-conservative systems
• Hyperbolic systems of conservation laws II
• Nonlinear projection methods for multi-entropies Navier--Stokes systems
• Godunov method for nonconservative hyperbolic systems
• Riemann Solvers and Numerical Methods for Fluid Dynamics
• Existence theory for nonlinear hyperbolic systems in nonconservative form
• Why Nonconservative Schemes Converge to Wrong Solutions: Error Analysis
• Entropy-stable space–time DG schemes for non-conservative hyperbolic systems
• Numerical methods with controlled dissipation for small-scale dependent shocks
• Representation of Weak Limits and Definition of Nonconservative Products
• Path-conservative central-upwind schemes for nonconservative hyperbolic systems
• Schemes with Well-Controlled Dissipation
• Schemes with Well-Controlled Dissipation. Hyperbolic Systems in Nonconservative Form
• Numerical methods for nonconservative hyperbolic systems: a theoretical framework.

This page was built for publication: Numerical path preserving Godunov schemes for hyperbolic systems