Convergence of Second-Order Schemes for Isentropic Gas Dynamics

DOI10.2307/2153243zbMath0784.76058OpenAlexW4232106168WikidataQ57386585 ScholiaQ57386585MaRDI QIDQ4274386

Jian-Guo Liu, Gui-Qiang G. Chen

Publication date: 23 March 1994

Full work available at URL: https://doi.org/10.2307/2153243

zbMATH Keywords

MUSCL schemeshock-capturing schemepiston problementropy dissipation measuresentropy near shock wavesvacuum problem

Mathematics Subject Classification ID

Shock waves and blast waves in fluid mechanics (76L05) Finite difference methods applied to problems in fluid mechanics (76M20) Gas dynamics (general theory) (76N15) 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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Classical solutions for the Euler equations of compressible fluid dynamics: A new topological approach ⋮ A well-balanced Runge-Kutta discontinuous Galerkin method for the shallow-water equations with flooding and drying ⋮ On wavewise entropy inequalities for high-resolution schemes. I: The semidiscrete case

Cites Work

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• Convergence of the viscosity method for isentropic gas dynamics
• The numerical simulation of two-dimensional fluid flow with strong shocks
• Uniformly high order accurate essentially non-oscillatory schemes. III
• Efficient implementation of essentially nonoscillatory shock-capturing schemes. II
• The embedding of the positive cone of $H^{-1}$ in $W^{-1,\,q}$ is compact for all $q<2$ (with a remark of Haim Brezis)
• Approximate Riemann solvers, parameter vectors, and difference schemes
• Mixed problems for nonlinear conservation laws
• An introduction to the article ``Reminiscences about difference schemes by S. K. Godunov
• Convergence of Generalized MUSCL Schemes
• Uniformly High-Order Accurate Nonoscillatory Schemes. I
• High-Order Schemes and Entropy Condition for Nonlinear Hyperbolic Systems of Conservation Laws
• Convergence of Finite Difference Schemes for Conservation Laws in Several Space Dimensions: The Corrected Antidiffusive Flux Approach
• Hyperbolic systems of conservation laws with a symmetry
• Initial boundary value problems for isentropic gas dynamics
• Numerical viscosity and the entropy condition
• Spectral Viscosity Approximations to Multidimensional Scalar Conservation Laws
• Convergence of a Shock-Capturing Streamline Diffusion Finite Element Method for a Scalar Conservation Law in Two Space Dimensions
• Systems of conservation laws
• A Method for the Numerical Calculation of Hydrodynamic Shocks

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