Variants of relaxed schemes and two-dimensional gas dynamics

Authors:
Mapundi Kondwani Banda
Affiliations:
Fachbereich Mathematik, Arbeitsgruppe Numerische Mathematik und Wissenschaftliches Rechnen, Schlossgartenstr. 7, D-64289 Darmstadt, Germany
Venue:
Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
Year:
2005

Citing 16
Cited 0

Efficient implementation of essentially non-oscillatory shock-capturing schemes

Journal of Computational Physics
Uniformly Accurate Schemes for Hyperbolic Systems with Relaxation

SIAM Journal on Numerical Analysis
Relaxation Schemes for Nonlinear Kinetic Equations

SIAM Journal on Numerical Analysis
Solution of Two-Dimensional Riemann Problems of Gas Dynamics by Positive Schemes

SIAM Journal on Scientific Computing
Numerical Passage from Systems of Conservation Laws to Hamilton--Jacobi Equations, and Relaxation Schemes

SIAM Journal on Numerical Analysis
Diffusive Relaxation Schemes for Multiscale Discrete-Velocity Kinetic Equations

SIAM Journal on Numerical Analysis
New high-resolution central schemes for nonlinear conservation laws and convection—diffusion equations

Journal of Computational Physics
A third order central WENO scheme for 2D conservation laws

Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
Convergence Rates for Relaxation Schemes Approximating Conservation Laws

SIAM Journal on Numerical Analysis
Discrete Kinetic Schemes for Multidimensional Systems of Conservation Laws

SIAM Journal on Numerical Analysis
Two-dimensional Riemann solver for Euler equations of gas dynamics

Journal of Computational Physics
A class of approximate Riemann solvers and their relation to relaxation schemes

Journal of Computational Physics
A Third-Order Semidiscrete Central Scheme for Conservation Laws and Convection-Diffusion Equations

SIAM Journal on Scientific Computing
Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton--Jacobi Equations

SIAM Journal on Scientific Computing
Strong Stability-Preserving High-Order Time Discretization Methods

SIAM Review
High Resolution Relaxed Upwind Schemes in Gas Dynamics

Journal of Scientific Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a relaxed scheme with more precise information about local speeds of propagation and a multidimensional construction of the cell averages. The physical domain of dependence is simulated correctly and high resolution is maintained. Relaxation schemes have advantages that include high resolution, simplicity and explicitly no (approximate) Riemann solvers and no characteristic decomposition is necessary. Performance of the scheme is illustrated by tests on two-dimensional Euler equations of gas dynamics.