The Relaxation Schemes for Systems of Conservation Laws in Arbitrary Space Dimensions
نویسندگان
چکیده
We present a class of numerical schemes (called the relaxation schemes) for systems of conservation laws in several space dimensions. The idea is to use a local relaxation approximation. We construct a linear hyperbolic system with a stii lower order term that approximates the original system with a small dissipative correction. The new system can be solved by under-resolved stable numerical discretizations without using either Riemann solvers spatially or a nonlinear system of algebraic equations solver temporally. Numerical results for 1-D and 2-D problems are presented. The second order schemes are shown to be total variation diminishing (TVD) in the zero relaxation limit for scalar equations.
منابع مشابه
The comparison of two high-order semi-discrete central schemes for solving hyperbolic conservation laws
This work presents two high-order, semi-discrete, central-upwind schemes for computing approximate solutions of 1D systems of conservation laws. We propose a central weighted essentially non-oscillatory (CWENO) reconstruction, also we apply a fourth-order reconstruction proposed by Peer et al., and afterwards, we combine these reconstructions with a semi-discrete central-upwind numerical flux ...
متن کاملStability and Convergence of a Class of Finite Element Schemes for Hyperbolic Systems of Conservation Laws
We propose a class of finite element schemes for systems of hyperbolic conservation laws that are based on finite element discretizations of appropriate relaxation models. We consider both semidiscrete and fully discrete finite element schemes and show that the schemes are stable and, when the compensated compactness theory is applicable, do converge to a weak solution of the hyperbolic system....
متن کاملA total variation diminishing high resolution scheme for nonlinear conservation laws
In this paper we propose a novel high resolution scheme for scalar nonlinear hyperbolic conservation laws. The aim of high resolution schemes is to provide at least second order accuracy in smooth regions and produce sharp solutions near the discontinuities. We prove that the proposed scheme that is derived by utilizing an appropriate flux limiter is nonlinear stable in the sense of total varia...
متن کاملNonoscillatory Central Schemes for Hyperbolic Systems of Conservation Laws in Three-Space Dimensions
We extend a family of high-resolution, semidiscrete central schemes for hyperbolic systems of conservation laws to three-space dimensions. Details of the schemes, their implementation, and properties are presented together with results from several prototypical applications of hyperbolic conservation laws including a nonlinear scalar equation, the Euler equations of gas dynamics, and the ideal ...
متن کاملConvergence and Error Estimates of Relaxation Schemes for Multidimensional Conservation Laws
M. A. Katsoulakis, G. Kossioris and Ch. Makridakis Abstract. We study discrete and semidiscrete relaxation schemes for multidimensional scalar conservation laws. We show convergence of the relaxation schemes to the entropy solution of the conservation law and derive error estimates that exhibit the precise interaction between the relaxation time and the space/time discretization parameters of t...
متن کامل