The Numerical Viscosity of Entropy Stable Schemes for Systems of Conservation Laws
نویسندگان
چکیده
Discrete approximations to hyperbolic systems of conservation laws are studied. We quantify the amount of numerical viscosity present in such schemes, and relate it to their entropy stability by means of comparison. To this end, conservative schemes which are also entropy conservative are constructed. These entropy conservative schemes enjoy second-order accuracy; moreover, they can be interpreted as piecewise linear finite element methods, and hence can be formulated on various mesh configurations. We then show that conservative schemes are entropy stable, if and—for three-point schemes—only if they contain more viscosity than that present in the above-mentioned entropy conservative ones.
منابع مشابه
Perfect Derivatives, Conservative Differences and Entropy Stable Computation of Hyperbolic Conservation Laws
Entropy stability plays an important role in the dynamics of nonlinear systems of hyperbolic conservation laws and related convection-diffusion equations. Here we are concerned with the corresponding question of numerical entropy stability — we review a general framework for designing entropy stable approximations of such systems. The framework, developed in [28, 29] and in an ongoing series of...
متن کاملEntropy Stable Approximations of Nonlinear Conservation Laws
A central problem in computational fluid dynamics is the development of the numerical approximations for nonlinear hyperbolic conservation laws and related time-dependent problems governed by additional dissipative and dispersive forcing terms. Entropy stability serves as an essential guideline in the design of new computationally reliable numerical schemes. My dissertation research involves a ...
متن کاملThe 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 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 کاملEntropy Stable Schemes
We review the topic of entropy stability of discrete schemes, finite-difference and finite-volume schemes, for the approximate solution of nonlinear systems of conservation laws. The question of entropy stability plays an important role in both, the theory and computation of such systems, which is reflected by the extensive literature on this topic. Here we focus on a several key ingredients in...
متن کامل