ON WAVEWISE ENTROPY INEQUALITIES FOR HIGH-RESOLUTION SCHEMES WITH SOURCE TERMS I: THE SEMI-DISCRETE CASE

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 ...

Adaptation and Assessment of a High Resolution Semi-discrete Numerical Scheme for Hyperbolic Systems with Source Terms and Stiffness

In this work we outline the details required in adapting the third-order semi-discrete numerical scheme of Kurganov and Levy [SIAM J. Sci. Comput. 22 (2000) 1461-1488.] to handle hyperbolic systems which include source terms. The performance of the scheme is then assessed against a fully discrete scheme, as well as reference solutions, on such problems as shock propagation in a Broadwell gas an...

A Convergence Rate for Semi-discrete Splitting Approximations for Degenerate Parabolic Equations with Source Terms

We study a semi-discrete splitting method for computing approximate viscosity solutions of the initial value problem for a class of nonlinear degenerate parabolic equations with source terms. It is fairly standard to prove that the semi-discrete splitting approximations converge to the desired viscosity solution as the splitting step ∆t tends to zero. The purpose of this paper is, however, to c...

High-Order Schemes, Entropy Inequalities, and Nonclassical Shocks

We are concerned with the approximation of undercompressive, regularizationsensitive, nonclassical solutions of hyperbolic systems of conservation laws by high-order accurate, conservative, and semidiscrete finite difference schemes. Nonclassical shock waves can be generated by diffusive and dispersive terms kept in balance. Particular attention is given here to a class of systems of conservati...

On the Discrete Cumulative Residual Entropy