Entropy convergence of new two-value scheme with slope relaxation for conservation laws

doi:10.1007/s10483-016-2109-8

Abstract

Abstract:

This paper establishes the entropy convergence of a new two-value high resolution finite volume scheme with slope relaxation for conservation laws.This scheme,motivated by the general method of high resolution schemes that have high-order accuracy in smooth regions of solutions and are free of oscillations near discontinuities,unifies and evolves slopes directly with a slope relaxation equation that governs the evolution of slopes in both smooth and discontinuous regions.Proper choices of slopes are realized adaptively via a relaxation parameter.The scheme is shown to be total-variation-bounded (TVB) stable and satisfies cell-entropy inequalities.

Key words: two-value scheme, slope relaxation, conservation law

2010 MSC Number:

Yue WANG, Jiequan LI. Entropy convergence of new two-value scheme with slope relaxation for conservation laws. Applied Mathematics and Mechanics (English Edition), 2016, 37(11): 1551-1570.

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