Applied Mathematics and Mechanics >
Entropy convergence of new two-value scheme with slope relaxation for conservation laws
Received date: 2016-01-25
Revised date: 2016-07-11
Online published: 2016-11-01
Supported by
Project supported by the National Natural Science Foundation of China (Nos.11371063,11501040,and 91530108) and the Doctoral Program from the Education Ministry of China (No.20130003110004)
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
Yue WANG, Jiequan LI . Entropy convergence of new two-value scheme with slope relaxation for conservation laws[J]. Applied Mathematics and Mechanics, 2016 , 37(11) : 1551 -1570 . DOI: 10.1007/s10483-016-2109-8
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