Entropy Stable Flux Correction for Scalar Hyperbolic Conservation Laws

被引：2

作者：

Kivva, Sergii ^{[1
]}

机构：

[1] Ukrainian Natl Acad Sci, Inst Math Machines & Syst Problems, Kiev, Ukraine

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2022年 / 91卷 / 01期

关键词：

Entropy solution; Flux corrected transport; Scalar conservation laws; Difference scheme; Linear programming; HIGH-ORDER ACCURATE; FULLY DISCRETE; NUMERICAL VISCOSITY; SCHEMES; ALGORITHMS; TRANSPORT; SYSTEMS;

D O I：

10.1007/s10915-022-01792-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is known that Flux Corrected Transport algorithms can produce entropy-violating solutions of hyperbolic conservation laws. Our purpose is to design flux correction with maximal antidiffusive fluxes to obtain entropy solutions of scalar hyperbolic conservation laws. To do this we consider a hybrid difference scheme that is a linear combination of a monotone scheme and a scheme of high-order accuracy. The flux limiters for the hybrid scheme are calculated from a corresponding optimization problem. Constraints for the optimization problem consist of inequalities that are valid for the monotone scheme and applied to the hybrid scheme. We apply the discrete cell entropy inequality with the proper numerical entropy flux to single out a physically relevant solution of scalar hyperbolic conservation laws. A nontrivial approximate solution of the optimization problem yields expressions to compute the required flux limiters. We present examples that show that not all numerical entropy fluxes guarantee to single out a physically correct solution of scalar hyperbolic conservation laws.

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页数：21

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