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Study of Flux Limiters to Minimize the Numerical Dissipation Based on Entropy-Consistent Scheme

Published online by Cambridge University Press:  24 July 2017

J. Ren ,
G. Wang ,
J. H. Feng  and
M. S. Ma
J. Ren
Affiliation:
Department of Fluid DynamicsSchool of AeronauticsNorthwestern Polytechnical UniversityXi'an, China
G. Wang*
Affiliation:
Department of Fluid DynamicsSchool of AeronauticsNorthwestern Polytechnical UniversityXi'an, China
J. H. Feng
Affiliation:
College of ScienceChang'an UniversityXi'an, China
M. S. Ma
Affiliation:
Computational Aerodynamics InstituteChina Aerodynamics Research and Development CenterMianyang, China
*
*Corresponding author ([email protected])
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Abstract

The use of limiters may impact both accuracy and resolution of a solution. And the accuracy and resolution are highly dependent on the amount of numerical dissipation in a scheme, so the ability of limiters to control numerical dissipation should be improved. In this view, based on the examination of several classical limiters to control dissipation, a class of general piecewise-linear flux limiters (termed GPL limiters) are presented in this paper for Multi-step time-space-separated unsteady schemes. The GPL limiters can satisfy the second-order TVD criterion and contain some existing limiters such as Superbee and Minmod. Using the decrement of discrete total entropy to represent the amount of numerical dissipation, an entropy dissipation function of GPL limiters is defined with three parameter variables. By proving the monotonicity of this function, a new GPL type limiter (named MDF individually), which can minimize the numerical dissipation and improve the calculation accuracy, is proposed. A high resolution entropy-consistent scheme is obtained by MDF limiter, which will be proved to satisfy entropy stability and entropy consistency. Computational results of this scheme for several 1-D and 2-D Euler test cases are presented, demonstrating the accuracy, monotonicity and robustness of MDF limiter.

Keywords

Flux-limiterHigh resolutionSecond order TVD criterionNumerical dissipation
Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 2 , April 2018 , pp. 135 - 149
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

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