Sequential limiting in continuous and discontinuous Galerkin methods for the Euler equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:356

Article

Dobrev, V.¹  Kolev, T. Z.¹  Kuzmin, D.²  Rieben, R.³  Tomov, V.¹ 

[1] Lawrence Livermore Natl Lab, Ctr Appl Sci Comp, POB 808,L-561, Livermore, CA 94551 USA

[2] TU Dortmund Univ, Inst Appl Math LS 3, Vogelpothsweg 87, D-44227 Dortmund, Germany

[3] Lawrence Livermore Natl Lab, Sci B Div, Weapons & Complex Integrat, 7000 East Ave,L-095, Livermore, CA 94551 USA

关键词: Systems of conservation laws;    Finite element methods;    Local maximum principles;    Limiting techniques;    Positivity preservation;   

DOI  :  10.1016/j.jcp.2017.12.012

来源: Elsevier

【 摘 要 】

We present a new predictor-corrector approach to enforcing local maximum principles in piecewise-linear finite element schemes for the compressible Euler equations. The new element-based limiting strategy is suitable for continuous and discontinuous Galerkin methods alike. In contrast to synchronized limiting techniques for systems of conservation laws, we constrain the density, momentum, and total energy in a sequential manner which guarantees positivity preservation for the pressure and internal energy. After the density limiting step, the total energy and momentum gradients are adjusted to incorporate the irreversible effect of density changes. Antidiffusive corrections to bounds-compatible low-order approximations are limited to satisfy inequality constraints for the specific total and kinetic energy. An accuracy-preserving smoothness indicator is introduced to gradually adjust lower bounds for the element-based correction factors. The employed smoothness criterion is based on a Hessian determinant test for the density. A numerical study is performed for test problems with smooth and discontinuous solutions. (c) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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