Enforcing the Courant-Friedrichs-Lewy condition in explicitly conservative local time stepping schemes

JOURNAL OF COMPUTATIONAL PHYSICS

卷:359

Article

Gnedin, Nickolay Y.^1,2,3  Semenov, Vadim A.^2,3  Kravtsov, Andrey V.^2,3,4 

[1] Fermilab Natl Accelerator Lab, Particle Astrophys Ctr, POB 500, Batavia, IL 60510 USA

[2] Univ Chicago, Kavli Inst Cosmol Phys, Chicago, IL 60637 USA

[3] Univ Chicago, Dept Astron & Astrophys, 5640 S Ellis Ave, Chicago, IL 60637 USA

[4] Univ Chicago, Enrico Fermi Inst, 5640 S Ellis Ave, Chicago, IL 60637 USA

关键词: Numerical methods;    Computational fluid dynamics;    Partial differential equations;   

DOI  :  10.1016/j.jcp.2018.01.008

来源: Elsevier

【 摘 要 】

An optimally efficient explicit numerical scheme for solving fluid dynamics equations, or any other parabolic or hyperbolic system of partial differential equations, should allow local regions to advance in time with their own, locally constrained time steps. However, such a scheme can result in violation of the Courant-Friedrichs-Lewy (CFL) condition, which is manifestly non-local. Although the violations can be considered to be weak in a certain sense and the corresponding numerical solution may be stable, such calculation does not guarantee the correct propagation speed for arbitrary waves. We use an experimental fluid dynamics code that allows cubic patches of grid cells to step with independent, locally constrained time steps to demonstrate how the CFL condition can be enforced by imposing a constraint on the time steps of neighboring patches. We perform several numerical tests that illustrate errors introduced in the numerical solutions by weak CFL condition violations and show how strict enforcement of the CFL condition eliminates these errors. In all our tests the strict enforcement of the CFL condition does not impose a significant performance penalty. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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