Fully discrete explicit locally entropy-stable schemes for the compressible Euler and Navier–Stokes equations
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Ranocha_Dalcin_Parsani__2020__Fully_discrete_explicit_locally_ES_schemes_for_the_compressible_Euler_and_NS_eqs__arXiv.pdf
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Accepted manuscript
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ArticleKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionExtreme Computing Research Center
Applied Mathematics and Computational Science Program
Date
2020-07-09Preprint Posting Date
2020-03-19Online Publication Date
2020-07-09Print Publication Date
2020-09Embargo End Date
2022-07-09Submitted Date
2020-03-19Permanent link to this record
http://hdl.handle.net/10754/662321
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Recently, relaxation methods have been developed to guarantee the preservation of a single global functional of the solution of an ordinary differential equation. Here, we generalize this approach to guarantee local entropy inequalities for finitely many convex functionals (entropies) and apply the resulting methods to the compressible Euler and Navier–Stokes equations. Based on the unstructured hp-adaptive SSDC framework of entropy conservative or dissipative semidiscretizations using summation-by-parts and simultaneous-approximation-term operators, we develop the first discretizations for compressible computational fluid dynamics that are primary conservative, locally entropy stable in the fully discrete sense under a usual CFL condition, explicit except for the parallelizable solution of a single scalar equation per element, and arbitrarily highorder accurate in space and time. We demonstrate the accuracy and the robustness of the fully-discrete explicit locally entropy-stable solver for a set of test cases of increasing complexity.Citation
Ranocha, H., Dalcin, L., & Parsani, M. (2020). Fully discrete explicit locally entropy-stable schemes for the compressible Euler and Navier–Stokes equations. Computers & Mathematics with Applications, 80(5), 1343–1359. doi:10.1016/j.camwa.2020.06.016Sponsors
The research reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST), Saudi Arabia . We are thankful for the computing resources of the Supercomputing Laboratory and the Extreme Computing Research Center at KAUST.Publisher
Elsevier BVarXiv
2003.08831Additional Links
https://linkinghub.elsevier.com/retrieve/pii/S0898122120302650ae974a485f413a2113503eed53cd6c53
10.1016/j.camwa.2020.06.016