Fully discrete explicit locally entropy-stable schemes for the compressible Euler and Navier–Stokes equations
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Extreme Computing Research Center
Applied Mathematics and Computational Science Program
Preprint Posting Date2020-03-19
Online Publication Date2020-07-09
Print Publication Date2020-09
Embargo End Date2022-07-09
Permanent link to this recordhttp://hdl.handle.net/10754/662321
MetadataShow full item record
AbstractRecently, 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.
CitationRanocha, 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.2020.06.016
SponsorsThe 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.