TY - JOUR

T1 - Fully discrete explicit locally entropy-stable schemes for the compressible Euler and Navier–Stokes equations

AU - Ranocha, Hendrik

AU - Dalcin, Lisandro

AU - Parsani, Matteo

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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.

PY - 2020/7/9

Y1 - 2020/7/9

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/662321

UR - https://linkinghub.elsevier.com/retrieve/pii/S0898122120302650

UR - http://www.scopus.com/inward/record.url?scp=85087591869&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2020.06.016

DO - 10.1016/j.camwa.2020.06.016

M3 - Article

SN - 0898-1221

VL - 80

SP - 1343

EP - 1359

JO - Computers & Mathematics with Applications

JF - Computers & Mathematics with Applications

IS - 5

ER -