Entropy-stable p-nonconforming discretizations with the summation-by-parts property for the compressible Navier–Stokes equations

Abstract
The entropy-conservative/stable, curvilinear, nonconforming, p-refinement algorithm for hyperbolic conservation laws of Del Rey Fernández et al. (2019) is extended from the compressible Euler equations to the compressible Navier–Stokes equations. A simple and flexible coupling procedure with planar interpolation operators between adjoining nonconforming elements is used. Curvilinear volume metric terms are numerically approximated via a minimization procedure and satisfy the discrete geometric conservation law conditions. Distinct curvilinear surface metrics are used on the adjoining interfaces to construct the interface coupling terms, thereby localizing the discrete geometric conservation law constraints to each individual element. The resulting scheme is entropy conservative/stable, element-wise conservative, and freestream preserving. Viscous interface dissipation operators that retain the entropy stability of the base scheme are developed. The accuracy and stability of the resulting numerical scheme are shown to be comparable to those of the original conforming scheme in Carpenter et al. (2014) and Parsani et al. (2016), i.e., this scheme achieves ∼p+1/2 convergence on geometrically high-order distorted element grids; this is demonstrated in the context of the viscous shock problem, the Taylor–Green vortex problem at a Reynolds number of Re=1,600, and a subsonic turbulent flow past a sphere at Re=2,000.

Citation
Fernández, D. C. D. R., Carpenter, M. H., Dalcin, L., Fredrich, L., Winters, A. R., Gassner, G. J., & Parsani, M. (2020). Entropy-stable p-nonconforming discretizations with the summation-by-parts property for the compressible Navier–Stokes equations. Computers & Fluids, 210, 104631. doi:10.1016/j.compfluid.2020.104631

Acknowledgements
Special thanks are extended to Dr. Mujeeb R. Malik for partially funding this work as part of NASA's “Transformational Tools and Technologies” (T3) project. The research reported in this publication was also supported by funds from King Abdullah University of Science and Technology (KAUST). We are thankful for the computing resources of the Supercomputing Laboratory and the Extreme Computing Research Center at KAUST. Gregor Gassner and Lucas Friedrich were supported by the European Research Council (ERC) under the European Union's Eights Framework Program Horizon 2020 with the research project Extreme, ERC grant agreement no. 714487.

Publisher
Elsevier BV

Journal
Computers & Fluids

DOI
10.1016/j.compfluid.2020.104631

arXiv
1909.12546

Additional Links
https://linkinghub.elsevier.com/retrieve/pii/S0045793020302036

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2020-03-31 10:27:56
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2019-09-30 07:58:40
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