Entropy-stable p-nonconforming discretizations with the summation-by-parts property for the compressible Navier–Stokes equations
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Preprint
Embargo End Date:
2022-07-23
Type
ArticleAuthors
Fernández, David C.Del ReyCarpenter, Mark H.
Dalcin, Lisandro
Fredrich, Lucas
Winters, Andrew R.
Gassner, Gregor J.
Parsani, Matteo

KAUST Department
Extreme Computing Research CenterComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
Date
2020-06-23Preprint Posting Date
2019-09-27Embargo End Date
2022-07-23Submitted Date
2019-09-06Permanent link to this record
http://hdl.handle.net/10754/656802
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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.2020.104631Sponsors
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 BVJournal
Computers and FluidsarXiv
1909.12546Additional Links
https://linkinghub.elsevier.com/retrieve/pii/S0045793020302036ae974a485f413a2113503eed53cd6c53
10.1016/j.compfluid.2020.104631