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Entropy Stable p-Nonconforming Discretizations with the Summation-by-Parts Property for the Compressible Navier–Stokes Equations
AuthorsFernandez, David C. Del Rey
Carpenter, Mark H.
Winters, Andrew R.
Gassner, Gregor J.
KAUST DepartmentExtreme Computing Research Center
Applied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Permanent link to this recordhttp://hdl.handle.net/10754/656802.1
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AbstractThe entropy conservative, curvilinear, nonconforming, p-refinement algorithm for hyperbolic conservation laws of Del Rey Fernandez 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 are developed that retain the entropy stability of the base scheme. The accuracy and stability properties of the resulting numerical scheme are shown to be comparable to those of the original conforming scheme (achieving ~p+1 convergence) 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.
SponsorsD. Del Rey Fernandez was partially supported by a NSERC Postdoctoral Fellowship, and gratefully acknowledges this support.
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 has been supported by the European Research Council (ERC) under the European Unions Eights Framework Program Horizon 2020 with the research project Extreme, ERC grant agreement no. 714487.