Optimized geometrical metrics satisfying free-stream preservation

Irving Reyna Nolasco, Lisandro Dalcin, David C. Del Rey Fernández, Stefano Zampini, Matteo Parsani

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Computational fluid dynamics and aerodynamics, which complement more expensive empirical approaches, are critical for developing aerospace vehicles. During the past three decades, computational aerodynamics capability has improved remarkably, following advances in computer hardware and algorithm development. However, for complex applications, the demands on computational fluid dynamics continue to increase in a quest to gain a few percent improvements in accuracy. Herein, we numerically demonstrate, in the context of tensor-product discretizations on hexahedral elements, that computing the metric terms with an optimization-based approach leads to a solution whose accuracy is overall on par and often better than the one obtained using the widely adopted Thomas and Lombard metric terms computation (Geometric conservation law and its application to flow computations on moving grids, AIAA Journal, 1979). We show the efficacy of the proposed technique in the context of low and high-order accurate nonlinearly stable (entropy stable) schemes on distorted, high-order tensor product elements, considering smooth three-dimensional inviscid and viscous compressible test cases for which an analytical solution is known. The methodology, originally developed by Crean et al. (2018) in the context of triangular/tetrahedral grids, is not limited to tensor-product cells and it can be applied to other cell-based diagonal-norm summation-by-parts discretizations, including spectral differences, discontinuous Galerkin finite elements, and flux reconstruction schemes.
Original languageEnglish (US)
Pages (from-to)104555
JournalComputers and Fluids
StatePublished - May 26 2020

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The research reported in this paper was funded by King Abdullah University of Science and Technology. We are thankful for the computing resources of the Supercomputing Laboratory and the Extreme Computing Research Center at King Abdullah University of Science and Technology.


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