Entropy Stable Split Forms for the Flux Reconstruction High-Order Method: Three-Dimensional Numerical Validation
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Bibliographic record
Abstract
View Video Presentation: https://doi.org/10.2514/6.2021-2703.vid The flux reconstruction method has gained popularity in the research community as it recovers promising high-order methods through modally filtered correction fields, such as the discontinuous Galerkin (DG) method, on unstructured grids over complex geometries. Under a class of energy stable flux reconstruction (ESFR) schemes also known as Vincent-Castonguay-Jameson-Huynh (VCJH) schemes, the flux reconstruction method allows for larger time-steps than DG while ensuring stability for linear advection on affine elements. For nonlinear problems, split forms emerged as the popular approach proving stability for unsteady problems on coarse unstructured grids; albeit only having been proved for the strong form DG scheme. This paper derives a new approach for general, modal, uncollocated ESFR schemes in split forms that ensure energy and entropy stability. The methodology is derived for the three-dimensional Euler equations and provides numerical results validating stability for the inviscid Taylor-Green vortex for all ESFR schemes, while preserving the correct orders of accuracy.
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|---|---|---|
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