Compact Direct Flux Reconstruction for the Navier-Stokes Equations on Dynamic Meshes
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Type of Work16 pages
conference papers and proceedings
Citation of Original PublicationLai Wang and Meilin Yu. "Compact Direct Flux Reconstruction for the Navier-Stokes Equations on Dynamic Meshes", 23rd AIAA Computational Fluid Dynamics Conference, AIAA AVIATION Forum, (AIAA 2017-3098) https://doi.org/10.2514/6.2017-3098
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compact direct ﬂux reconstruction
quadrilateral unstructured dynamic meshes
ﬁnite diﬀerence techniques
In this study, the high-order discontinuous compact direct ﬂux reconstruction (CDFR) method is used to solve the two-dimensional (2D) Navier-Stokes equations on quadrilateral unstructured dynamic meshes. Within a standard element, the CDFR method employs com-pact ﬁnite diﬀerence (FD) techniques to directly construct the nodal spatial derivatives on Gauss-Legendre solution points. In the procedure of constructing an arbitrary CDFR method, the spatial derivatives are approximated with local ﬂuxes on solution points and common ﬂuxes on element interfaces (ﬂux points) in FD forms. No polynomial reconstruction needs to be employed explicitly. It is observed that the CDFR method is identical with the direct ﬂux re-construction (DFR) method and the nodal ﬂux reconstruction-discontinuous Galerkin (FR-DG) method if Gauss-Legendre points are selected as solution points. For simulations with dynamic meshes, the geometric conservation law (GCL) has been incorporated into the Navier-Stokes equations. The performance of CDFR methods has been veriﬁed with various test cases, in-cluding the Euler vortex propagation on deformable meshes, and the Couette ﬂow. Laminar ﬂows of Ma = 0.2 over a static circular cylinder (Re = 100, 185) and an oscillating circular cylinder (Re = 185) have been studied to demonstrate the capability of the solver developed in this study.