Anisotropic quad dominant mesh adaptations for high-order Discontinuous Galerkin methods
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The abstract highlights the efficiency of anisotropic meshes in simulating flows with anisotropic features like boundary layers and shocks. The presented algorithm uses the Riemannian metric field concept for adapting quad-dominant mesh for high-order Discontinuous Galerkin (DG) methods. This is done by analytically deriving an optimal metric field, which generates an anisotropic triangular mesh when passed to a metric-conforming mesh generator. This triangular mesh is then recombined using the Blossom-Quad algorithm to get the quad-dominant mesh, as quads provide better accuracy than triangles in the boundary layer for similar degrees of freedom. The framework is validated with two test cases: scalar advection-diffusion test case and turbulent flat plate test case (from NASA TMR website). An optimal error convergence of order p+1 is achieved for the scalar advection-diffusion test case, where p is the degree of the approximating polynomial. This shows that the adaptation methodology is suitable for higher-order methods. Notably, for turbulent flat plate test case, the adaptation achieves drag convergence at 30,000 degrees of freedom, outperforming CFL3D's 200,000 degrees of freedom.
