Date Nov. 2, 2007
Speaker Krzysztof J. Fidkowski (Massachusetts Institute of Technology)
Topic Towards Automated Mesh Adaptation Using Simplex Cut Cells

Even with today's computing resources, high-fidelity Computational Fluid Dynamics (CFD) remains a time-consuming and user-intensive process. Error estimation and mesh generation/adaptation in industry applications are largely performed by experienced practitioners. This lack of automation prevents widespread use of CFD in design and optimization, especially for complex configurations.

Methods for rigorous error estimation exist, but have yet to be applied on a large scale to complex three-dimensional cases. The bottleneck is primarily a lack of automated metric-driven meshing. Currently, the generation of boundary-conforming meshes with anisotropic boundary layers requires heavy user involvement. One solution is the Cartesian cut-cell method, in which the computational mesh is obtained by cutting the geometry out of a lattice-bound structured mesh. However, current finite volume Cartesian methods are at best second-order accurate and require impractically high mesh counts for problems exhibiting anisotropy, such as thin boundary layers.

This talk presents a simplex cut cell method, in which the computational mesh is obtained by cutting the geometry out of a triangular or tetrahedral background mesh that does not need to conform to the geometry boundary. Use of triangles and tetrahedral allows the mesh to be stretched in arbitrary directions to efficiently resolve anisotropic flow features. The target application for this work is the discontinuous Galerkin (DG) finite element discretization of the compressible Navier-Stokes equations in both two and three dimensions. Accuracy of cut-cell solutions is demonstrated by comparison to boundary-conforming solutions when available. Adaptive results for anisotropic problems in two dimensions and isotropic problems in three dimensions indicate that automated output-driven adaptation is possible with cut cells. Finally, a possible extension of simplex cut cells for dealing with curved anisotropic features is discussed.



We thank the generous support of MIT IS&T, CSAIL, and the Department of Mathematics for their support of this series.

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