A Cut-Cell Adaptive Method for High-Order Discretizations of the Compressible Navier-Stokes Equations

Krzysztof Fidkowski, Massachusetts Institute of Technology

While an indispensable tool in analysis and design applications, Computational Fluid Dynamics (CFD) is still plagued by insufficient automation and robustness in the geometry-to-solution process. This talk presents two ideas for improving automation and robustness in CFD: output-based mesh adaptation for high-order discretizations, and simplex, cut-cell mesh generation. First, output-based mesh adaptation consists of generating a sequence of meshes in an automated fashion, with the goal of minimizing an estimate of the error in an engineering output. This technique is proposed as an alternative to current CFD practices, in which error estimation and mesh generation are largely performed by experienced practitioners. Second, cut-cell mesh generation is a potentially more automated and robust technique compared to boundary-conforming mesh generation for complex, curved geometries. Cut-cell meshes are obtained by cutting a given geometry of interest out of a background mesh that need not conform to the geometry boundary. Specifically, this work develops the idea of simplex cut cells; that is, background meshes consisting of triangles or tetrahedra, which can be stretched in arbitrary directions to efficiently resolve boundary-layer and wake features.

This talk will motivate the ideas of output-based adaptation and cut-cell meshing and present the results of a recently-developed implementation. The target application is the discontinuous Galerkin (DG) finite element discretization of the compressible Navier-Stokes equations, in both two and three dimensions. Results will demonstrate the robustness of cut-cell mesh generation as well as the automation and efficiency made possible by output-based adaptation.

Abstract Author(s): Krzysztof Fidkowski<br />David Darmofal