Grid Adaptation for High-Order Finite Element Discretizations

Krzysztof Fidkowski, Massachusetts Institute of Technology

In numerical simulations, grid adaptation is the process of changing the mesh structure, usually based on the solution, or some features of the solution. Mesh refinement (making elements smaller) is necessary in regions where the solution contains singularities or where the solution is changing rapidly. Conversely, mesh coarsening may be advantageous in regions where the solution is smooth, in order the reduce the number of degrees of freedom in the resulting system. Grid adaptation is especially important in high-order finite element methods: singularities must be isolated via very small elements so as not to affect the rest of the solution through oscillations or loss of accuracy, and the elements should be as coarse as possible in smooth regions so as to take the full advantage of the benefits of high-order accuracy.

In the current work, we are considering grid adaptation for the Discontinuous Galerkin Finite Element Method applied to aerodynamic computations. Specifically, we are looking at output-based adaptation, in which elements are adapted based on their contribution to an engineering output, such as drag or lift on an airfoil. The motivation for such adaptation is that in applied aerodynamics, the most important aspect of a flow solution consists of a couple key outputs rather than the entire solution. Being able to effectively adapt the computation to these outputs could then save computational resources, especially in the design phase of engineering.

In this poster, we present the preliminary results from isotropic output-based grid adaptation applied to 2-D high-order Discontinuous Galerkin discretizations of the Euler Equations. Future work will be in the areas of robust meshing, anisotropic adaptation, and the full compressible Navier-Stokes Equations.

Abstract Author(s): Krzysztof Fidkowski