## UC Berkeley / Lawrence Berkeley Laboratory

#### Theory and Applications of Unstructured h-p Mesh Optimization for Computational Fluid Dynamics

**Krzysztof Fidkowski, University of Michigan**

##### December 13th, 2017 at 4:00PM–5:00PM in 891 Evans Hall [Map]

This presentation first reviews existing methods for adapting and optimizing
computational meshes in an output-based setting. The target discretization is
the high-order discontinuous Galerkin finite element method, on unstructured
meshes with variable-order elements. While high-order discretizations have
the potential for high accuracy, they may not show a clear benefit in
efficiency over low-order methods when applied to problems with discon
inuities in the solution or derivatives. In such cases, the performance of
high-order methods can be improved through adaptive mesh optimization. We
focus on adaptive methods in which the mesh size and order distribution are
modified in an a posteriori manner based on the solution. To drive the
optimization, we use an output-based technique that requires the solution of
an adjoint problem for a chosen output and calculations of residuals on finer
approximation spaces. The mesh size is encoded in a node-based metric, and
the approximation order, when adapted, is stored as a scalar field. An
optimal distribution of both quantities is found by deriving cost and error
models for h and p refinement, and by iteratively equidistributing the
marginal error to cost ratios of refinement. The result is an optimal
anisotropic mesh and order field for a particular flow problem. We
demonstrate this h-p optimization technique for several representative flow
problems in aerospace engineering, and we compare the results to other
refinement techniques, including h-only and p-only refinement.