Output-Driven Anisotropic Mesh Adaptation for Viscous Flows Using Discrete Choice Optimization

Abstract

This paper presents a mesh adaptation scheme for direct minimization of output error using a selection process for choosing the optimal refinement option from a discrete set of choices. The scheme is geared for viscous aerodynamic flows, in which solution anisotropy makes certain refinement options more efficient compared to others. No attempt is made, however, to measure the solution anisotropy directly or to incorporate it into the scheme. Rather, mesh anisotropy arises naturally from the minimization of a cost function that incorporates both an output error estimate and a count of the additional degrees of freedom for each refinement option. The method is applied to output-based adaptive simulations of the laminar and Reynolds-averaged compressible Navier-Stokes equations on body-fitted meshes in two and three dimensions. Two-dimensional results for laminar flows show a factor of 2-3 reduction in the degrees of freedom on the final adapted meshes when the discrete choice optimization is used compared to pure isotropic adaptation. Preliminary results on a wing-body configuration show that these savings improve in three dimensions and for higher Reynolds-number flows.

An Optimization Framework for Anisotropic Simplex Mesh Adaptation: Application to Aerodynamic Flows

“…This is in contrast to the anisotropic adaptation methods based on hierarchical subdivision of parent elements, 17,18 in which the allowable anisotropy is restricted by the topology of the initial mesh.…”

An optimization-based framework for anisotropic simplex mesh adaptation

“…For anisotropic adaptation on quadrilateral meshes, a common approach is to combine a fixed-fraction marking strategy with a competitive anisotropy selection based on the minimum error-to-dof configuration [12,13]. Unfortunately, the anisotropic error samples collected on a simplex can be noisy and can compromise the quality of adaptation decision, as documented in [16,17].…”

“…Both Georgoulis et al [12] and Ceze and Fidkowski [13] used local solves to guide their anisotropy decisions on quadrilateral 1 meshes. However, the perspective set forth in those works is that of steepest descent in the discrete space, in which the local solves are used to guide the sequence of anisotropic subdivision of quadrilateral elements, which permit orthogonal directional decomposition.…”

Entropy-Based Drag-Error Estimation and Mesh Adaptation in Two Dimensions

“…To avoid uniformly refining the entire mesh at once, the fine space is constructed individually for each element using local meshes that consist of the element and its immediate neighbors [29]. Fine-space residual evaluation is performed on this local mesh.…”