Mesh Topology Preserving Boundary-Layer Adaptivity Method for Steady Viscous Flows

The efficiency and accuracy of viscous flow simulations depend crucially on the quality of the boundary-layer mesh. Too coarse meshes can result in inaccurate predictions and in some cases lead to numerical instabilities, whereas too fine meshes produce accurate predictions at the expense of long simulation times. Constructing an optimal (or near-optimal) boundary-layer mesh has been recognized as an important problem in computational fluid dynamics. For few simple flows, one may be able to construct such a mesh a priori before simulation. For most viscous flow simulations, however, it is difficult to generate such mesh in advance. In this paper, a boundary-layer adaptivity method is developed for the efficient computation of steady viscous flows. This method turns the problem of determining the location of the mesh nodes into a set of equations that are solved simultaneously with the flow equations. The mesh equations are designed so that the boundary-layer mesh adapts to the viscous layers as the flow solver marches toward the converged solution. Extensive numerical experiments are presented to demonstrate the performance of the method.