Curving for Viscous Meshes

Abstract

Finite-element flow solvers can utilize high-order meshes to achieve improved accuracy over traditional linear meshes. High order meshes are generally created by elevating linear meshes. For high Reynold’s number viscous flows, the linear mesh is tightly clustered to no-slip surfaces. For curved boundaries the high-order mesh must also curve to match the geometry curvature. An optimization-based node perturbation scheme is described that used a two-component cost function to optimize the high order mesh. The first component uses element Weighted Condition Number (WCN) to enforce element shape. The second component uses a normalized Jacobian to enforce element size and validity. The method is applied to several complex linear meshes with highly curved boundaries and tightly clustered normal spacing.