A PDE-Based Mesh Update Method for Moving and Deforming High Reynolds Number Meshes

摘要

The Navier equation governing classical linear elastostatics is used as the basis for a mesh update method applicable to flow simulations involving moving and deforming body-fitted high Reynolds number meshes. A modified form of the equation is presented that produces higher quality meshes compared to the unmodified equation and extends the range of flow problems where deforming body-fitted meshes can be successfully employed. Two modifications to the Navier equation are presented. The first modification addresses shear distortion in the mesh while the second modification addresses size distortion. An attractive feature of the method is that the basic governing equation involves terms that are identical to terms in the compressible Navier-Stokes equation and can be readily implemented using an existing Navier-Stokes discretization as a template. Edge formulas are presented for a vertex-centered finite volume implementation of the method. A near wall node blanking procedure is adopted as an ad hoc approach to resolving a numerical pathology that arises with high aspect ratio cells with sliding boundary conditions. Several two-dimensional model problems are used to demonstrate the role of the various terms in the modified equation as well as demonstrate the efficacy of the method in a variety of situations. The method is then applied to the case of the biomimetic swimming robot, RoboTurtle, where complex geometry combined with large three-dimensional motion demonstrates the limits of the approach. Finally, the method is applied to the case of a Wigley hull form to demonstrate it's applicability to high Reynolds number free surface flows via an interface tracking procedure.