Petrov–Galerkin Overset Grid Scheme for the Navier–Stokes Equations with Moving Domains

Abstract

J053925In terms of mesh resolution requirements, higher order finite element discretization methods offer a more economic means of obtaining accurate simulations and/or to resolve physics at scales not possible with lower order schemes. For simulations that may have large relative motion between multiple bodies, overset grid methods have demonstrated distinct advantages over mesh movement strategies. Combining these approaches offers the ability to accurately resolve the flow phenomena and interaction that may occur during unsteady moving boundary simulations. Additionally, overset grid techniques when used within a finite element setting mitigate many of the difficulties encountered in finite volume implementations. This paper presents the development of an overset grid methodology for use within a streamline/upwind Petrov-Galerkin formulation for unsteady, viscous, moving boundary simulations. Furthermore, a novel hole cutting procedure based on solutions to Poisson equations is introduced and compared with existing techniques. Order of accuracy is examined via the method of manufactured solutions and the extent of the overlapped region is studied. Overset grid results are presented for several steady-state and timedependent moving boundary simulations with linear, quadratic, and cubic elements.

An overset mesh approach for 3D mixed element high-order discretizations

“…Flux Reconstruction (FR) has been used to solve the two-dimensional, compressible Navier-Stokes equations on sliding meshes [31]. Streamline/upwind Petrov-Galerkin (SUPG) has been used to solve the two-dimensional, compressible, Navier-Stokes equations along with the Reynolds Averaged Navier-Stokes (RANS) equations on steady and unsteady moving mesh problems [32]. Spectral Element Method (SEM) has been used to solve the three-dimensional, incompressible Navier-Stokes equations on moving, overlapping, hexahedral grids [33].…”

“…Streamline/upwind Petrov-Galerkin (SUPG) has been used to solve the two-dimensional, compressible, Navier-Stokes equations along with the Reynolds Averaged Navier-Stokes (RANS) equations on steady and unsteady moving mesh problems [32]. Spectral Element Method (SEM) has been used to solve the three-dimensional, incompressible Navier-Stokes equations on moving, overlapping, hexahedral grids [33]. This has demonstrated the feasibility and high level of accuracy that can be obtained using compact-stencil, high-order methods (DG, FR, SUPG, and SEM) in an overset framework.…”