A 3-D finite-volume method for the Navier-Stokes equations with adaptive hybrid grids

Abstract

This paper describes the development and application of a numerical scheme for the three-dimensional Navier-Stokes equations of viscous flow using hybrid (prismatic/tetrahedral) grids. Employment of prisms is a relatively new approach towards complex geometry high Reynolds number viscous flow computations. The body surface is covered with triangles, which provides geometric flexibility, while the structure of the mesh in the direction normal to the surface provides better resolution of the viscous stresses. The irregular areas between different prismatic layers covering the surfaces of the domain are filled with tetrahedral elements. Their triangular faces match the corresponding triangular faces of the prisms. A dual adaptation scheme is developed which employs both directional and isotropic local refinement/coarsening of the prisms and tetrahedra. The structure of the prisms is preserved by avoiding interfaces with mid-edge nodes. Spatial discretization consists of a finite-volume, node-based scheme that is of the central-differencing type. The solution is marched in time using a Taylor series expansion following the Lax-Wendroff approach. The scheme employs a dual cells arrangement for evaluation of the viscous terms, which has the property of suppressing odd-even modes in the solution. A storage-efficient data structure is employed, which utilizes the structure of the prismatic grid in one of the directions.