Embedded mesh multigrid treatment of two-dimensional transonic flows

Abstract

We report the development of a highly flexible computer code which uses a hierarchy of embedded meshes, communicating via multigrid, to solve the axisymmetric or planar viscous transonic flow problem. The purpose of the code is to demonstrate the practicality of techniques sufficiently general to be applicable to complex three-dimensional geometries, and to serve as a test vehicle for mesh communication and relaxation procedures. The code is also of interest in its own right for the fast solution of planar and axisymmetric problems in a very large domain. It consists of a multigrid solver for the full-potential equation (which incorporates the embedded meshes), with a provision for later coupling mass injection to a separate boundary layer program. The principal feature of the code is its treatment of the geometry by means of several levels of locally defined body-fitted meshes embedded in a system of coarser global grids which do not conform to the body. The user may define meshes as large and coarse as desired, in order to solve the problem in a large domain, and also as fine as desired, in order to resolve body geometry and flow field details. The grids need not be coextensive, so that mesh lines placed close to detail features need not extend throughout the field. The intent throughout has been to do nothing whose extension to three dimensions is not straightforward; in particular, global mappings are avoided. We have also emphasized flexible data structures and modular code, with a view toward the development of a highly vectorized three-dimensional version.