Stream Surface Generation for Fluid Flow Solutions on Curvilinear Grids

Abstract

A stream surface in a steady-state three-dimensional fluid flow vector field is a surface across which there is no flow. Stream surfaces can be useful for visualization because the amount of data presented in one visualization can be confined to a manageable quantity in a physically meaningful way. This paper describes a method for generation of stream surfaces, given a threedimensional vector field defined on a curvilinear grid. The method can be characterized as semi-global; that is, it tries to find a surface that satisfies constraints over a region, expressed as integrals (actually sums, due to discreteness), rather than locally propagating the solution of a differential equation. The solution is formulated as a series of quadratic minimization problems in n variables, where n is the cross-wind resolution of the grid. An efficient solution method is developed that exploits the fact that the matrix of each quadratic form is tridiagonal and symmetric. Significant numerical issues are addressed, including degeneracies in the tridiagonal matrix and degeneracies in the grid, both of which are typical for the applications envisioned.