A 3-D streamline tracking algorithm using dual stream functions

Abstract

A new methodology has been developed for constructing streamlines and particle paths in numerically generated fluid velocity fields. A graphical technique is used to convert the discretely defined flow within a cell into one represented by two three-dimensional stream functions. Streamlines are calculated by tracking constant values of each stream function, a process which corresponds to finding the intersection of two stream surfaces. The tracking process is mass conservative and does not use a time stepping method for integration, thus eliminating a computationally intensive part of traditional tracking algorithms. The method can be applied generally to any three-dimensional compressible or incompressible steady flow. Results presented here compare the performance of the new method to the most commonly used scheme and show that calculation times can be reduced by an order of magnitude.