Automated analysis of fluid flow topology

Abstract

Much research has been devoted to image understanding and the automated analysis of images of two-dimensional scalar data, but comparatively little work has been devoted to understanding higher dimensional data. Experiments and numerical simulations of fluid flows yield extremely large multivariate data sets which are often too complicated for manual inspection, manipulation, comparison and display. As with scene analysis, an abstract representation of the data set would greatly facilitate these tasks. In the analysis of vectorial data such a representation can be based on the topology of the vector field. A new method is presented for the representation and visualization of vector fields, in particular those derived from fluid flows. It is based on critical point analysis. The method can be applied to general vector fields, but as our main interest is in fluid flows, we have included in the analysis walls (no-slip boundaries) on which the vector field vanishes. Singular points on the walls and critical points in the external flow serve as a basis for building a representation of the global topology as determined by the tangent curves of the vector field. The resulting representations, which consist of critical points, dividing stream surfaces, surfaces of separation, vortical cores, etc., may then be displayed and compared to study the development of flow topology with time or as a function of a parameter such as angle of attack. The representation may also be used as a "road map" for further investigation of the original data set in its entirity. Results are presented from the application of these methods to two-dimensional and two-dimensional parameter-dependent fluid flow data sets.