Model equations describing unsteady fluid motion

A system of nonlinear differential equations with four variables, based on a bulk viscosity concept, is presented and tested numerically. The solution by an explicit finite difference method permits the simulation of fairly general flow fields. Three dimensional flow over a backward facing step, vortex separation after a rectangular block, and the longitudinal vortex after an inclined half-plate are calculated. For step flow, qualitative agreement is obtained with experimental results on wall pressure and flow reattachment length. The physical interpretation of the equations emphasizes the effects of pressure distribution on the formation of large scale structures and on unsteady fluid motion.