SIMULATION OF FLUID MIXING USING LEAST-SQUARES FINITE-ELEMENTS AND PARTICLE TRACING

A least-squares finite element analysis of viscous fluid flow together with a trajectory integration technique for tracers is formulated and provides a mechanism for investigating mixing. Tracer integration is carried out using an improved Heun predictor-corrector. Results from our supporting numerical studies on the GRAY and Connection Machine (CM) closely resemble the patterns of mixing observed in experiments. A 'box-counting' scheme and other measures to characterize the level of mixing are developed and investigated. This measure is utilized in numerical experiments to determine an optimal forcing frequency for mixing by periodic boundary motion in a rectangular enclosure. Some details concerning the numerical schemes and vector-parallel implementation are also included.