PARALLEL ADAPTIVE FINITE-ELEMENT ANALYSIS OF VISCOUS FLOWS BASED ON ACOMBINED COMPRESSIBLE-INCOMPRESSIBLE FORMULATION

Describes a new finite element scheme for the large-scale analysis of compressible and incompressible viscous flows. The scheme is based on a combined compressible-incompressible Galerkin least-squares space-ti me variational formulation. Three dimensional unstructured meshes are employed, with piecewise-constant temporal interpolation, local time-s tepping for steady flows, and linear continuous spatial interpolation in all the variables. The scheme incorporates automatic adaptive mesh refinement, with a choice of various error indicators. it is implement ed on a distributed-memory parallel computer, and includes an automati c load-balancing procedure. Demonstrates the ability to solve both com pressible and incompressible viscous flow problems using the parallel adaptive framework via numerical examples. These include Mach 3 flow o ver a flat plate, and a divergence-free buoyancy-driven flow in a cavi ty. The latter is a model for the steady melt flow in a Czochralski cr ystal-growth process.