Parallel Adaptive Finite Element Analysis of Viscous Flows
with Application to Czochralski Melt Flows
This area of research concerns a finite element scheme for the large-scale three-dimensional analysis of compressible and incompressible viscous flows. The main application considered is the simulation of transient and steady-state melt flows in a Czochralski (CZ) crystal growth process. This involves the solution of the Navier-Stokes equations with the Boussinesq approximation. The finite element scheme is based on a Galerkin Least-Squares (GLS) space-time variational formulation. Unstructured meshes of tetrahedral elements are employed, with linear spatial interpolation in all the variables. Piecewise-constant temporal interpolation is used with local time-stepping. The code incorporates automatic adaptive mesh refinement, with a choice of various error indicators. It runs on a distributed-memory MIMD parallel computer, and includes an automatic load-balancing procedure. GMRES is used to iteratively solve the nonsymmetric system of algebraic equations. Both compressible and incompressible flow problems may be simulated.
Example :
The following plots describe the flow in a melt of Indium Phosphide (InP) contained in a crucible, in various configurations, during a Czochralski (CZ) process of crystal growth. The colors represent the temperature distribution (cold from above, hot near the walls and bottom), and the arrows represent the velocity vectors, projected on the vertical plane.
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The colors in the following figures represent the result of partitioning finite element meshes for parallel solution.
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