The use of overset grids in CFD started more than two decades ago, and has achieved tremendous success in handling complex geometries. In particular, overset grids have the advantage of avoiding grid remeshing when dealing with moving boundary flow problems. Traditionally overset grids were mainly used with structured grids to simplify the grid generation process, because a complex computational domain can be more easily meshed after it is partitioned into sub-domains with overset interfaces than with patched interfaces. More recently, unstructured grids are also used in the overset grid system to further simplify grid generation for each sub-domain. In this paper, two particular unstructured grids are advocated for moving boundary flow simulation, i.e., the use of overset adaptive Cartesian/prism grids. Semi-structured prism grids are generated around solid walls. These prism grids then overlap a single adaptive Cartesian background grid. With the adaptive Cartesian grid, the mesh resolution of the prism grid near the outer boundary can easily match that of the oversetting Cartesian grid cells. In addition, the tree-based data structure of the Cartesian grid can be used efficiently in hole-cutting and donor cell identification. The overset adaptive Cartesian/prism grid method is tested for both steady and unsteady flow computation. It is demonstrated that moving boundary flow computations can be automated with minimum user interferences. c = Position vector of the centroid of triangle j Re = Reynolds number v g = Grid velocity v gn = Surface normal grid velocity component V i = Volume of control volume i
The level set method, introduced by Osher and Sethian in 1988, is a powerful numerical approach for computing multi-phase flow problems. In 1994, Sussman, et al employed the level set approach to solve 2D incompressible two-phase flow problems. This approach was improved again by Sussman, et al in 1998. These methods are accurate but designed for structured uniform meshes only. In this paper, a quadtree-based fast Semi-Lagrangian level set method is coupled with a characteristics upwind finite volume incompressible flow solver to tackle multi-phase flow problems. By using unstructured adaptive Cartesian grids with automatic refinement near the interface, the solution accuracy and efficiency is dramatically improved. Several representative multi-phase flow problems are tackled to evaluate the effectiveness of the method. The computational results using the adaptive grids are compared with the results using uniform grids to demonstrate the ability of the method.
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