An Optimization-Based Rezoning for ALE Methods (Communications in Computational Physics, 2008)
Based on the theory of optimization, we use edges and angles of cells to represent the geometric quality of computational grids, employ the local gradients of theflow variables to describe the variation of flow field, and construct a multi-objectiveprogramming model. The solution of this optimization problem gives appropriatebalance between the geometric quality and adaptation of grids. By solving the optimization problem, we propose a new grid rezoning method, which not only keepsgood geometric quality of grids, but also can track rapid changes in the flow field. Inparticular, it performs well for some complex concave domains with corners. We alsoincorporate the rezoning method into an Arbitrary Lagrangian-Eulerian (ALE) methodwhich is widely used in the simulation of high-speed multi-material flows. The proposed rezoning and ALE methods of this paper are tested by a number of numericalexamples with complex concave domains and compared with some other rezoningmethods. The numerical results validate the robustness of the proposed methods.