Mathematical Modeling and Analysis
Mathematical Modeling and Analysis
The philosophy of the Arbitrary Lagrangian-Eulerian (ALE) methodology for solving multidimensional fluid flow problems is to move the computational grid, using the flow as a guide, to improve the robustness, accuracy and efficiency of the simulation. One of the main elements in the ALE simulation is a rezone phase in which a new grid is defined. In most multidimensional ALE codes, the main goal of the rezone phase is to maintain geometrical quality of the mesh.
We developed a new Error-Minimization-Based (EMB) rezone strategy which minimizes the L2 norm of a global error and maintains smoothness of the mesh. The global error is a superposition of an interpolation error, an error due to the time advancing method, and the space discretization error. . The goal of the EMB rezone strategy is to achieve balance (if possible) between these errors to minimize the global error. We demonstrated with 1D numerical experiments the superiority of the new rezone strategy over a geometric rezone strategy and the pure Lagrangian method.
