The Error-Minimization-Based Strategy for Moving Mesh Methods (Communications in Computational Physics, 2018)
The typical elements in a numerical simulation of fluid flow using moving meshesare a time integration scheme, a rezone method in which a new mesh is defined, and a remapping(conservative interpolation) in which a solution is transferred to the new mesh. Theobjective of the rezone method is to move the computational mesh to improve the robustness,accuracy and eventually efficiency of the simulation. In this paper, we consider the one-dimensionalviscous Burgers' equation and describe a new rezone strategy which minimizesthe L2 norm of error and maintains mesh smoothness. The efficiency of the proposed methodis demonstrated with numerical examples.