Analysis and computation of adaptive moving grids by deformation

Abstract

We develop and analyze a numerical method for creating an adaptive moving grid in one-, two-, and three-dimensional regions. The method distributes grid nodes according to a given analytic or discrete weight function of the spatial and time variables, which reflects the fine structure of the solution. The weight function defines a vector field, which is used to construct a transformation of the computational domain into the physical domain. We prove that the resulting grid has the prescribed cell sizes and that no “mesh tangling” occurs. Numerical implementation of the method utilizes an efficient and robust least-squares solver to compute the vector field and a fourth-order Runge-Kutta scheme to determine the transformation. Results of several numerical experiments in one- and two-dimensions are also presented. These results indicate, among other things, that the method accurately redistributes the nodes and does not tangle the mesh. © 1996 John Wiley & Sons, Inc.