Level-Set-Based Deformation Methods for Adaptive Grids

A new method for generating adaptive moving grids is formulated based on physical quantities. Level set functions are used to construct the adaptive grids, which are solutions of the standard level set evolution equation with the Cartesian coordinates as initial values. The intersection points of the level sets of the evolving functions form a new grid at each time. The velocity vector in the evolution equation is chosen according to a monitor function and is equal to the node velocity. A uniform grid is then deformed to a moving grid with desired cell volume distribution at each time. The method achieves precise control over the Jacobian determinant of the grid mapping as the traditional deformation method does. The new method is consistent with the level set approach to dynamic moving interface problems.