| In the first part of this study an adaptive moving grid algorithm is formulated based on the deformation method, which may enhance accuracy and efficiency in the numerical simulation of partial differential equations. The method redistributes the nodes of an initial grid according to a vector field calculated from a Poisson equation. The forcing term of this equation is the time derivative of a positive monitor function. It adapts the grid at each time-step by keeping the volume of each cell proportional to a monitor function. This is combined with a finite-difference solver to solve a time-dependent differential equation. The method transforms the partial differential equation using a computed nodal mapping and then numerically simulates the transformed equations on orthogonal grids in the logical domain.; In the second part of this study, a level set deformation method is formulated. It predicts precisely the velocity field needed in the level set evolution equations so that the cell size is directly controllable as in the traditional deformation method. This vector field is used to evolve the level set functions using the evolution partial differential equations and the intersection of the level sets gives the new grid point locations of the grid. |
