A multigrid strategy for accelerating steady-state computations of waves propagating with curvature dependent speeds

Abstract

A multigrid strategy is developed for accelerating the steady state computations of waves propagating with curvature dependent speeds. This will allow the rapid computation of a burn table. In a high explosive material, the creation of a burn table will allow the elimination of solving chemical reaction ODEs and feed in source terms to the reactive flow equations for solution of the system of ignition of the high explosive material. Standard iterative methods show a quick reduction of the residual followed by a slow final convergence to the solution at high iterations. Such systems are excellent choices for the use of multigrid methods to speed up convergence, even on a nonlinear system such as this. Numerical steady-state solutions to the eikonal equation on a rectangular grid are conducted. Results are presented for a square grid in 2D and a cubic grid in 3D using a Runge-Kutta time iteration for the smoothing operator until steady-state is reached