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

Abstract

AbstractA multigrid strategy using upwind finite differencing is developed for accelerating the steady state computations of waves, [14] propagating with curvature‐dependent speeds. This will allow the rapid computation of a “burn table.” In a high explosive material, a burn table will allow the elimination of solving chemical reaction ODEs by feeding 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, including a nonlinear system such as this, are excellent choices for the use of multigrid methods to speed up convergence. Numerical steady‐state solutions to the eikonal equation on several test grids are conducted. Results are presented for these cases in 2D and a cubic grid in 3D using a Runge‐Kutta time iteration for the smoothing operator until steady state is reached. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 179–192, 2002; DOI 10.1002/num.1002