EFFICIENT UPWIND FINITE-DIFFERENCE SCHEMES FOR WAVE EQUATIONS ON OVERSET GRIDS

We describe an algorithm to easily and efficiently incorporate upwinding into finitedifference schemes for solving wave equations in second-order form and apply this scheme to solve problems on complex geometry using overset grids. Upwinding can be added to an existing discretization, such as a centered and dissipation-free scheme, as a modular corrector stage, and takes the form of a special artificial dissipation. This new upwind predictor-corrector scheme significantly improves the run-time performance compared to our original formulation, with typical speedups of factors of ten or more. As with the original upwind formulation, theory and numerical results show that the new algorithm remains robust and stable even for the difficult cases of overset grids with ``thin"" boundary fitted grids, where nondissipative schemes are generally unstable. Numerical results simulating Maxwell's equations in second-order form to second- and fourth-order accuracy are used to assess the run-time performance of the new scheme.