New high-resolution semi-discrete central schemes for Hamilton-Jacobi equations

We introduce a new high-resolution central scheme for multidimensional Hami lton-Jacobi equations. The scheme retains the simplicity of the non-oscilla tory central schemes developed by C.-T. Lin and E. Tadmor (in press, SIAM J . Sci. Comput.), yet it enjoys a smaller amount of numerical viscosity, ind ependent of 1/Delta t. By letting Delta t down arrow 0 we obtain a new seco nd-order central scheme in the particularly simple semi-discrete form, alon g the lines of the new semi-discrete central schemes recently introduced by the authors in the context of hyperbolic conservation laws. Fully discrete versions are obtained with appropriate Runge-Kutta solvers. The smaller am ount of dissipation enables efficient integration of convection-diffusion e quations, where the accumulated error is independent of a small time step d ictated by the CFL limitation. The scheme is non-oscillatory thanks to the use of nonlinear limiters. Here we advocate the use of such limiters on sec ond discrete derivatives, which is shown to yield an improved high resoluti on when compared to the usual limitation of first derivatives. Numerical ex periments demonstrate the remarkable resolution obtained by the proposed ne w central scheme. (C) 2000 Academic Press.