New High-Resolution Semi-discrete Central Schemes for Hamilton–Jacobi Equations |
| |
Authors: | Alexander Kurganov Eitan Tadmor |
| |
Affiliation: | Department of Mathematics, University of Michigan, Ann Arbor, Michigan, 48109, f1;Department of Mathematics, University of California at Los Angeles, Los Angeles, California, 90095, , f2 |
| |
Abstract: | We introduce a new high-resolution central scheme for multidimensional Hamilton–Jacobi equations. The scheme retains the simplicity of the non-oscillatory 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, independent of 1/Δt. By letting Δt↓0 we obtain a new second-order central scheme in the particularly simple semi-discrete form, along 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 amount of dissipation enables efficient integration of convection-diffusion equations, where the accumulated error is independent of a small time step dictated 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 second discrete derivatives, which is shown to yield an improved high resolution when compared to the usual limitation of first derivatives. Numerical experiments demonstrate the remarkable resolution obtained by the proposed new central scheme. |
| |
Keywords: | Abbreviations: multidimensional Hamilton– Jacobi equationsAbbreviations: semi-discrete central schemesAbbreviations: high resolutionAbbreviations: non-oscillatory time differencing |
本文献已被 ScienceDirect 等数据库收录! |
|