An efficient local time-stepping scheme for solution of nonlinear conservation laws

Authors:
Lilia Krivodonova
Affiliations:
Department of Applied Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1
Venue:
Journal of Computational Physics
Year:
2010

Citing 12
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Abstract

We develop an efficient local time-stepping algorithm for the method of lines approach to numerical solution of transient partial differential equations. The need for local time-stepping arises when adaptive mesh refinement results in a mesh containing cells of greatly different sizes. The global CFL number and, hence, the global time step, are defined by the smallest cell size. This can be inefficient as a few small cells may impose a restrictive time step on the whole mesh. A local time-stepping scheme allows us to use the local CFL number which reduces the total number of function evaluations. The algorithm is based on a second order Runge-Kutta time integration. Its important features are a small stencil and the second order accuracy in the L^2 and L^~ norms.