Multirate Explicit Adams Methods for Time Integration of Conservation Laws

Authors:
Adrian Sandu;Emil M. Constantinescu
Affiliations:
Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, USA 24061;Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, USA 24061
Venue:
Journal of Scientific Computing
Year:
2009

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Abstract

This paper constructs multirate linear multistep time discretizations based on Adams-Bashforth methods. These methods are aimed at solving conservation laws and allow different timesteps to be used in different parts of the spatial domain. The proposed family of discretizations is second order accurate in time and has conservation and linear and nonlinear stability properties under local CFL conditions. Multirate timestepping avoids the necessity to take small global timesteps--restricted by the largest value of the Courant number on the grid--and therefore results in more efficient computations. Numerical results obtained for the advection and Burgers' equations confirm the theoretical findings.