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Multirate Timestepping Methods for Hyperbolic Conservation Laws

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Abstract

This paper constructs multirate time discretizations for hyperbolic conservation laws that 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 algorithms. Numerical results obtained for the advection and Burgers’ equations confirm the theoretical findings.

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Authors and Affiliations

  1. Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, 24061, USA

    Emil M. Constantinescu & Adrian Sandu

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  1. Emil M. Constantinescu
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  2. Adrian Sandu
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Correspondence to Adrian Sandu.

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This work was supported by the National Science Foundation through award NSF CCF-0515170.

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Constantinescu, E.M., Sandu, A. Multirate Timestepping Methods for Hyperbolic Conservation Laws. J Sci Comput 33, 239–278 (2007). https://doi.org/10.1007/s10915-007-9151-y

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  • DOI: https://doi.org/10.1007/s10915-007-9151-y

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