Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 30, Issue 4, Pages 2018-2054Publisher
SIAM PUBLICATIONS
DOI: 10.1137/070688018
Keywords
time-stepping; adaptivity; convection-diffusion
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Even the simplest advection-diffusion problems can exhibit multiple time scales. This means that robust variable step time integrators are a prerequisite if such problems are to be efficiently solved computationally. The performance of the second order trapezoid rule using an explicit Adams-Bashforth method for error control is assessed in this work. This combination is particularly well suited to long time integration of advection-dominated problems. Herein it is shown that a stabilized implementation of the trapezoid rule leads to a very effective integrator in other situations: specifically diffusion problems with rough initial data; and general advection-diffusion problems with different physical time scales governing the system evolution.
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