Adaptive time-stepping for incompressible flow. Part I: scalar advection-diffusion

Gresho, Philip and Griffiths, David and Silvester, David (2008) Adaptive time-stepping for incompressible flow. Part I: scalar advection-diffusion. SIAM Journal on Scientific Computing, 30 (4). pp. 2018-2054. ISSN 1064-8275

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Abstract

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.

Item Type:	Article
Additional Information:	This is the revised published version of the work.
Uncontrolled Keywords:	Time-Stepping, Adaptivity, Convection-Diffusion.
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis MSC 2010, the AMS's Mathematics Subject Classification > 76 Fluid mechanics
Depositing User:	professor david silvester
Date Deposited:	19 May 2008
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1099

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