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2006.409: Adaptive time-stepping for incompressible flow. Part I: scalar advection-diffusion

2006.409: Philip Gresho, David Griffiths and David Silvester (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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DOI: 10.1137/070688018

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 2000 > 35 Partial differential equations
MSC 2000 > 65 Numerical analysis
MSC 2000 > 76 Fluid mechanics
MIMS number:2006.409
Deposited By:professor david silvester
Deposited On:19 May 2008

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