An Operator-integration-factor splitting method for time-dependent problems: Application to incompressible fluid flow |
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Authors: | Y Maday Anthony T Patera Einar M Rønquist |
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Affiliation: | (1) Analyse Numérique, Université Pierre et Marie Curie, Paris, France;(2) Department of Mechanical Engineering, MIT, 02139 Cambridge, Massachusetts;(3) Nektonics, 02139 Cambridge, Massachusetts |
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Abstract: | In this paper we present a simple, general methodology for the generation of high-order operator decomposition ( splitting ) techniques for the solution of time-dependent problems arising in ordinary and partial differential equations. The new approach exploits operator integration factors to reduce multiple-operator equations to an associated series of single-operator initial-value subproblems. Two illustrations of the procedure are presented: the first, a second-order method in time applied to velocity-pressure decoupling in the incompressible Stokes problem; the second, a third-order method in time applied to convection-Stokes decoupling in the incompressible Navier-Stokes equations. Critical open questions are briefly described. |
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Keywords: | Splitting methods operator decomposition Navier-Stokes equations pressure |
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