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High Order Compact Schemes in Projection Methods for Incompressible Viscous Flows

Published online by Cambridge University Press:  20 August 2015

Michel Fournié  and
Alain Rigal
Michel Fournié*
Affiliation:
Institut de Mathématiques de Toulouse, Université de Toulouse et CNRS (UMR 5219), France
Alain Rigal*
Affiliation:
Institut de Mathématiques de Toulouse, Université de Toulouse et CNRS (UMR 5219), France
*
Corresponding author.Email:michel.fournie@math.univ-toulouse.fr
Email:alain.rigal@math.univ-toulouse.fr
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Abstract

Within the projection schemes for the incompressible Navier-Stokes equations (namely “pressure-correction” method), we consider the simplest method (of order one in time) which takes into account the pressure in both steps of the splitting scheme. For this scheme, we construct, analyze and implement a new high order compact spatial approximation on nonstaggered grids. This approach yields a fourth order accuracy in space with an optimal treatment of the boundary conditions (without error on the velocity) which could be extended to more general splitting. We prove the unconditional stability of the associated Cauchy problem via von Neumann analysis. Then we carry out a normal mode analysis so as to obtain more precise results about the behavior of the numerical solutions. Finally we present detailed numerical tests for the Stokes and the Navier-Stokes equations (including the driven cavity benchmark) to illustrate the theoretical results.

Keywords

65M0676D05Incompressible Navier-Stokesfractional step methodhigh order compact schemeboundary conditions
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 4 , April 2011 , pp. 994 - 1019
Copyright
Copyright © Global Science Press Limited 2011

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