Volume 9, Issue 4
High Order Compact Schemes in Projection Methods for Incompressible Viscous Flows

Michel Fournié & Alain Rigal

Commun. Comput. Phys., 9 (2011), pp. 994-1019.

Published online: 2011-09

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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.

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@Article{CiCP-9-994, author = {Michel Fournié and Alain Rigal}, title = {High Order Compact Schemes in Projection Methods for Incompressible Viscous Flows}, journal = {Communications in Computational Physics}, year = {2011}, volume = {9}, number = {4}, pages = {994--1019}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.230709.080710a}, url = {http://global-sci.org/intro/article_detail/cicp/7532.html} }
TY - JOUR T1 - High Order Compact Schemes in Projection Methods for Incompressible Viscous Flows AU - Michel Fournié & Alain Rigal JO - Communications in Computational Physics VL - 4 SP - 994 EP - 1019 PY - 2011 DA - 2011/09 SN - 9 DO - http://dor.org/10.4208/cicp.230709.080710a UR - https://global-sci.org/intro/cicp/7532.html KW - AB -

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.

Michel Fournié & Alain Rigal. (1970). High Order Compact Schemes in Projection Methods for Incompressible Viscous Flows. Communications in Computational Physics. 9 (4). 994-1019. doi:10.4208/cicp.230709.080710a
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