@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 = {<p style="text-align: justify;">Within the projection schemes for the incompressible Navier-Stokes equations
(namely &quot;pressure-correction&quot; 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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.230709.080710a},
url = {http://global-sci.org/intro/article_detail/cicp/7532.html}
}