Volume 4, Issue 1
Colocated Finite Volume Schemes for Fluid Flows

S. Faure, J. Laminie & R. Temam

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Commun. Comput. Phys., 4 (2008), pp. 1-25.

Published online: 2008-04

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  • Abstract

Ouraiminthis articleis toimprovethe understanding ofthe colocatedfinite volume schemes for the incompressible Navier-Stokes equations. When all the variables arecolocated, that meansherewhen the velocities andthe pressurearecomputed atthesameplace(atthecentersofthecontrolvolumes), theseunknowns mustbeproperly coupled. Consequently, the choice of the time discretization and the method used to interpolate the fluxes at the edges of the control volumes are essentials. In the first and second parts of this article, two different time discretization schemes are considered with a colocated space discretization and we explain how the unknowns can be correctly coupled. Numerical simulations are presented in the last part of the article. This paperisnot acomparisonbetweenstaggeredgridschemes andcolocatedschemes (for this, see, e.g., [15,22]). We plan, in the future, to use a colocated space discretization and the multilevel method of [4] initially applied to the two dimensional Burgers problem, inordertosolve the incompressible Navier-Stokesequations. One advantage of colocated schemes is that all variables share the same location, hence, the possibility to use hierarchical space discretizations more easily when multilevel methods are used. For this reason, we think that it is important to study this family of schemes. 

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@Article{CiCP-4-1, author = {}, title = {Colocated Finite Volume Schemes for Fluid Flows}, journal = {Communications in Computational Physics}, year = {2008}, volume = {4}, number = {1}, pages = {1--25}, abstract = {

Ouraiminthis articleis toimprovethe understanding ofthe colocatedfinite volume schemes for the incompressible Navier-Stokes equations. When all the variables arecolocated, that meansherewhen the velocities andthe pressurearecomputed atthesameplace(atthecentersofthecontrolvolumes), theseunknowns mustbeproperly coupled. Consequently, the choice of the time discretization and the method used to interpolate the fluxes at the edges of the control volumes are essentials. In the first and second parts of this article, two different time discretization schemes are considered with a colocated space discretization and we explain how the unknowns can be correctly coupled. Numerical simulations are presented in the last part of the article. This paperisnot acomparisonbetweenstaggeredgridschemes andcolocatedschemes (for this, see, e.g., [15,22]). We plan, in the future, to use a colocated space discretization and the multilevel method of [4] initially applied to the two dimensional Burgers problem, inordertosolve the incompressible Navier-Stokesequations. One advantage of colocated schemes is that all variables share the same location, hence, the possibility to use hierarchical space discretizations more easily when multilevel methods are used. For this reason, we think that it is important to study this family of schemes. 

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7779.html} }
TY - JOUR T1 - Colocated Finite Volume Schemes for Fluid Flows JO - Communications in Computational Physics VL - 1 SP - 1 EP - 25 PY - 2008 DA - 2008/04 SN - 4 DO - http://dor.org/ UR - https://global-sci.org/intro/cicp/7779.html KW - AB -

Ouraiminthis articleis toimprovethe understanding ofthe colocatedfinite volume schemes for the incompressible Navier-Stokes equations. When all the variables arecolocated, that meansherewhen the velocities andthe pressurearecomputed atthesameplace(atthecentersofthecontrolvolumes), theseunknowns mustbeproperly coupled. Consequently, the choice of the time discretization and the method used to interpolate the fluxes at the edges of the control volumes are essentials. In the first and second parts of this article, two different time discretization schemes are considered with a colocated space discretization and we explain how the unknowns can be correctly coupled. Numerical simulations are presented in the last part of the article. This paperisnot acomparisonbetweenstaggeredgridschemes andcolocatedschemes (for this, see, e.g., [15,22]). We plan, in the future, to use a colocated space discretization and the multilevel method of [4] initially applied to the two dimensional Burgers problem, inordertosolve the incompressible Navier-Stokesequations. One advantage of colocated schemes is that all variables share the same location, hence, the possibility to use hierarchical space discretizations more easily when multilevel methods are used. For this reason, we think that it is important to study this family of schemes. 

S. Faure, J. Laminie & R. Temam. (1970). Colocated Finite Volume Schemes for Fluid Flows. Communications in Computational Physics. 4 (1). 1-25. doi:
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