Collocated finite-volume method for the incompressible Navier-Stokes problem
The author considers a collocated finite volume method to approximate incompressible Navier-Stokes equations. The approach of the finite volume method used here is the integration of the equation over subsets of the physical domain, called control volumes, the use of integration by parts, and then the approximation of the terms which appear after integration. These terms are defined over the interfaces of the control volumes. The velocity components and the pressure are approximated by piecewise-linear continuous and piecewise-constant fields, respectively. The scheme obtained satisfies some important physical properties, e.g., it conserves both the mass and momentum. In addition, the method can be applied to general polyhedral grids. It is stated, but without a ``clear'' rigorous proof, that the method demonstrates higher than the first order of accuracy. Several numerical tests are presented to show the efficiency of the method. In particular, this efficiency is shown numerically for both the cases of high and low Reynolds numbers.
scientific article; zbMATH DE number 7347666
scientific article