A New Co-Located Pressure-Based Discretization Method for the Numerical Solution of Incompressible Navier-Stokes Equations

Abstract

There are two commonly used numerical strategies for the solution of incompressible Navier-Stokes equations in the context of the finite-volume method. These equations are either discretized using geometric interpolations and solved on staggered grids, or solved on co-located grids using geometric and momentum-based interpolations for convected and convecting velocities, respectively. This article presents an alternative finite-volume method for the solution of incompressible Navier-Stokes equations on co-located grids without resorting to two different interpolation formulas for convected and convecting velocities. The key idea for achieving physical coupling between pressure and velocity fields in the numerical model is the employment of proper closure equations during the discretization. These closure equations are used to convert the finite-volume balance equations to proper computational molecules at nodal points. A number of steady two-dimensional test problems are solved which show the applicability and excellent performance of the proposed method. The method does not have any inherent limitation and is extendable to three-dimensional flows as well.