Pressure Based Method for Solving Viscous Incompressible Flows using Rhie and Chow Interpolation

Abstract

In this paper a pressure based finite volume method is formulated to solve the viscous incompressible flows using rhie chow interpolation. The method involves employing a different interpolation for advective velocities and provides a connection between the nodal velocity and pressure so there is no odd-even decoupling. The present solver is tested for one Dimensional diffusion problem with and without source term, potential flow equation, and laminar viscous incompressible flows. The results are compared with existing results in the literature. The present study has established that numerical method can provide a reasonable good solution for incompressible viscous flows. Goldstein(9) proposed a model called virtual boundary formulation, was used to simulate turbulent flow over a ribelt- covered surface. Ye (10) propose a method called Cartesian grid method for simulating two dimensional viscous, incompressible flows over complete geometry. Lai & Peskin (11) have proposed another method second order accurate boundary which was used for a flow over a stationary cylinder. Present solver is a useful to validate the potential flow is such that an analytical solution exists for cases whose geometries are relatively simple. Lid driven cavity flow is the motion of a fluid inside a square cavity and it serves as the benchmark for the numerical method in terms of accuracy and efficiency. It is easy to code and apply boundary condition for the driven cavity flow due to simplicity of the geometry. Erturk & Gokcol(12), Liao & Zhu (13) have presented the solution of two dimensional incompressible flow in the driven cavity for Re≤100. Prasad & Koseff(14) have done few experiments on three dimensional driven cavity flows. These experimental studies present important information about the physics of the flows in the driven cavity. In the present study we have used two dimensional navier stokes equation and all of the solution presented based on the assumption that the flow is two dimensional.