Using Simpler Algorithm for Cavity Flow Problem

Abstract

Selecting compute nodes and solution grid generation are the first steps of numerical solutions. The most distinct manner is storing the values of dependent variables in the same set of nodes and using the identical control volumes for all variables. Such a grid is called Collocated. Collocated grid arrangement has many positive results in problems with complex solving range, especially with discontinuous boundary conditions. But this arrangement was not used for a long time for incompressible flow due to pressure and velocity isolation problems and creation of fluctuations in pressure. So the researchers in the mid-60s, have developed a new arrangement to reduce this isolation and increase the coupling between pressure and velocity. This new arrangement called staggered grid, provided the field of a new method for solving fluid flow problems called SIMPLE (Semi-Implicit Method for Pressure-Linked Equation) algorithm [1]. This report presents the solution to the continuity, Navier-Stokes equations. Standard fundamental methods like SIMPLER and primary variable formulation have been utilized. The results were analyzed for standard CFD test case- cavity flow. Different Reynold number (1000, 3000) and grid sizes with the finest meshes ie. (100×100), (1000×1000) have been studied.