NUMERICAL INVESTIGATION OF THE FLOW IN A TWO-DIMENSIONAL CAVITY: MESHLESS, FINITE VOLUMES AND FINITE DIFFERENCES METHODS

Abstract

THIS STUDY COMPARES THE FINITE VOLUMES, FINITE DIFFERENCES AND MESHLESS METHODS APPLIED TO THE CLASSIC SQUARE DRIVEN CAVITY PROBLEM. IT GIVES A BRIEF EXPOSITION OF THE DRIVEN CAVITY FLOW PROBLEM, THE SCIENTIFIC MOTIVATION OF THIS STUDY, THE APPROACH EMPLOYED, AND THE GOALS TO BE ACHIEVED. THE PROJECTION METHOD WAS USED TO SOLVE THE NAVIER-STOKES EQUATIONS. A STRUCTURED MESH WAS EMPLOYED FOR THE FINITE DIFFERENCES METHOD AND AN UNSTRUCTURED MESH FOR THE FINITE VOLUMES METHOD. CELL CENTERED WAS USED FOR THE VELOCITY FIELD U AND THE PRESSURE FIELD P IN THE FINITE VOLUMES METHOD. THE CONVERGENCE WAS ACCELERATED THROUGH THE BI-CONJUGATED GRADIENT STABILIZED METHOD. THE NECESSARY POINTS TO THE MESHLESS METHOD WERE OBTAINED FROM THE COMPUTATIONAL NODES GENERATED BY THE FINITE VOLUMES MESH. THE EXPONENTIAL WEIGHT FUNCTION AND THE LEAST SQUARE METHOD WAS USED IN THE MESHLESS METHOD. THE PRIMITIVE VARIABLES WERE ADOPTED IN ALL THE FORMULATIONS AND REYNOLDS NUMBERS 0.1, 10, 50 AND 100 WERE USED. THE FORMULATIONS ARE SECOND ORDER IN SPATIAL VARIABLES AND FIRST ORDER EXPLICIT IN TIME VARIABLES. INTERESTING CHARACTERISTICS OF THE FLOW ARE PRESENTED IN DETAILS - THE VELOCITY FIELD IN THE CENTRAL LINES AND THE STREAMLINES. THE RESULTS ARE LISTED IN TABLES AND THE PRIMARY VORTEX POSITION IS COMPARED WITH OTHER AUTHORS. THE FINITE VOLUMES, MESHLESS AND FINITE DI®ERENCES METHODS ARE COMPARED AND THE ERRORS AMONG THEM ARE PRESENTED AND DISCUSSED.