SIMULATION OF UNSTEADY TRANSPORT PHENOMENA USING NEW FINITE VOLUME METHOD

Abstract

Based on the finite volume method (FVM), a numerical scheme is constructed to simulate the unsteady convection–diffusion transport problem. New expressions are obtained for interface approximation of the field variable, subsequently, these newly obtained interface expressions are used to develop the numerical scheme. Convection-dominant and diffusion-dominant phenomena are simulated by taking different values of convective velocity [Formula: see text] and diffusion coefficient [Formula: see text]. This newly proposed numerical scheme gives second order of convergence along space and time. Experiments are carried out to test the new proposed upwind approach. Numerical results produced by the proposed approach are compared with the conventional finite volume method, step-wise approach FVM and quadratic upwind interpolation finite volume approach. This comparative study indicates that for different cases for convection-dominant and diffusion-dominant problems, our proposed approach gives highly accurate and stable solution. The conventional finite volume method and other approaches result solution with non-physical oscillations. Our obtained numerical results are consistent and support our theoretical approach.