Numerical investigation of convection–diffusion model by using the new upwind finite volume approach

Abstract

In this study, we constructed a numerical technique for the simulation of the convection–diffusion problem under convection dominancy. Lagrange interpolation technique is applied to obtain new expressions for the approximation of variable at the interfaces of control volume. Moreover, based on these interface approximations new numerical scheme is developed to approximate convection–diffusion phenomena. The Crank–Nicolson approach is applied for the temporal approximation. This newly constructed numerical scheme is unconditionally stable with second-order accuracy in time and space both. Numerical tests are carried out for the justification of the new algorithm. A comparison of numerical results produced by proposed technique and some other numerical approaches is presented. This comparison indicates that for convection dominant phenomena, the numerical solution of conventional finite volume method contains with non-physical oscillations which analyze that proposed numerical technique results in a high accurate and stable solution.