Numerical solution of convection-dominated diffusion problem using modified upwind finite volume method

Abstract

In this paper, an attempt has been made to developed a numerical scheme for numerical approximation of the convection-diffusion problem in convection dominant situations. Applying Lagrange interpolation technique, new expressions are obtained to approximate the variable at spatial interfaces of the computational domain. Subsequently, these interface approximations are used to developed a numerical scheme based on upwind approach in the finite volume method. Crank-Nicolson technique is used for the approximation along temporal direction. This newly constructed numerical scheme is unconditionally stable with second order accuracy along space and time both. The numerical experiments are performed using the proposed upwind approach and numerical results confirm the theoretical algorithm. Numerical results produce by our constructed numerical are compared with conventional finite volume method. This comparison indicates for convection dominant phenomena the numerical solution of conventional finite volume method contains with non-physical oscillations where are our proposed numerical schemes give a high accurate and stable solution.