Solution of the convection-diffusion equation by a finite-element method using quadrilateral elements

Numerical solution of the convection-diffusion equation at high Peclet numbers is subject to problems of numerical oscillations and false diffusion. This paper proposes the use of shape functions for quadrilateral elements that are sensitive to the Peclet number and the mean streamline direction over each element. A control-volume approach for obtaining the discretization equations using these shape functions is described. The results of several test problems show that use of the proposed shape function considerably reduces numerical oscillations without introducing the false diffusion effect.