UPWIND SPLITTING SCHEME FOR CONVECTION-DIFFUSION EQUATIONS

A new class of numerical schemes is proposed to solve convection-diffusion equations by combining the upwind technique and the method of operator splitting. For every time step, the multi-dimensional approximation is performed in several independent directions alternatively, while the upwind technique is applied to treat the convection term in every individual direction. This scheme possesses maximum principle. Stability and convergence are analysed by energy method.