Finite Volume Method for Time-Dependent Convection Diffusion Large Reynolds Number Problem

Time-dependent convection diffusion equation, with a discontinuous data and large Reynolds number, is examined. This kind of problem leads to interior layer phenomena due to the discontinuity. The solution changes rapidly near interior layer. Traditional finite volume method is applied. Two efficient numerical methods are constructed. One is Shishkin's finite volume method. Another is Improved-Shishkin's finite volume method. Shishkin's finite volume method applies Shishkin's idea to construct mesh partition. Improved-Shishkin's finite volume method applies multi-transition points technique to reconstruct mesh partition near interior layer. Numerical experiments indicate that both methods are well fitted the property of interior layer. Both methods are uniformly convergence scheme. Improved-Shishkin's finite volume method is more accurate than finite difference method, which is constructed by Farrell in his previous paper.