Explicit numerical solution of three-dimensional advection-diffusion equation using simultaneously temporal and spatial weighted parameters

Two numerical techniques have been developed and compared for solving the three-dimensional advectiondiffusion equation with constant coefficients. These techniques are based on the finite difference methods (FDM). By changing the values of temporal and spatial weighted parameters, solutions are obtained for explicit techniques such as FTCS, FTBSCS schemes. Numerical solution is given for a special case which has been dealt with in the literature and for which an analytical solution has been provided. Comparison of the results has confirmed that the FTBSCS numerical approach matches successfully with the analytical solution while the other technique result in some levels of discrepancy.

Keywords:

finite difference methods , advection–diffusion equation , spatial weight , temporal weight , explicit techniques