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

Three numerical techniques have been developed and compared for solving the three-dimensional advection-diffusion 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 implicit techniques such BTCS, BTBSCS and Crank–Nicholson 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 Crank-Nicholson numerical approach matches successfully with the analytical solution while the other techniques result in some levels of discrepancy.

Keywords:

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