Finite difference methods for convective-diffusive equations

Methods for the integration of the heat equation describing temperature evolution in a homogeneous one dimensional solid body are extended to the resolution of general convective-diffusive equations. For two-dimensional problems, alternating direction implicit methods are introduced. Locally one dimensional methods are described. When the cell Reynolds number in advective-diffusive equations is 2, the modeled equation differs from the original. Second order centered differencing with no artificial diffusion gives a physically meaningless solution spoiled by oscillations. Upwind differencing can be applied, giving another equation to solve. Solutions to this dilemma are discussed.