EXPONENTIALLY FITTED DISCRETIZATION SCHEMES FOR DIFFUSION PROCESS SIMULATION ON COARSE GRIDS

This paper examines formulation of the discretization schemes for diff usion process simulation that allow coarse grid spacings in the areas of exponentially varying concentrations and fluxes. The method of inte gral identities is used as a common framework for exponential fitting of both the finite difference and finite element schemes, An exponenti ally fitted finite difference scheme, with discrete flux terms analogo us to those used in Scharfetter-Gummel scheme is Justified. An extensi on of the integral identities in projection form to higher dimensions and a corresponding multidimensional exponentially fitted finite eleme nt scheme are proposed. Two-dimensional test computations show clear s uperiority of the exponentially fitted schemes over the standard appro aches as well as robustness of a new finite elepment scheme regarding irregular grid geometry.