High order conservative difference methods for 2D drift-diffusion model on non-uniform grid Original Research Article

A new accurate compact finite difference scheme for solving the 2D drift-diffusion system is introduced. The scheme is based on the computation on staggered grids of the current densities given by advection-dominated equations. Conservativity is preserved and the compactness of the scheme leads to a good treatment of boundary conditions. The discretization is realized on uniform and non-uniform grids. This last grid is analytically defined using mapping techniques (spline functions). A new accurate compact finite difference scheme for solving the 2D drift-diffusion system is introduced. The scheme is based on the computation on staggered grids of the current densities given by advection-dominated equations. Conservativity is preserved and the compactness of the scheme leads to a good treatment of boundary conditions. The discretization is realized on uniform and non-uniform grids. This last grid is analytically defined using mapping techniques (spline functions). Several numerical tests show the robustness of the method.