INTERMEDIATE DIRICHLET BOUNDARY-CONDITIONS FOR OPERATOR SPLITTING ALGORITHMS FOR THE ADVECTION-DIFFUSION EQUATION

When operator splitting algorithms are used to solve the advection-diffusion equation, it is necessary to derive boundary conditions applicable to the split advection and diffusion equations. In this paper intermediate Dirichlet boundary conditions are formulated for Strang type splitting algorithms for the one-dimensional advection-diffusion equation. The derived boundary conditions are applicable to advection dominated problems and are O(min(k epsilon(3), k(2) epsilon(2))) accurate, where k is the computational time step and epsilon << 1 is the reciprocal of Peclet number.