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

When operator splitting algorithms are used to solve the advection-dif fusion equation, it is necessary to derive boundary conditions applica ble to the split advection and diffusion equations. In this paper inte rmediate Dirichlet boundary conditions are formulated for Strang type splitting algorithms for the one-dimensional advection-diffusion equat ion. The derived boundary conditions are applicable to advection domin ated 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 recipro cal of Peclet number.