Three-point scheme and two-point boundary formulations for unsteady diffusion with flow

摘要

A three-point scheme of Crank-Nicolson type and two-point boundary formulations are derived that accurately model both long- and short-scale branches of gradual time-variation solutions for unsteady diffusion on low-resolution grids. Inadequacies in the resolution are compensated, to second order in the rate of change, with interior and boundary weights that have elementary function dependence on the grid spacing. Numerical testing suggests that the computations are robust to rapid variation, improve with interior grid points at tuned uniform spacing and become accurate if the design assumption of gradual time variation is satisfied.