A New ADI Scheme for Solving Three-Dimensional Parabolic Equations with First-Order Derivatives and Variable Coefficients

摘要

An ADI scheme for solving three-dimensional parabolic equations with first-order derivatives and variable coefficients has been developed based on our previous papers and the idea of the modified upwind difference scheme. This ADI scheme is second-order accurate and unconditionally stable. Further, a small parameter can be chosen which makes it suitable for simulating fast-transient phenomena or for computations on fine spatial meshes. The method is illustrated with numerical examples.