Controlling numerical diffusion in solving advection-dominated transport problems

Abstract

Numerical schemes for advection-dominated transport problems are are evaluated in a comparative study. Explicit and implicit finite difference methods are analyzed together with a global random walk algorithm in the frame of a splitting procedure. The efficiency of the methods with respect to the control of the numerical diffusion is investigated numerically on one-dimensional problems with constant coefficients and two-dimensional problems with variable coefficients consisting of realizations of space-random functions.

Keywords

• Advection-dominated transport
• Numerical diffusion
• Finite differences
• Method of lines
• Global random walk