A semi-Lagrange numerical scheme involving advection - diffusion properties of transport equations

摘要

Previously, we have derived a solution to an initial value problem of unsteady linear advection-diffusion equations by applying the spectral technique. The resulting solution is suitable for constructing a numerical scheme fully explicit with respect to time. Based on the solution, a new numerical scheme renormalizing advection-diffusion properties of transport equations is proposed, which is absolutely stable for any large velocity and for any steep gradient of transported quantities. Numerical experiments for both uniform velocity and nonuniform velocity fields showed good solutions.