An efficient explicit numerical scheme for diffusion-type equations with a highly inhomogeneous and highly anisotropic diffusion tensor

• Published in: Journal of computational physics Vol. 223; no. 1; pp. 436 - 450
• Main Author: Larroche, O.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 10.04.2007; Elsevier
• Subjects: ADVECTION; Advection-diffusion; ALGORITHMS; ANISOTROPY; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Computational techniques; DIFFUSION EQUATIONS; Exact sciences and technology; Explicit schemes; FOKKER-PLANCK EQUATION; ITERATIVE METHODS; Mathematical methods in physics; MATHEMATICAL SOLUTIONS; Physics; SLOWING-DOWN; TENSORS; Thermonuclear fusion; Thermonuclear fusion; Fokker–Planck equation; Explicit schemes; Advection-diffusion; Linear systems; Advection diffusion equation; Fokker-Planck equation; Calculation methods; Advection; Algorithms; Particle slowing down; Diffusion equation; Models; Calculation; Diffusion; Iterative methods; Charged particles; Slowing-down
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2006.09.016

A locally split-step explicit (LSSE) algorithm was developed for efficiently solving a multi-dimensional advection-diffusion type equation involving a highly inhomogeneous and highly anisotropic diffusion tensor, which makes the problem very ill-conditioned for standard implicit methods involving the iterative solution of large linear systems. The need for such an optimized algorithm arises, in particular, in the frame of thermonuclear fusion applications, for the purpose of simulating fast charged-particle slowing-down with an ion Fokker–Planck code. The LSSE algorithm is presented in this paper along with the results of a model slowing-down problem to which it has been applied.