Fast Algorithms for Numerical, Conservative, and Entropy Approximations of the Fokker–Planck–Landau Equation

✍ Scribed by C. Buet; S. Cordier; P. Degond; M. Lemou

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 482 KB
• Volume: 133
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1997.5669

✦ Synopsis

We present fast numerical algorithms to solve the nonlinear Fokker-Planck-Landau equation in 3D velocity space. The discretization

of the collision operator preserves the properties required by the

physical nature of the Fokker-Planck-Landau equation, such as the conservation of mass, momentum, and energy, the decay of the entropy, and the fact that the steady states are Maxwellians. At the and ⌽(v) is the 3 ϫ 3 matrix:

end of this paper, we give numerical results illustrating the efficiency of these fast algorithms in terms of accuracy and CPU time.

(1.3) 1. INTRODUCTION: THE FOKKER-PLANCK-LANDAU S(v) is the orthogonal projector onto the plane orthogonal EQUATION 1 This work was partially completed with CEA-CEL-V under Contract W 003 772/216. characterization of the equilibrium states by Maxwellians. 310