𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A Numerical Method for the Accurate Solution of the Fokker–Planck–Landau Equation in the Nonhomogeneous Case

✍ Scribed by Francis Filbet; Lorenzo Pareschi

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
384 KB
Volume
179
Category
Article
ISSN
0021-9991

No coin nor oath required. For personal study only.

✦ Synopsis

A new approach for the accurate numerical solution of the Fokker-Planck-Landau (FPL) equation in the nonhomogeneous case is presented. The method couples, through a time-splitting algorithm, a finite-volume scheme for the transport with a fast spectral solver for the efficient solution of the collision operator recently introduced. The scheme allows the use of different grids in the velocity space for the transport and the collision phases. The use of a suitable explicit Runge-Kutta solver for the time integration of the collision phase permits avoid once of excessive small time steps induced by the stiffness of the diffusive collision operator. Numerical results for both space homogeneous and space nonhomogeneous situations show the efficiency and the accuracy of the present method.

📜 SIMILAR VOLUMES

Fast Algorithms for Numerical, Conservat
Fast Algorithms for Numerical, Conservative, and Entropy Approximations of the Fokker–Planck–Landau Equation
✍ C. Buet; S. Cordier; P. Degond; M. Lemou 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 482 KB

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, an

A Numerical Method for Solution of the G
A Numerical Method for Solution of the Generalized Liouville Equation
✍ J. Candy 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 354 KB

dq N dp N ϭ const, (3a) A numerical method for the time evolution of systems described by Liouville-type equations is derived. The algorithm uses a lattice of numerical markers, which follow exactly Hamiltonian trajectories, to represent the operator d/dt in moving (i.e., Lagrangian) coordinates. H

Numerical methods for the solution of th
Numerical methods for the solution of the turbulence energy equations in shelf seas
✍ J.D. Annan 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 116 KB 👁 3 views

This paper investigates the accuracy of numerical finite difference methods for solving the turbulence kinetic energy equations in thermally stratified shelf seas with wind and tidal mixing. Alternative discretisation methods are presented for both the source terms and the diffusion term in the turb

A Wavelet Collocation Method for the Num
A Wavelet Collocation Method for the Numerical Solution of Partial Differential Equations
✍ S. Bertoluzza; G. Naldi 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 355 KB

We describe a wavelet collocation method for the numerical solution of partial differential equations which is based on the use of the autocorrelation functions of Daubechie's compactly supported wavelets. For such a method we discuss the application of wavelet based preconditioning techniques along