论文信息 - A particle method for collisional kinetic equations. I. Basic theory and one-dimensional results

A particle method for collisional kinetic equations. I. Basic theory and one-dimensional results

Abstract A new method is introduced for describing the collisional term in the framework of a particle scheme. The equations of motion of the particles contain an additional term which takes into account the collisions. Numerical techniques are shown to compute this extra term and to solve the equations. Exact results concerning stability and consistency of the schemes for the diffusion equation are derived. Some numerical results for the one-dimensional case are reported.

Giovanni Russo | G. Russo

[1] Point approximation of a space-homogeneous transport equation , 1989 .

[2] Keith Miller,et al. The moving finite element method: Applications to general partial differential equations with multiple large gradients☆ , 1981 .

[3] R. D. Richtmyer,et al. Difference methods for initial-value problems , 1959 .

[4] Keith Miller,et al. Moving Finite Elements. I , 1981 .

[5] S. Mas-Gallic,et al. A deterministic particle method for the linearized Boltzmann equation , 1987 .

[6] L. L. Carter,et al. Particle Transport Simulation with the Monte Carlo Method; Prepared for the Division of Military Application, U.S. Energy Research and Development Administration , 1975 .

[7] J. M. Sanz-Serna,et al. On simple moving grid methods for one-dimensional evolutionary partial differential equations , 1988 .

[8] J. A. White,et al. On the Numerical Solution of Initial/Boundary-Value Problems in One Space Dimension , 1982 .

[9] Raphael Aronson,et al. Theory and application of the Boltzmann equation , 1976 .

[10] F. Hermeline. A deterministic particle method for transport diffusion equations: Application to the Fokker-Planck equation , 1989 .

[11] C. Birdsall,et al. Plasma Physics via Computer Simulation , 2018 .

[12] J. Ziman. Principles of the Theory of Solids , 1965 .

[13] P. Degond,et al. Deterministic particle simulations of the Boltzmann transport equation of semiconductors , 1988 .