The Modified Friction and Diffusion Coefficients of Fokker-Planck Equation and Relaxation Rates for Non-Maxwellian Scattering

In this paper, a new method to derive the Fokker-Planck coefficients defined by a non-Maxwellian velocity distribution function for the field particles is presented. The three- fold integral and the new Debye cutoff parameter, which were introduced by CHANG and LI, are applied. Therefore, divergence difficulties and the customary replacement of relative velocity g by thermal velocity vth are naturally avoided. The probability function P（v, Av） for non- Maxwellian scattering is derived by the method of choosing velocity transfer Av, which is a true measure of collision intensity, as an independent variable. The method enables the difference between small-angle scattering and small-momentum-transfer collisions of the inverse-square force to be well clarified. With the help of the probability function, the Fokker-Planck coefficients are obtained by a normal original Fokker-Planck approach. The friction and diffusion coefficients of the Fokker-Planck equation are modified for non-Maxwellian scattering and are used to investigate the relaxation processes for the weakly coupled plasma. The profiles of the relaxation rates show that the slowing down and deflection processes are weakened in the conditions of non-Maxwellian scattering.

Electrical Conductivity in a Non-Maxwellian Plasma with Adjustable High-Energy-Tail Distribution

In this paper, a solution to the Fokker-Planck equation is presented, which is extended to the field particles＇ high-energy-tail non-Maxwellian velocity distribution function in transport theory. Based on the correct physical concept of collision intensity, introduced by CHANG and LI, the electrical conductivities for like-particles collisions are obtained in different conditions. The modified Fokker-Planck coefficients for non-Maxwellian scattering are applied in the study. It is found that the parallel part of the collision operator plays an important role. The non-Maxwellian scattering will stimulate the transport processes in various degrees with mutative deviation parameters.

Analysis of shock wave reflection from fixed and moving boundaries using a stabilized particle method

In the present paper, the efficiency of an enhanced formulation of the stabilized corrective smoothed particle method （CSPM） for simulation of shock wave propagation and reflection from fixed and moving solid boundaries in compressible fluids is investigated. The Lagrangian nature and its accuracy for imposing the boundary conditions are the two main reasons for adoption of CSPM. The governing equations are further modified for imposition of moving solid boundary conditions. In addition to the traditional artificial viscosity, which can remove numerically induced abnormal jumps in the field values, a velocity field smoothing technique is introduced as an efficient method for stabilizing the solution. The method has been implemented for one- and two-dimensional shock wave propagation and reflection from fixed and moving boundaries and the results have been compared with other available solutions. The method has also been adopted for simulation of shock wave propagation and reflection from infinite and finite solid boundaries.