An artificial viscosity splitting strategy for Lagrangian algorithm of two-dimensional three-temperature radiation magnetohydrodynamics is proposed to solves unphysical pinnacle problem in ion temperature around shock wave as edge viscosity and tensor viscosity are used. The strategy divides kinetic ernergy dissipated by artificial viscosity between electron interior energy and ion interior energy according to ratio of electron pressure and ion pressure. It is realized in two-dimensional three-temperature radiation magnetohydrodynamics code MARED and is used to simulate imploding process of Z-pinch. Unphysical pinnacle in ion temperature around shock wave is removed.

A Langevin equation of fluctuating velocity of fluid ‘seen’ by particle is simplified in Minier's model.Autocorrelation of turbulence fluctuating velocity is obtained,which has non-isotropic property.Corresponding PDF model of particle is obtained and a simplified form is used to predict turbulent particle dispersion in grid-generating turbulence flow.PDF model is solved analytically and solutions are compared with experimental results of Wells and Stock.

A set of nonlinear second order parabolic partial differential equations with initial-boundary values is approxinated by Crank-Nicholson difference method, and successfully solved by means of Loop-Iteration method. The computation of energy transport in tokamak plasma by ohmic heating provides numerical results in agreement with the theoretial analysis.

A kind of singular boundary value problems for second order systems with a singularity at the origin and a non-normal singularity at the resonance layer are solved by means of the three-point difference method. Comparing with the method proposed by Ross et al.,_[1] the present method is not only computationally simpler and more distinct but also can save much computer time. Our numerical results are in agreement with those given in Ref. 1.