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.

Computing methods for perturbation corner forces in electron pressure,ion pressure and photon pressure are investigated.We propose two kinds of subzonal pressure method for Lagrangian algorithm of two-dimensional three-temperature radiation hydrodynamics.Numerical tests show that both methods work well in eliminating unphysical deformation of Lagrangian mesh.

The natural boundary reduction,suggested by Feng and Yu^[2,3],is applied to deal with the exterior boundary value problem of 3-D Helmholtz equation.First,it explains how to derive the natural integral equation,namely the exact Dirichlet-to-Neumann condition,of Helmholtz problem in exterior spherical domain by expansion of spherical harmonics.Second,a numerical method for solving the hypersingular integral equation is developed.Third,some numerical examples are given to illustrate this method.