An integrated gradient total symmetry-preserving(IGTSP) scheme for momentum equations of Lagrangian hydrodynamics in cylindrical coordinates is presented.The scheme inherits advantages of both IGT and IGA schemes,that is,the scheme not only overcomes nonsymmetry of the IGT scheme but also has a momentum conservation error of order O(h),one order higher than that of IGA scheme.A number of numerical examples are tested to demonstrate advantages of IGTSP scheme.

In a cylinderical coordinate system, integrated gradient method is an effective discrctization for equations of Lagrangian hydrodynamics. In the method IGT (Integral Gradient Total) scheme does not preserve spherical symmetry while IGA (Integral Gradient Average) scheme overcomes nonsymmetry in cylinderical coordinate system. However, IGA results in abnormally large acceleration in case of large mass ratios, where the mass of one subcell around a node is smaller than that of the other three subcells. If boundary force between neighbouring cells is taken as weighted mass average, IGA scheme is equivalent to IGT scheme in both a planar problem and a cylinderical problem even if there exists a large mass ratio. It is shown that IGT scheme preserves total momentum conservation but IGA scheme does not. Numerical results demonstrate advantages and disadvantages of the two schemes.

A nine-point rezone strategy is presented,which improves geometric quality of computational grids and keeps the rezoned grids close to Lagrangian meshes.The scheme is proved an approximation to elliptic equation with spherical symmetry.Numerical examples demonstrate robustness and effectiveness of the scheme in ALE (Arbitrary Lagrangian Eulerian) calculation of high speed impact and denotation driving.

In order to untangle serious distortion in a hohlraum for ICF (Inertial Confinement Fusion),a nine-point rezone strategy is developed.The scheme is approximate to an elliptic or a parabolic equation,and preserves spherical symmetry.The scheme includes several forms of the nine-point rezone scheme according to different requirement in practical problems.The ALE (Arbitrary Lagrangian-Eulerian) method is used in code LARED-H. Suitable results for a hohlraum is illustrated.

A method of couple node velocity is given for reducing distortion of quadrilateral mesh in Lagrangian numerical computation of two dimensional compressible hydrodynamics. It is verified that this method is equivalent to introducing four order smooth term with dissipation property in the momentum equation, thus it plays a role of damping the unphysical oscillation of velocity.

The nine point scheme of refrence(1) is considered and computational scheme of general boundary condition is presented.Numerical test results show that these refinements improved the precision of calculated results.

EPM method for two dimensional elastic-plastic hydrodynamic calculation, which couples Eulerian and Lagrangian methods, is presented in this paper. The difference scheme is constructed by means of contour integral. This method includes sliding interfaces treatment, several generating meshes technique, and so on. It can be widely applied to calculations of many hydrodynamic problems.