Interaction between magnetic field and fluids is crucial in Z pinch process. Since Z pinch involves with multi materials and severe deformation, we develop 3D compatible Lagrangian staggered and cell-centered schemes for ideal MHD on unstructured meshes. Both of the schemes are of first order in space and time discretization. Accuracy and robustness of the schemes are validated with typical numerical tests.

We present an element free Galerkin method(EFGM) for nonlinear transient field involving phase change.It needs no element connectivity.Compared with other methods such as the finite element method(FEM),it is easy in tracking the growth of phase boundaries.Essential boundary conditions are enforced using a penalty function method.The MATLAB codes are developed to obtain numerical solutions.Two classical examples show that,compared with the FEM,EFGM has more advantages such as high accuracy,good convergence and simple post-process,etc.

The perturbational finite volume(PFV) scheme has the same terse formulation as the first-order upwind scheme.However,PFV scheme is a mixed one in which the integration approximation is of second order accuracy and the reconstruction(or interpolation) approximation is of higher order.PFV scheme is still of second order accuracy in theory.The practical effect and benefit offered by higher-order reconstruction approximation in the upwind and central PFV schemes are verified numerically in this paper.

In this paper, a modified scheme is developed, which can be used for calculation of axisymmetric fluid flow. A set of Euler equations of generalized Rieman variable is derived and solved by two step upwind scheme. The convergence is good because of the consideration of dependent domain of information. Because of using only one point except the unknown one, this scheme is simple and coding is easy. As a example, this scheme has been used for the inviscid subsonic-supersonic flow around blunt bodies at supersonic speeds, the merits of this scheme is demonstrated by these numerical experiments.

A kind of exponential finite difference schemes with h⁴ consistency are developed in this study. The h⁴ scheme is obtained from a second-order modification of the convective coefficients and the source term in an h² scheme, and the modification could be determined once and for all from computational information of the h² scheme, which bring great convenience to the h⁴ scheme. The proposed exponential scheme are unconditionally stable, and show a excellent accuracy and adaptability to great gradient variation when applicated in illustrative computations of 1D to 3D fluid flow model problems.