We present a second order cell-centered finite volume method of 2D Lagrangian hydrodynamics based on semi-discrete framework.Velocity and pressure on vertex of a cell are computed with characteristics theory,Then,they are used to compute numerical flux through cell interface by trapezoidal integration rule.With a reconstruction procedure,the method is extended to second order.Several numerical experiments confirm convergence and symmetry of the method.The method permits large CFL numbers and can be applied on structured and unstructured grids.It is robust in multi-material flow simulations.

A general high-order unstructured-grid finite volume method based on least-square reconstruction and WENO limiter is presented.Some of the neighboring cells are employed to construct high-order polynomials.a least-square method is used tO solve overdetermined problem.The number of neighboring cells can be reduced with a general method,which saves memory and computing time. To achieve uniform accuracy and depress non-physical oscillation of conservation laws,a WENO limiter and rotated Riemann solver are employed.Two classical cases are provided to show resolution differences between high-order schemes and the second order scheme based on gradient reconstruction and Bath and Jesperson limiter.

We present a cell-centered finite volume method for 2D invicsous Lagrangian hydrodynamics.Velocity and pressure on vertex of a cell are computed with characteristics theory,which is derived from governing equations of Lagrangian form linearized by freezing Jacobian matrices about a known reference state.The velocity is used to update coordinate of vertex of a cell.Product of two variables is used to compute numerical flux through cell interface by a trapezoidal integration rule.Convergency,symmetry and conservation of total energy of the method are demonstrated.The method can be applied to structured or unstructured grids,and does well spontaneously for multi-material flows in a robust way.The scheme is one order precision,and can be easily draw on two order precision.

A second-order rotational upwind transport scheme for multidimensionul compressible Euler equations on unstructured meshes is presented. Cell-centered FVM is employed in which gradient calculation is node-based with more neighbor cells. Slope limiter schemes are constructed for unstructured meshes. Numerical fluxes are evaluated by solving two Riemann problems in two upwind directions, including velocity-difference vector and perpendicular direction. The scheme eliminate shock instabilities or carbuncle phenomena in flux-difference splitting type schemes completely. A hybrid rotated Riemann solver is employed to form an economical numeric flux function and base Riemann solvers employ HLL and Roe FDS.

A derivate's formula is presented based on the analytical discrete method and can achieve arbitrary order of accuracy firstly.It is combinated with Roe's flux differential splitting technique and high accuracy flux filter midmod,to construct a kind of nonoscillatory shock-capturing method with high order of accuracy and high resolution.