With margins and their uncertainties, QMU (Quantification of Margin and Uncertainty) method can be used to make decisions on whether performances of a product reach demands or not. Recur to new methods of UQ (Uncertainty Quantification) for M&S (Modeling & Simulation), QMU is actualized with input information directly from M&S and its uncertainties. With reliability assessment for a stockpiled product, main ideas and executing details of QMU decision are demonstrated.

A 2D cell-centered multi-material arbitrary Lagrangian-Eulerian(MMALE) method based on moment of fluid(MOF) interface reconstruction is developed. Hydrodynamic equations are discretized and solved by cell-centered Lagrangian scheme. Tipton's pressure relaxation model is adopted as closure model for mixed cells. MOF method is simplified and improved to reconstruct interface in mixed cells. A conservative integral remapping algorithm based on cell-intersection is used in remapping phase. Several numerical examples are given, such as 2D periodic vortex problem, Sedov problem, interaction of a shock wave with an helium bubble,a strong water shock impacting on a cylindrical air bubble in water,2D Rayleigh-Taylor instability, etc.It shows that the method is of second order accurate, and is capable of computing problems involving large density and/or pressure ratios across interface. Its robustness is better than that of staggered MMALE method and it is applicable to complex multi-material hydrodynamic problems.

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.

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.