In mesh free methods, discrete equations are built according to physics information of micro-bodies arbitrarily spread in vicinal space. As requirements about topology of micro-bodies are reduced, simulations with Lagrangian approach may be easier even with large distortions. Owing to insufficiency of topological information, there is a challenge for mesh-free method to reflect physics especially as discontinuities exist. In this paper a new mesh free systematic method PECM (Physics Evoked Cloud Method) based on physical laws and developing trend of numerical simulation is shown, which has excellent applicability. High fidelity to physics of the method is demonstrated through several 1-dimentional problems in which strong discontinuities exist.

Based on wavelet analysis theory and reproducing kernel function, a multiscale diagnostic tool for meshfree method SPH is developed.Multi-scale reproducing kernel function make it possible to separate numerical computation response at different scales.Frequency characteristics of computational domain at different position is depicted by dynamic retractable window function, which constructs "adaptive mesh" in mesh method for meshfree system to carry multi-resolution analysis at different position of flow field.With wavelet decomposition algorithm in multi-scale diagnostic tool, a kernel smoothing length optimal selection rule is developed on the basis of estimated energy error ratio of SPH kernel function in frequency domain.Finally, for shock/rarefaction wave coexistence in compressible flow field and defects of traditional method, we construct a numerical method to avoid "tailing" phenomenon.

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.

Propagation analysis often overrate uncertainty of numerical simulation, especially as many uncertain inputs exist. Taking advantage of the reality that calibration can reduce epistemic uncertainty of system-level numerical simulation, a method for uncertainty quantification is offered synthetically using comparison information based on available test data and additional propagation information of modeling and simulation. An example with virtual test is displayed in which the method is demonstrated and validated.

Main cause for uncertainty of atomic structure theory is indicated. A method for uncertainty of temperature-and-density-dependent atomic models in radiative opacity calculation is described via various functional exchange potentials. Uncertainty quantification(UQ) calculation of atomic structures in density-functional at arbitrary temperature and density is carried out by definition of algorithms of modulus. Several procedures indispensable for uncertainty study, and formulae about UQ of electron energy levels and of matrix elements are given. A criterion is proposed to estimate atomic models quantificationally. Feasibility of UQ method is verified by of data of mercury, gold and iron compared with data from‘quasi true’atomic model.

According to demands of uncertainty quantification for reliability certification, in hierarchy of complex engineering system and development from calibration, verification & validation to prediction ability of modeling & simulation (M&S), the principle and method of uncertainty quantification of M & S are investigated. An example on detonation process is shown in which the ideas are demonstrated.

According to the principles of Modeling & Simulation(M&S)and charactersitic of detonation system that final performances are determined by initial conditions,total uncertainties are sorted to three parts that varying along with initial conditions.It reveals how uncertainties are brought on and evolve from benchmark models to new models.Based on engineering practices and technology of verification & validation,a framework of quantification about uncertainty is brought forward in detonation simulation.An example is presented to demonstrate general idea in quantifying uncertainty of M&S.

Kernel functions approximate physical quantities in smoothed particle hydrodynamics (SPH) method.However,approximation accuracy decreases near boundaries.By reconstruction of a kernel with correcting function,reproducing kernel particle method (RKPM) improves approximation accuracy and computational stability at internal or boundary points.Though correction is proposed to approximate functions accurately,it also benefits in approximation of derivatives.