In data-driven modeling, Bayesian sparse identification method with Laplace priors was found and confirmed to recover sparse coefficients of governing partial differential equations(PDEs) by spatiotemporal data from measurement or simulation. Verification results of Bayesian sparse identification method for various canonical models (KdV equation, Burgers equation, Kuramoto-Sivashinsky equation, reaction-diffusion equations, nonlinear Schr dinger equation and Navier-Stokes equations) are compared with those of Rudy's PDE-FIND algorithm. Very well agreement between these two methods shows Bayesian sparse method has strong identification capability of PDE. However, it is also found that the Bayesian sparse method is much more sensitive to noise, which may identify more extra terms. In addition, relatively small error variances of Bayesian sparse solutions are obtained and exhibit clearly the successful identification of PDE.

We give a semi-Lagrangian scheme for Vlasov-Poisson equation using third order upwind interpolation polynomial with limiter. The scheme is conservative and keeps solution positive. We use the scheme to compute typical examples that include Landau damping, two stream instability and symmetric two stream instability. These simulations are compared with other numerical results. In conclusion, the conservative scheme works well in solving Vlasov-Poisson equation.

We develop an open void method of slide line, based on unstructured arbitrary N-polygon grids managed system and tied slide technology, for simulation of large deformation problem of frequently multi-medium loading and unloading. Validity verification was done with metal hit and leave model. Method of distinguishing point and grid's open or closed void state and calculating velocity of point on slide line is given. This slide technology extends open void method of traditional structured grid to unstructured arbitrary N-polygon grids, and keeps merit of no void connectivity and simulating interface well. It has capability of simulating open and closed interface in practical problem. We did test in metal hit and leave model with conditions of many grids, different velocity and multi-medium, which proves validity of the method.

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.

We introduce asymptotic order of convergence,asymptotic range of convergence and concepts under behavior of Lagrangian computations.We also introduce grid convergence index to Lagrangian computation,and give a program using GCI method.These concepts and methods are used to measure computed values away from numerical asymptotic values.

We present a closed void interface method for computational models with void interface in multi-material problems.It simulates void successfully in complicated engineering.It bases on a technique of changeable mesh topology.It avoids using a straight line to replace a curve in traditional method,and overcomes difficulty in solving contact points.Numerical simulations confirm that the technique is effective.It shows characteristic of no void connectivity.

Mode inverse problem for a beam with overhangs is discussed.Flexural rigidity and density of beam with overhangs are solved with two groups of displacement modes or two groups of strain modes and corresponding frequency.Necessary and sufficient conditions for unique existence of solution of the problem are discussed.An algorithm is proposed and numerical calculations are carried out.Two examples show that better results can be attained if strain modes instead of displacement mode are employed.

To investigate mechanism in TUDOG(Transeverse Uniform Droplet Oxygen Generator),a one-dimensional chemical reactive flow model is established to describe physical and chemical performance as mixed Cl₂/He gases passing through BHP(KOH,H₂O₂,H₂O)droplet field transeversely.Gas-phase flowfield is approximately considered as 1-D homogeneous flow according to incompressibility hypothesis.Chemical reaction in liquid droplet is described by reactive-diffusion equations with 4 gasous components.Concentration of gasous components are described with convective-diffusive equations. Droplets are gasous source or sink. It is shown that chlorine utility,singlet oxygen yield and generator efficiency are close to experiment results.The model is verified in simulating interactions between mixing gases and BHP droplets.

Considering potential configuration of a silicon nanocrystal based memory and the mixing effect of valence bands,we calculate direct tunneling time of electron and hole with sequential tunnel theory and in the Bardeen's transfer Hamiltonian formalism.The programming and retention times of a silicon nanocrystal based memory are calculated.Influences of structure and bias on the performance of device are discussed.It is shown that new devices are expected in order to improve the retention property of silicon nanocrystal based memories.

Definiting the slope y/x as a new variable z, the variable transformation from (x, y) to (x, z) is presented. It is found that such a set of new variable (x,z) almost makes the singular integrals dependent on the distance reciprocal r in potential fields become non-singular. By using the new variable, analytical expressions concerning common singular integrals in potential fields are derived as well. Numerical results show that the numerical integration con verges very fast with the method.