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.

Spectral Chebyshev collocation method and high-order FD-q finite difference method are used for global instability analysis of magetohydrodynamic(MHD) duct flows and compared for their merits and drawbacks. Spectral Chebyshev collocation method has faster convergence rate and high-order accuracy, while it needs to construct full general eigenvalue matrix which would consume large memory storage and a great deal of computational cost. High-order FD-q finite difference method adopts modified Chebyshev collocation points as discretization mesh grids based on Kosloff-Tal-Ezer transformation. FD-q method can maintain high convergence rate of mesh grids, and resulted general eigenvalue matrix is very sparse and can be stored with sparse matrix, which greatly reduces computational resource. In contrast to traditional spectral collocation method, non-uniform mesh based FD-q method obtains remarkable progress on computational efficiency, which is further demonstrated by computation of linear optimal transient growth for MHD duct flows.

Global sensitivity analysis method based on polynomial chaos and variance decomposition is reviewed comprehensively. In order to alleviate "curse of dimensionality" coming from high-dimensional random spaces or high-order polynomial chaos expansions, several approaches such as least square regression, sparse grid quadrature and sparse recovery based on l₁ minimization (i. e. compressive sensing) are used to reduce sample size of collocation points that needed by non-intrusive polynomial chaos method. With computation of Sobol global sensitivity indices for several benchmark response models including Ishigami function, Sobol function, Corner peak function and Morris function, effective implementations of polynomial chaos method for variance-based global sensitivity analysis are exhibited.

An iterative method for unstructured dynamic-grid using springs based on LU-SGS (lower-upper symmetric Gauss-Seidel) is presented to reduce time of iterative in dynamic discontinuities simulation. Dynamic grid iterative time is as much as time of field itemtive as shock and flex-wall are numerical fitting by time-dependent Euler equations, because dynamic boundary is moving and whole unstructured grids are updated in every step of field iterative. A sparse matrix mapping grid topology based on spring strategy is presented. LU-SGS strategy is used in numerical simulation and dynamic grid is managed in order to solve the time choke point. Numerical results show that LU-SGS iterative method can be used to dynamic discontinuities fitting by implicit scheme. The presented method decreases more than 20% iterative time than classical SOR method.

The flow of a falling liquid film on an oscillating inclined plane is simulated numerically with Galerkin finite element method. The effects of oscillating frequency and initial perturbation frequency are investigated. A low-frequency modulation signal is observed in the flow field. Nonlinear effect of the low-frequency signal in the flow field promotes the coalescence of waves on a free surface, and accelerates the development of the waves. For higher oscillating frequencies, this effect is more apparent. A solitary hump is observed in the flow.

A Lagrangian finite element method is ued to simulate a uniformly heated film flowing down an inclined plate. An example with periodic inlet disturbances of different frequencies is computed,and the agreement with the linear stability theory shows that the Lagrangian finite element method has good resolution.The film flow is fully developed to saturated periodic wave,quasiperiodic wave,multipeaked wave and solitary hump.

Based on the interaction of all particles in solution,a mixture of ions and point dipoles as an electrolyte solution is proposed.The partition functions,Virial coefficient and internal energy are calculated by using cluster expansion method. It is found that the partition function can be expanded in cluster integrals whi ch are easily calculated without three body interaction.Related numerical resul ts have been given and discussed.

Effect of a magnetic field on potential energy of liquid water are investigated for first time using classical Monte-Carlo computer simulation and a water model L-J. The relationships between energy and magnetic flux density and temperature have been studied by calculating potential energy and radial distribution function (RDF) of a system containing 64 water molecules. Comparisons with the field-off system are made throughout. It is found that the computer simulation is in agreement with experimental results.

For electromagnetic scattering and inverse scattering problem in inhomogeneous media,calculating Hankel transform rapidly,accurately is often required in order to perform efficient forward calculation.Here,fast Fourier transform is used to finish the calculation of Hankel transform in case of a dipole exciting in arbitrary planar layer-media.