With study of finite volume(FV) methods and discontinuous Galerkin(DG) method,"static reconstruction" and "dynamic reconstruction" are proposed for high-order numerical schemes.Based on the concept of "hybrid reconstruction",a new class of hybrid DG/FV schemes is presented for two-dimensional(2D) unstructured grids to solve the 2D conservation law,including 2D scalar equations and Euler equations.In the hybrid DG/FV schemes,lower-order derivatives of the piecewise polynomial are computed locally in a cell by a traditional DG method(called "dynamic reconstruction"),and the higher-order derivatives are reconstructed by the "static reconstruction" of the FV method by using lower-order derivatives in the cell and immediate neighbour cells.Typical 2D cases are given,and accuracy study is carried out.Numerical results show that the hybrid DG/FV scheme reaches desired order of accuracy.In addition,the hybrid DG/FV scheme saves great CPU time and memory compared with same order DG schemes.

Flowfield around a blunt body at transonic speed is simulated numerically.It indicates that plentiful flowfield structures behind the blunt body determine base pressure distribution.Numerical simulation of free pitch oscillation shows that limited cycle oscillation is observed as a result of dynamic instability in transonic regime.During a free pitch oscillation,front part blunt body conducts work to the flow field which releases blunt body energy and inhibits swing.The rear part of the blunt body gains energy from the flow field which increases the blunt body energy and the motion is considered unstable.As energy of the front blunt body and the rear body is equal,the capsule falls into a limited cycle oscillation.

A three-dimensional molecular dynamics method with Finnis-Sinclair embedded atom potentials is used to study relaxtion of fcc Ag nanorods with crystallographic orientation[111] .Homeostasis of Ag nanorod relaxation is shown.Stable structures and potential energies and structure evolution of Ag nanorod are studied. A critical temperature of destabilization(T_c) is found.As temperature of the nanorod is less than T_c,the system keeps intact line form of crystal.As temperature is higher than T_c and less than melting point,the system collapses,fuses and then recrystallizes.As temperature is near melting point,a stable polyhedron bounded by(111) and(100) facets forms. As cross-section of Ag nanorod increases T_c and melting point decrease.As cross-section dimension is larger than 2 nm,T_c is close to the melting point.Destabilization exists in a narrow temperature range.

To design a high-order accurate shock capturing method for hyperbolic conservation laws,we introduce a new power limiter to obtain a second-order power NND scheme and a third order power WNND scheme based on modification of NND scheme and WNND scheme.By applying the limiter to first-order differences of the candidate stencils,the power NND scheme and the power WNND scheme reduce the smearing near discontinuities.The power NND scheme and the power WNND scheme show less dissipation and less spurious oscillations,and catch the discontinuities more accurately than NND scheme and WNND scheme.The results of power NND scheme are similar to those of WNND scheme,and even better in some examples.The simulation of forced oscillation of the NACA0012 airfoil by power WNND scheme is in good agreement with experiments.

Regarding to degeneration of dynamics characteristics in a traditional single chaotic system,we propose a switch controller chaos pseudo random bit generator(SCS-PRBG) based on multiple chaotic systems and switch control.Theoretic analysis of random key stream and its performance show that the key stream has better randomicity and security.With parallel computation,the speed of encryption is improved. The expriment indicates better security of this algorithm.

The momentary state of a semiconductor device is described with three nonlinear partial differential equations. A finite difference scheme for transient behaviors of two-dimensional semiconductor devices on grids with local refinement in time and space is constructed and studied.The electrostatic potential equation is approximated by a five-point difference scheme.The electron and the hole density equations are discretized by a modified upwind scheme.The construction uses a linear interpolation at slave nodes.An error analysis is presented and illustrated with a numerical example.