Kuramoto-like model is adopted to model a power grid reasonably. And critical synchronization coupling strength and average synchronization error are used to describe synchronization ability and robustness of a power grid, respectively. It is found that power distribution of generators has a great influence on transmission power of lines, and the more high-load lines in power grid, the more difficult the network synchronization. Based on the discovery, we calculate transmission power of each line under uniform power distribution method of generators (EG mode). Then, based on a power flow tracking algorithm, an non-uniform power distribution method (TG mode) of the generators is further proposed. With this method, as the total amount of power generated is given, power of the hub generator node is increased and power of the edge generator node is reduced. It shows that the new power distribution strategy reduces effectively critical synchronization coupling strength and average synchronization error. Thus the method improves synchronization performance and robustness of a power grid.

With gas-kinetic unified algorithm (GKUA) based on Boltzmann equation for various flows regimes, rotational non-equilibrium effect is investigated in Rykov model, in which spin movement of gas molecules is described with moment of inertia. Numerical method of Boltzmann model equation involving rotational non-equilibrium effect is developed. Nitrogen shock wave structure, flows around a 2D blunt-head body and flows around a 3D tine bicone are simulated to validate the method in various flows regimes.

To investigate effect of rotational degree of freedom on gas flows covering various flow regimes,Boltzmann-Rykov model is studied and reduced velocity distribution functions are introduced with quadrature to rotational degree of freedom of molecular velocity distribution function.A single gas-kinetic model equation is translated into simultaneous equations of three reduced velocity distribution functions at discrete velocity ordinate points with discrete velocity ordinate method and numerical integration technique.One-and two-dimensional Boltzmann-Rykov model equations for diatomic gases are computed with finite-difference method of computational fluid dynamics.One-dimensional shock-tube and the two-dimensional flow past erect plate are analyzed in the whole range of Knudsen numbers.Reliability of gas-kinetic unified algorithm(GKUA) is validated in solving one-and two-dimensional flows from free molecular flow to continuum regimes.It is indicated that the gas rarefaction degree and molecular inner degree of freedom affect flow field greatly.And rarefied gas flows with high Knudsen numbers take serious non-equilibrium effect.

In a numerical study of Bohzmann model equation, a gas-kinetic finite difference scheme with coupling and iteration is constructed to solve molecular velocity distribution function directly. The parallel strategy is established by using parallel technique of domain decomposition based on variable dependency relation, data communication and parallel expansibility. Gas-kinetic HPF(High Performance Fortran) parallel algorithm is developed to solve three-dimensional problems in various flow regimes. Hypersonic gas flows around a sphere and a spacecraft at various Knudsen numbers, Mach numbers and flying angles are computed at a high performance computer with massive scale HPF parallel. The computational results are in good agreement with experimental and theoretical ones. It is shown that the parallel speed-up increases approximately linearly with the numbers of processors. It indicates high parallel efficiency and expansibility with good load balance and data communication. It suggests that a gas-kinetic parallel algorithm on large scale can be used for three-dimensional complex hypersonic flow problems in various flow regimes.