To investigate influence mechanism of the second viscosity on internal flow of a normal shock wave, one-dimensional Navier-Stokes equations are numerically solved. It indicates that the second viscosity has a smoothing effect on density, heat flow and energy distribution in the shock wave, which results in a decrease of peak value of heat and entropy flows, and an increase of shock thickness. Due to the production of normal viscous dissipation, some lost mechanical energy is converted into internal energy. As considering the second viscosity, density distribution and shock thickness are greatly improved. They are in good agreement with experimental data. In addition, Knudsen number is obtained 0.12≤Kn≤0.4 within Mach number range from 1.2 to 10. It indicates that Navier-Stokes equations with the second viscosity simulate normal shock structure more accurately.

In EAST tokamak high confinement mode discharge, a plasma current belt was found experimentally at the edge plasmas region. For EAST plasma with non-circular cross-section equilibrium configuration, effect of high parallel refractive index N_‖ component of lower hybrid wave on current drive was numerically studied. Results of the ray-tracing platform shows that kA plasma current emerges in a region of normalized radius from 0.7 to 1.0 for 6≤N_‖≤8. For electron temperature profile with pedestal and higher plasma edge temperature, the region of drive current is r/a>0.9.A theoretical analysis of lower hybrid Landau damping in EAST tokamak was also performed. Effects of electron density profile and formation of lower hybrid wave spectrum on current drive were discussed.

Fourier property of nonlinear weights and limiters in wave-space are analyzed. Firstly, a statistical method is designed to analyze Fourier property of nonlinear weights. Secondly, averaged values and deviations of nonlinear weights are shown, and values with change of wave-number are analyzed. It is helpful to comprehension of nonlinear schemes. The method is a guidance for designing shock-capture schemes.

We present a modified surface hopping method for Schrödinger equation with conical crossings. At the crossing manifold, Landau-Zener formula gives probability that electrons hop to another energy level. Kammerer and Mehats raised a scheme with jump operators ensuring good energy conservation for transport of electrons in a graphene layer which is similar to the physics above. We employ these jump operators to improve a surface hopping method and obtain accurate numerical results.

To improve finite difference scheme, Fourier analysis is used to optimize dispersion and dissipation of WENO scheme. And optimal linear weights are given. A class of hybrid schemes is designed by combing optimized WENO schemes with monotonicity-preserving scheme. A weighted hybrid WENO scheme(H-WENO) is obtained. The scheme is tested with one-dimensional shock tube problem, Shu-Osher problem, two-dimensional Mach reflection problem and R-T instability problem. It shows that the scheme has strong ability to capture shock wave and high resolution for small scale wave structure, which is improved obviously compared with original WENO scheme.

With kinetic and continuum theories of bulk viscosity coefficient, bulk-viscosity effect on two-dimensional toroidal shock-wave focus (Mach number Ma=2.0) is studied numerically. It shows that bulk-viscosity effect on toroidal shock-wave focusing is not negligible for perfect gases. Due to bulk viscous effect in compressible flows, pressure, temperature and density at the central focus perform 20% reduction, 10% increase and 30% reduction, respectively. Compared with rotational mode, shock wave focusing present obvious bulk-viscosity effect in vibrational mode, since bulk viscous stress has same order of magnitude with thermodynamic pressure.

We study numerical integration over arbitrary interface and arbitrary domain on block-structured adaptive mesh.Arbitrary interface and arbitrary domain are described by a level set function.We first describe numerical methods on uniform Cartesian grid.Then we extend the methods to block-structured adaptive mesh.Numerical calculations demonstrate that adaptive mesh methods are second-order accurate.Compared with uniform mesh methods, the adaptive mesh methods reduce needs on computer storage significantly.

With given total toroidal current and central current density of plasma, temperature, density and magnetic field profiles of tokamak plasma with different elongation and triangularity are obtained numerically with Grad-Shafranov equation. Electron cyclotron wave ray trajectories and current drive in configurations are investigated with Fokker-Planck equation incorporated into a ray tracing code. It shows that as electron cyclotron wave of X-mode are launched from top, rays propagate toward low-field side with increasing elongation. As electron cyclotron wave are launched from mid-plane and low-field-side, high quotient power deposition is obtained with greater elongation, and driven current profile is close to central plasma with increase of triangularity. Current drive profile moves toward central plasma and peak current density increases with decreasing poloidal or toroidal injection angle.

According to advection upstream splitting method,a flux splitting method called K-CUSP is proposed.The greatest difference between K-CUSP and two traditional CUSP schemes,namely H-CUSP and E-CUSP,is splitting of total energy:All kinematic quantities and thermodynamic quantities should be separately split into convective term and pressure term by K-CUSP scheme.Numerical tests indicate that:① K-CUSP scheme inherits the simplicity and robustness of FVS scheme.It is less prone to pressure overshoot after shock and no oscillations in expansion area,which is better than AUSM and WPS schemes.② K-CUSP scheme also inherits resolution of FDS scheme.Shock resolution is almost the same with H-CUSP and E-CUSP schemes.Contact discontinuity resolution is better than FVS schemes,a little worse than Roe,AUSM and WPS schemes.However,velocity of contact discontinuity in AUSM and WPS schemes exist large oscillation,while our scheme does not.

We introduce an ignition hohlraum 2D-simulation design method with 2D code.A design sequence,in which X-rays drive tempetature is tuned before P² asymmetry,is put forward.Details in designing laser power is studied.It indicates that control of P² asymmetry during trough pulse limits the maximum of filling gas density and expansion of capsule ablator can be restrained by longer drive pulse.An ignition hohlraum 2D-simulation design is given.

Shear flows in resonant surfaces of Tokamka devices induced by nonhnear evolution of double tearing modes(DTM) are studied numerically in the framework of resistive magnetohydronamic model with slab geometry.It is found that in early phases of nonlinear evolution of DTM,no remarkable shear flows is generated in resonant surfaces.Effective shear flows emerge during the phase of fast magnetic reconnection and disappear finally.Both amplitude and distribution of shear flows are found vary with nonlinear evolution of magnetic islands.Moreover,by taking into account plasma resistivity,it is shown that greater plasmas resistivity results in faster magnetic reeonection, but it hardly affects shear flows of resonant surfaces in Tokamka devices.

Based on a high-order compact upwind scheme,a high-order shock-fitting finite difference scheme is studied for numerical simulation of the generation of boundary layer disturbance waves due to free-stream waves.Both steady and unsteady flow solutions of the receptivity problem are obtained by computing full Navier-Stokes equations.Numerical simulation of receptivity to free-stream disturbances for hypersonic boundary layers is performed.

Based on the close relationship between Hamilton-Jacobi (H-J) equations and hyperbolic conservation laws,a high-order numerical method is developed to solve the H-J equations in the 3rd order and 5th order compact schemes.The upwind compact schemes are tested on a variety of one-dimensional and two-dimensional problems,including a problem related to the Richtmyer-Meshkov instability accelerated by planar shocks.Numerical results show that these schemes yield uniform high-order accuracy in smooth regions and satisfactorily resolve discontinuities in the derivatives.Moreover,since the present methods have less numerical dissipation than WENO scheme with the same order,they could be used to solve the H-J equations more accurately in the simulation of multi-scale complex flows.

It introduces the principle of local tomography algorithm with a new filter.The second order error estimation is obtained.The local reconstruction of simulation and experimental projection data show that the local tomography algorithm is simple and fast,by which the resolution and Gibbs effect of the reconstructed images can be improved.

Through examples, the mechanism of the generation of the aliasing error associated with upwind compact difference schemes and spectral method is studied and compared. The comparison shows the upwind compact difference schemes have some advantages in treating the aliasing error.

According to the seismic data processing, we give a algorithm for computing Radon transform and its inverse transform, then we state the principle of appling the transform for processing the seismic data and illustrate the result of post-stack section noise-surpressing by this method.

A Monte Carlo code applied to radiation protection and medical radiology is presented. It simulates the irradiation caused by photons and can give the effective dose equivalent (H_e)and absorbed dose equivalents of 20 organs (tissues) in a reference man. A special method which divides all photon histories into several kinds and traces each kind separately was adopted to improve the precision of the calculated results.The code can be also used to other calculations of doses in systems with complex geometry.

ORIGEN-2 is a versatile point depletion and decay computer code. Its functions, major charactaristics, and theoreticahmodels are briefly introduced in here. The transplantation of the code on IBM 4300 series computers and its augmentation of output photon data and application in calculating gamma-ray spectra of fission products are described.