Numerical hydrodynamics from gas-kinetic theory
Journal of Computational Physics
Rarefied flow computations using nonlinear model Boltzmann equations
Journal of Computational Physics
A robust and accurate LED-BGK solver on unstructured adaptive meshes
Journal of Computational Physics
Gas-kinetic description of shock wave structures by solving Boltzmann model equation
International Journal of Computational Fluid Dynamics
Gas-kinetic numerical studies of three-dimensional complex flows on spacecraft re-entry
Journal of Computational Physics
Gas-kinetic numerical study of complex flow problems covering various flow regimes
Computers & Mathematics with Applications
WENO-enhanced gas-kinetic scheme for direct simulations of compressible transition and turbulence
Journal of Computational Physics
Scaling the RMG quantum mechanics code
Proceedings of the Extreme Scaling Workshop
Implicit multiblock method for solving a kinetic equation on unstructured meshes
Computational Mathematics and Mathematical Physics
Solving the discrete S-model kinetic equations with arbitrary order polynomial approximations
Journal of Computational Physics
Journal of Scientific Computing
Hydrodynamic shock wave studies within a kinetic Monte Carlo approach
Journal of Computational Physics
Hi-index | 31.47 |
The modified BGK equation adapted to various flow regimes can be presented by the aid of the basic characteristics on molecular movement and collision approaching to equilibrium. The discrete velocity ordinate method is developed and applied to the velocity distribution function to remove its continuous dependency on the velocity space, and then the velocity distribution function equation is cast into hyperbolic conservation law form with nonlinear source terms. Based on the unsteady time-splitting method and the non-oscillatory, containing no free parameters, and dissipative (NND) scheme, the gas kinetic finite difference second-order scheme is constructed for the computation of the discrete velocity distribution functions. The mathematical model on the interaction of molecules with solid surface is studied and used in the numerical method. Four types of numerical quadrature rules, such as the modified Gauss-Hermite formula, the composite Newton-Cotes integration method, the Gauss-Legendre numerical quadrature rule, and the Golden Section number-theoretic integral method, are developed and applied to the discretized velocity space to evaluate the macroscopic flow parameters at each point in the physical space. As a result, a unified simplified gas kinetic algorithm is established for the flows from rarefied transition to continuum regime. Based on analyzing the inner parallel degree of the unified algorithm, the parallel strategy adapted to the gas kinetic numerical algorithm is studied, and then the HPF parallel processing software for the unified algorithm is developed. To test the present method, the one-dimensional shock-tube problems, the flows past two-dimensional circular cylinder, and the flows around three-dimensional sphere and spacecraft shape with various Knudsen numbers are simulated. The computational results are found in high resolution of the flow fields and good agreement with the theoretical, DSMC, N-S, and experimental results.