Capture on a vibrating cylinder is simulated. Flow field is obtained with lattice Boltzmann method combined multi-block lattice Boltzmann method. Motion of single particle is calculated with Langevin equation by Lagrange integration. Drag force and Brownian diffusion is considered only. Cylinder does harmonic motion in flow direction with various frequency and amplitude at Re=200. As a result, different flow pattern present. We found capture efficiency raises. Especially at AⅢ vortex pattern, distribution of initial position deviates from center.

The false scattering and ray effect in spherical harmonics method, including P₁ and P₃ approximation, is studied. Physical models of parallel and oblique laser incidence into two-dimensional gray media are constructed and the temperature profile within the medium is investigated to examine the false scattering. The ray effect is analyzed by the net radiative flux in the boundary. Simulation results show that both false scattering and ray effect exist in the spherical harmonics method, and the ray effect is mitigated higher in P₃ than that in P₁ approximation. In addition, the ray effect in the spherical harmonics approximation mitigates with increasing optical thickness within gray medium.

The various order explicit schemes based on exponential fitting and Newton interpolants are constructed for partial differential equations.The various precision can be achieved by employing the various order explicit schemes.When the schemes are applied to heat transport equations at the microscale and strong transient heat transport in thin film,the effects are admirable.Numerical calculations show the present method is high accurate and computationally efficient.

Common formulae for the free-order explicit multistep method of precise time integration are proposed. When the higher order explicit algorithms of precise time integration are applied for calculating the ray equation and the classical trajectories of diatomic system, the effect is admirable. The numerical results reveal that the pressent method is higher accurated and efficient, capable of keeping computational stability for long time simulation, and suitable for higher order numerical computation.