arXiv subjects

Xiaowen Shan

Publications and source records attributed to Xiaowen Shan.

25 records · Page 2Linked to original sources

arXiv2007

Shape changes and motion of a vesicle in a fluid using a lattice Boltzmann model

We study the deformation and motion of an erythrocyte in fluid flows via a lattice Boltzmann method. To this purpose, the bending rigidity and the elastic modulus of isotropic dilation are introduced and incorporated with the lattice Boltzmann simulation, and the membrane-flow interactions on both sides of the membrane are carefully examined. We find that the static biconcave shape of an erythrocyte is quite stable and can effectively resist the pathological changes on their membrane. Further, our simulation results show that in shear flow, the erythrocyte will be highly flattened and undergo tank tread-like motion. This phenomenon has been observed by experiment very long time ago, but it has feazed the boundary integral and singularity methods up to the present. Because of its intrinsically parallel dynamics, this lattice Boltzmann method is expected to find wide applications for both single and multi-vesicles suspension as well as complex open membranes in various fluid flows for a wide range of Reynolds numbers.

physics.flu-dyn↗

arXiv2006

Efficient kinetic method for fluid simulation beyond the Navier-Stokes equation

We present a further theoretical extension to the kinetic theory based formulation of the lattice Boltzmann method of Shan et al (2006). In addition to the higher order projection of the equilibrium distribution function and a sufficiently accurate Gauss-Hermite quadrature in the original formulation, a new regularization procedure is introduced in this paper. This procedure ensures a consistent order of accuracy control over the non-equilibrium contributions in the Galerkin sense. Using this formulation, we construct a specific lattice Boltzmann model that accurately incorporates up to the third order hydrodynamic moments. Numerical evidences demonstrate that the extended model overcomes some major defects existed in the conventionally known lattice Boltzmann models, so that fluid flows at finite Knudsen number (Kn) can be more quantitatively simulated. Results from force-driven Poiseuille flow simulations predict the Knudsen's minimum and the asymptotic behavior of flow flux at large Kn.

physics.comp-ph↗

arXiv1997

Discretization of the velocity space in solution of the Boltzmann equation

We point out an equivalence between the discrete velocity method of solving the Boltzmann equation, of which the lattice Boltzmann equation method is a special example, and the approximations to the Boltzmann equation by a Hermite polynomial expansion. Discretizing the Boltzmann equation with a BGK collision term at the velocities that correspond to the nodes of a Hermite quadrature is shown to be equivalent to truncating the Hermite expansion of the distribution function to the corresponding order. The truncated part of the distribution has no contribution to the moments of low orders and is negligible at small Mach numbers. Higher order approximations to the Boltzmann equation can be achieved by using more velocities in the quadrature.

comp-gas↗

arXiv1996

Simulation of Rayleigh-Bénard convection using lattice Boltzmann method

Rayleigh-Bénard convection is numerically simulated in two- and three-dimensions using a recently developed two-component lattice Boltzmann equation (LBE) method. The density field of the second component, which evolves according to the advection-diffusion equation of a passive-scalar, is used to simulate the temperature field. A body force proportional to the temperature is applied, and the system satisfies the Boussinesq equation except for a slight compressibility. A no-slip, isothermal boundary condition is imposed in the vertical direction, and periodic boundary conditions are used in horizontal directions. The critical Rayleigh number for the onset of the Rayleigh-Bénard convection agrees with the theoretical prediction. As the Rayleigh number is increased higher, the steady two-dimensional convection rolls become unstable. The wavy instability and aperiodic motion observed, as well as the Nusselt number as a function of the Rayleigh number, are in good agreement with experimental observations and theoretical predictions. The LBE model is found to be efficient, accurate, and numerically stable for the simulation of fluid flows with heat and mass transfer.

comp-gas↗

arXiv1996

Diffusion in a multi-component Lattice Boltzmann Equation model

Diffusion phenomena in a multiple component lattice Boltzmann Equation (LBE) model are discussed in detail. The mass fluxes associated with different mechanical driving forces are obtained using a Chapman-Enskog analysis. This model is found to have correct diffusion behavior and the multiple diffusion coefficients are obtained analytically. The analytical results are further confirmed by numerical simulations in a few solvable limiting cases. The LBE model is established as a useful computational tool for the simulation of mass transfer in fluid systems with external forces.

comp-gas↗

arXiv1995

Multi-component lattice-Boltzmann model with interparticle interaction

A previously proposed [X. Shan and H. Chen, Phys. Rev. E {\bf 47}, 1815, (1993)] lattice Boltzmann model for simulating fluids with multiple components and interparticle forces is described in detail. Macroscopic equations governing the motion of each component are derived by using Chapman-Enskog method. The mutual diffusivity in a binary mixture is calculated analytically and confirmed by numerical simulation. The diffusivity is generally a function of the concentrations of the two components but independent of the fluid velocity so that the diffusion is Galilean invariant. The analytically calculated shear kinematic viscosity of this model is also confirmed numerically.

comp-gas↗

arXiv1994

Simulation of non-ideal gases and liquid-gas phase transitions by lattice Boltzmann equation

We describe in detail a recently proposed lattice-Boltzmann model for simulating flows with multiple phases and components. In particular, the focus is on the modeling of one-component fluid systems which obey non-ideal gas equations of state and can undergo a liquid-gas type phase transition. The model is shown to be momentum-conserving. From the microscopic mechanical stability condition, the densities in bulk liquid and gas phases are obtained as functions of a temperature-like parameter. Comparisons with the thermodynamic theory of phase transition show that the LBE model can be made to correspond exactly to an isothermal process. The density profile in the liquid-gas interface is also obtained as function of the temperature-like parameter and is shown to be isotropic. The surface tension, which can be changed independently, is calculated. The analytical conclusions are verified by numerical simulations. (To appear in Phys. Rev. E)

comp-gas↗