Zhaoxia Yang

Outflow boundary conditions for the lattice Boltzmann method

In this paper, we propose lattice Boltzmann implementations of several Navier-Stokes outflow boundary conditions like the zero normal-stress, the Neumann, and the do-nothing rule. A consistency analysis using asymptotic methods is given and the algorithms are numerically tested in two space dimensions with respect to accuracy and interaction with the inner flow field.

Convergence of lattice Boltzmann methods for Navier–Stokes flows in periodic and bounded domains

Combining an asymptotic analysis of the lattice Boltzmann method with a stability estimate, we are able to prove some convergence results which establish a strict relation to the incompressible Navier–Stokes equation. The proof applies to the lattice Boltzmann method in the case of periodic domains and for specific bounded domains if the Dirichlet boundary condition is realized with the bounce back rule.

Asymptotic analysis of finite difference methods

With this article, we want to advocate the use of asymptotic methods for the analysis of finite difference schemes. We present several examples to demonstrate the applicability of the approach. Advantages over the modified equation and truncation error analysis are pointed out.

Convergence of lattice Boltzmann methods for Stokes flows in periodic and bounded domains

Combining an asymptotic analysis of the lattice Boltzmann method [M. Junk, Z. Yang, Asymptotic analysis of lattice Boltzmann boundary conditions, J. Stat. Phys. 121 (2005) 3-35] with the stability estimate presented in [M. Junk, W.-A. Yong, Weighted L^2 stability of the lattice Boltzmann equation, Preprint], we are able to prove some strict convergence results. The proof applies to the lattice Boltzmann method with linear collision operator both in the case of periodic domains and bounded domains if the Dirichlet boundary condition is realized with the bounce back rule.

Pressure boundary condition for the lattice Boltzmann method

We propose a lattice Boltzmann realization for the hydrodynamic pressure drop condition introduced in [J. Heywood, R. Rannacher, S. Turek, Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations, Int. J. Numer. Methods Fluids 22 (1996) 325-352]. This condition has the advantage that only the average pressure needs to be prescribed at the boundary. In general, a second order accurate velocity and a first order accurate pressure are recovered with the proposed lattice Boltzmann implementation. The analytical investigation is supported by numerical simulations of a Poiseuille flow and a less symmetric flow with nontrivial pressure field.

A combined lattice BGK/level set method for immiscible two-phase flows

We present a lattice Boltzmann method (LBM) for simulating immiscible multi-phase flows which is based on a coupling of LBM with the level set method. The computation of immiscible flows using the LBM with BGK collision operator is done separately in each of the fluid domains and coupled at the interface by an appropriate boundary condition. In this way we preserve sharp interfaces between different fluid phases. We apply a new interface condition that represents the fluid mechanical jump conditions at the interface in the kinetic LBM framework. The level set method is applied to compute the evolution of the interface between fluids. Numerical results demonstrate the applicability of the method even in the presence of large viscosity and density ratios.