A ghost fluid Lattice Boltzmann method for complex geometries

Abstract

SUMMARY A ghost fluid Lattice Boltzmann method (GF‐LBM) is developed in this study to represent complex boundaries in Lattice Boltzmann simulations of fluid flows. Velocity and density values at the ghost points are extrapolated from the fluid interior and domain boundary via obtaining image points along the boundary normal inside the fluid domain. A general bilinear interpolation algorithm is used to obtain values at image points which are then extrapolated to ghost nodes thus satisfying hydrodynamic boundary conditions. The method ensures no‐penetration and no‐slip conditions at the boundaries. Equilibrium distribution functions at the ghost points are computed using the extrapolated values of the hydrodynamic variables, while non‐equilibrium distribution functions are extrapolated from the interior nodes. The method developed is general, and is capable of prescribing Dirichlet as well as Neumann boundary conditions for pressure and velocity. Consistency and second‐order accuracy of the method are established by running three test problems including cylindrical Couette flow, flow between eccentric rotating cylinders and flow over a cylinder in a confined channel. Copyright © 2011 John Wiley & Sons, Ltd.

An extrapolation-based boundary treatment for using the lattice Boltzmann method to simulate fluid-particle interaction near a wall

“…When a solid object is close to a wall or two solid objects are near contact, the dynamic coupling between fluid and particles become important, but was not addressed by the previous methods Tiwari & Vanka, 2012). The motion of a sphere in a viscous fluid is governed-by…”

“…As shown in Figure 6, the slopes of the curves for the different values of Re are all close to 2, indicating that the boundary treatment is of second-order accuracy. The two previous extrapolation methods Tiwari & Vanka, 2012) were also applied to the same problem, and the numerical results showed that they are of second-order accuracy too. For the value of E, we remark that the present boundary treatment method gives numerical errors similar to the method of .…”

“…As an example, using Re = 30 and x/R 1 = 0.625, the values of E obtained by the method of and the present method are 7 × 10 −3 and 5 × 10 −3 , respectively. Since the numerical error given in the study of Tiwari and Vanka (2012) is the difference of the two numerical solutions using different grid sizes, no comparison with it is made here.…”

“…As mentioned in the introduction, the existing extrapolation methods can be further classified into two groups: link-based methods and normaldirection-based methods (Tiwari & Vanka, 2012). The advantage of the normal-direction-based method over the link-based method is its generality, but its extrapolation process is complicated.…”

“…Equilibrium parts are computed using the velocity and density extrapolated from the fluid domain, and non-equilibrium parts are directly extrapolated from the fluid domain. An extrapolation can be link-based (Guo, Zheng, & Shi, 2002) or normal-directionbased (Tiwari & Vanka, 2012). Extrapolation methods are also of second-order accuracy.…”