Alternative curved-boundary treatment for the lattice Boltzmann method and its application in simulation of flow and potential fields

Abstract

Since the lattice Boltzmann method originally carries out the simulations on the regular Cartesian lattices, curved boundaries are often approximated as a series of stair steps. The most commonly employed technique for resolving curved-boundary problems is extrapolating or interpolating macroscopic properties of boundary nodes. Previous investigations have indicated that using more than one equation for extrapolation or interpolation in boundary conditions potentially causes abrupt changes in particle distributions. Therefore, a curved-boundary treatment is introduced to improve computational accuracy of the conventional stair-shaped approximation used in lattice Boltzmann simulations by using a unified equation for extrapolation of macroscopic variables. This boundary condition is not limited to fluid flow and can be extended to potential fields. The proposed treatment is tested against several well-established problems and the solutions order of accuracy is evaluated. Numerical results show that the present treatment is of second-order accuracy and has reliable stability characteristics.

Lattice Boltzmann formulation for conjugate heat transfer in heterogeneous media

“…This in turn requires higher spatial resolution for capturing sharp curves. A hybrid implementation of the present formulation of LBM for the conservative energy equation with recently developed techniques on local grid refinements [33][34][35] and curve boundary treatment [15,36] seems to be very promising for heat transfer problems in complex geometries.…”

Choice of no-slip curved boundary condition for lattice Boltzmann simulations of high-Reynolds-number flows

“…Yin and Zhang [26] modified the Ladd scheme with the boundary velocity at the mid-grid computed using interpolation or extrapolation between the boundary node and fluid node. In addition to the above-mentioned boundary methods, several other approaches have been developed for simulating curved boundaries in the LBM [27][28][29][30]. The different boundary conditions of LBM are compared on different lattice configurations by Nash et al [31].…”

Numerical simulation of a flat electroosmotic driven flow in the presence of a charged mid-plate

“…In comparison with conventional numerical approaches, the LBM changes the target equations from secondorder partial di®erential equations to semi-linear¯rst-order ones, which provide many distinct advantages such as simple formulation, favorable parallel computing structure and reducing the computational cost. In this section, the LB evolution equations corresponding to all governing equations (11)- (17) are introduced. Details about the implementation and validation of the numerical model have well been described in Ref.…”

“…Here we follow the second-order accurate corrective part approach, described by Mohammadipour et al, 17 which is consistent with arbitrary 2D geometries. In this approach, the unknown populations are assumed to be composed from equilibrium, nonequilibrium and corrective parts, which are determined by the given boundary velocities.…”