Force evaluation in the lattice Boltzmann method involving curved geometry

The present work investigates two approaches for force evaluation in the lattice Boltzmann equation: the momentum-exchange method and the stress-integration method on the surface of a body. The boundary condition for the particle distribution functions on curved geometries is handled with second-order accuracy based on our recent works [Mei , J. Comput. Phys. 155, 307 (1999); ibid. 161, 680 (2000)]. The stress-integration method is computationally laborious for two-dimensional flows and in general difficult to implement for three-dimensional flows, while the momentum-exchange method is reliable, accurate, and easy to implement for both two-dimensional and three-dimensional flows. Several test cases are selected to evaluate the present methods, including: (i) two-dimensional pressure-driven channel flow; (ii) two-dimensional uniform flow past a column of cylinders; (iii) two-dimensional flow past a cylinder asymmetrically placed in a channel (with vortex shedding); (iv) three-dimensional pressure-driven flow in a circular pipe; and (v) three-dimensional flow past a sphere. The drag evaluated by using the momentum-exchange method agrees well with the exact or other published results.