Volumetric method for calculating the flow around moving objects in lattice-Boltzmann schemes

A method for calculating the fluid flow around moving objects is presented, based on a volumetric representation of the lattice-Boltzmann scheme and surfaces defined by facets. It enables us to move objects of arbitrary shape and orientation independent of the position of the grid nodes. To represent the motion of the object, additional momentum is added to the reflected particles from each facet in the propagation step. These particles are redistributed on nodes in the vicinity of the surface, depending on the position and orientation of the facet. Because the surface is considered to be closed, additional techniques need to be used to guarantee the conservation of mass. The flow field of a moving periodic cubic array of cubes at two Re numbers (Re=0.5 and Re=50) is compared with that of a fixed array. For Re=0.5, no significant deviations are found for the velocity field, pressure field, and the drag force. For Re=50, the drag and pressure field exhibit small fluctuations that relate to the position of the surface relative to the position of the grid. However, the influence of the pressure fluctuations on the velocity field is very small. Results on the velocity for a moving array of cubes show second-order accuracy in the lattice spacing. For physical consistency, the drag force on a periodic cubic array of moving spheres at Re=0.5 is compared with Hasimoto's analytical solution. The dependence on the grid spacing, the resolution of the surface of the object, and the viscosity have been studied. The discrepancies between simulations and the analytical results are smaller than 1.5%. For Re=50, the drag force, the streamline pattern, and the pressure field around a moving sphere in a large periodic domain showed good agreement with data from literature on a single sphere in an infinitely large flow field.