We discuss further developments of the finite-volume lattice Boltzmann formulation on unstructured grids. It is shown that the method tolerates significant grid distortions without showing any appreciable numerical viscosity effects at second order in the mesh size. A theoretical argument of plausibility for such a property is presented. In addition, a set of boundary conditions which permit to handle flows with open boundaries is also introduced and numerically demonstrated for the case of channel flows and driven cavity flows.
The onset of cavitating conditions inside the nozzle of liquid injectors is known to play a major role on spray characteristics, especially on jet penetration and break-up. In this work, we present a Direct Numerical Simulation (DNS) based on the Lattice Boltzmann Method (LBM) to study the fluid dynamic field inside the nozzle of a cavitating injector. The formation of the cavitating region is determined via a multi-phase approach based on the Shan-Chen equation of state. The results obtained by the LBM simulation show satisfactory agreement with both numerical and experimental data. In addition, numerical evidence of bubble break-up, following upon flow-induced cavitation, is also reported.
SUMMARYOver the last decade, the lattice Boltzmann method (LBM) has evolved into a valuable alternative to continuum computational uid dynamics (CFD) methods for the numerical simulation of several complex uid-dynamic problems. Recent advances in lattice Boltzmann research have considerably extended the capability of LBM to handle complex geometries. Among these, a particularly remarkable option is represented by cell-vertex ÿnite-volume formulations which permit LBM to operate on fully unstructured grids. The two-dimensional implementation of unstructured LBM, based on the use of triangular elements, has shown capability of tolerating signiÿcant grid distortions without su ering any appreciable numerical viscosity e ects, to second-order in the mesh size. In this work, we present the ÿrst three-dimensional generalization of the unstructured lattice Boltzmann technique (ULBE as unstructured lattice Boltzmann equation), in which geometrical exibility is achieved by coarse-graining the lattice Boltzmann equation in di erential form, using tetrahedrical grids. This 3D extension is demonstrated for the case of 3D pipe ow and moderate Reynolds numbers ow past a sphere. The results provide evidence that the ULBE has signiÿcant potential for the accurate calculation of ows in complex 3D geometries.
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