Moment-based boundary conditions for straight on-grid boundaries in three dimensional lattice Boltzmann simulations

In this article, moment‐based boundary conditions for the lattice Boltzmann method are extended to three dimensions. Boundary conditions for velocity and pressure are explicitly derived for straight on‐grid boundaries for the D3Q19 lattice. The method is compared against the bounce‐back scheme using both single and two relaxation time collision schemes. The method is verified using classical benchmark test cases. The results show very good agreement with the data found in the literature. It is confirmed from the results that the derived moment‐based boundary scheme is of second‐order accuracy in grid spacing and does not produce numerical slip, and therefore offers a transparent way of accurately prescribing velocity and pressure boundaries that are aligned with grid points in three‐dimensional

A parallel cellular automata Lattice Boltzmann Method for convection-driven solidification

This article presents a novel coupling of numerical techniques that enable three-dimensional convection-driven microstructure simulations to be con- ducted on practical time scales appropriate for small-size components or experiments. On the microstructure side, the cellular automata method is efficient for relatively large-scale simulations, while the lattice Boltzmann method provides one of the fastest transient computational fluid dynamics solvers. Both of these methods have been parallelized and coupled in a single code, allowing resolution of large-scale convection-driven solidification problems. The numerical model is validated against benchmark cases, extended to capture solute plumes in directional solidification and finally used to model alloy solidification of an entire differentially heated cavity capturing both microstructural and meso-/macroscale phenomena