Computations of Single and Multiphase Flows Using a Lattice Boltzmann Solver

Abstract

There is considerable interest in high fidelity simulation of both single phase incompressible flows and multiphase flows. Most commonly applied numerical methods include finite difference, finite volume, finite element and spectral methods. All of these methods attempt to capture the flow details by solving the Navier–Stokes equations. Challenges of solving the Navier–Stokes single phase incompressible flows include the non-locality of the pressure gradient, non-linearity of the advection term and handling the pressure-velocity coupling. Multiphase flow computations pose additional challenges, such as property and flow variable discontinuities at the interface, whose location and orientation is not known a priori. Further, capturing/tracking of the multiphase interface requires solution of an additional advection equation. Recently, the lattice Boltzmann method has been applied to compute fluid dynamics simulations both for single and multiphase configurations; it is considered a modern CFD approach with improved accuracy and performance. Specifically, we employ a multiple-relaxation time (MRT) technique for the collision term on a D3Q27 lattice. The multiphase interface is captured using the phase-field approach of Allen-Cahn. Test cases include lid driven cavity, vortex shedding for a double backward facing step, Rayleigh Taylor instability, Enright’s deformation test and rising bubble in an infinite domain. These test cases validate different aspects of the single and multiphase model, so that the results can be interpreted with confidence that the underlying computational framework is sufficiently accurate.