Flux modelling in the finite-volume lattice Boltzmann approach

In this article, a novel approach for flux treatment is presented in conjunction with cell-centred Finite-Volume Lattice Boltzmann Method (FVLBM). The distribution functions are determined by using a pressure-based flux weighting factor on a D2Q9 lattice. A consistent open and solid boundary treatment is also addressed, which resulted in a wider domain of stability and faster convergence. For time discretisation, a fifth-order Runge-Kutta algorithm was applied. An in-house FORTRAN code has been written by the authors which uses the time-marching along with FVLBM. Two test cases, namely, flow over a backward-facing step and around a circular cylinder are carried out. The results are compared with the available solutions in which favourable agreement was observed.