Finite-volume lattice Boltzmann method

We present a finite-volume formulation for the lattice Boltzmann method (FV LBM) based on standard bilinear quadrilateral elements in two dimensions. T he accuracy of this scheme is demonstrated by comparing the velocity field with the analytical solution of the Navier-Stokes equations for time depend ent rotating Couette flow and Taylor vortex how. To demonstrate the flexibi lity of the scheme, we have also simulated a modified rotating Couette how, where the inner cylinder has an elliptical shape. The results agree with t hose obtained from the traditional marker-and-cell method. The FVLBM scheme is applicable to arbitrarily shaped two-dimensional regions, and thus the range of applicability of the lattice Boltzmann method has been significant ly extended, [S1063-651X(99)14605-1].