Finite-volume lattice Boltzmann method

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Abstract
We present a finite-volume formulation for the lattice Boltzmann method (FVLBM) based on standard bilinear quadrilateral elements in two dimensions. The accuracy of this scheme is demonstrated by comparing the velocity field with the analytical solution of the Navier-Stokes equations for time dependent rotating Couette flow and Taylor vortex flow. To demonstrate the flexibility of the scheme, we have also simulated a modified rotating Couette flow, where the inner cylinder has an elliptical shape. The results agree with those 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 significantly extended.