An improved lattice Boltzmann model for simulations of single- and multiphase flows in porous media

During the last few years, the lattice Boltzmann method (LBM) has become a well established tool for simulating fluid flows [1,2], especially multi-phase flows in complex geometries. However, to the best of the authors' knowledge, available multiphase models are only first order accurate in space due to shortcomings with respect to the accuracy of the multi-phase coupling terms in the vicinity of walls. We propose extensions for a multi-phase model discussed in [3] to obtain the usual second order bulk accuracy also at solid walls. Extensions have also been added to simulate multi phase flows with high density ratios. Different approaches for the treatment of triple points (fluid-fluid-wall) are investigated by studying contact angle dynamics in 3D. Typical multi-phase problems such as flows in porous media are based on binarized porous media data (i.e. voxels) which usually imply that first-order accurate bounce-back schemes are applied and the voxel resolution thus automatically determines the numerical resolution which may result in a waste of CPU time. Instead, highly resolved tomographic data sets can be parameterized by utilizing a marching-cube algorithm. The resulting surfaces consisting of planar triangles allow the use of second order accurate no-slip conditions and decouple the numerical grid from the original voxel set. We demonstrate, that for saturated flow simulations this approach allows a considerable acceleration for comparable accuracies as well as convergence studies for porous media simulations. __________________________________ References [1] S. Succi. The Lattice Boltzmann Equation. For Fluid Dynamics and Beyond. Oxford University Press, 2001. [2] Y. H. Qian, D. d'Humieres, and P. Lallemand. Lattice BGK models for Navier- Stokes equation. Europhys. Lett., 17(6):479-484, Jan. 1992. [3] J. Tölke, S. Freudiger, M. Krafczyk: An adaptive scheme for LBE Multiphase Flow simulations on hierarchical grids, Computers and Fluids, in press.