Simulations of Fluid Flow in Porous Media in both 2 and 3 Dimensions with a New Lattice Boltzmann Simulator
R. Verberg and A. J. C. Ladd at the University of Florida have developed an improved algorithm for the lattice Boltzmann method for analyzing fluid flow through porous media. The algorithm is based on a new matrix method. Theoretical analyses of fluid flow in porous and fractured geological media underlie all predictive capabilities for contaminant transport, and for understanding production or leakage rates from subsurface reservoirs. The new method provides improvements of approximately 1 to 2 orders of magnitude in the speed of solution relative to the time-dependent lattice Boltzmann method for stationary, low-Reynolds number flows. Results of multiple iterations show that the time to convergence for the new method scales approximately linearly with system size, in comparison to a quadratic dependence using the time-dependent lattice Boltzmann approach. Error analysis of test cases using the permeability of arrays of spheres as a function of porosity shows that the number of iterations to convergence increases smoothly with decreasing porosity and at a porosity of 40% the matrix method is about 40 times faster than the time-dependent method. The matrix method can be extended to finite-Reynolds number flows, although the lattice Boltzmann equation is no longer linear in the velocity distribution function in that case. The work was published in Physical Review E.
