Hierarchical approach to diffusive flow in heterogeneous systems
Yüksel Günal, Pieter B. Visscher · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1997
Conventional methods for the simulation of diffusive systems are quite slow when applied to strongly inhomogeneous systems. We present a hierarchical approach motivated by dynamic renormalization-group ideas and based on the Walsh transform (or Haar wavelet) of signal-processing theory. The method is very efficient for simulation of petroleum reservoirs or other strongly inhomogeneous diffusive or pressure-driven flow systems. As we increase the number of cells N into which a sample inhomogeneous two dimensional test system is divided, the method becomes faster than conventional finite-difference methods by N=16\ifmmode\times\else\texttimes\fi{}16, and is roughly 40 times faster at N=64\ifmmode\times\else\texttimes\fi{}64; we argue that the speedup factor should asymptotically increase at least proportionally to ${\mathrm{N}}^{2}$.