HIERARCHICAL APPROACH TO DIFFUSIVE FLOW IN HETEROGENEOUS SYSTEMS

Conventional methods for the simulation of diffusive systems are quite slow when applied to strongly inhomogeneous systems. We present a hie rarchical approach motivated by dynamic renormalization-group ideas an d based on the Walsh transform (or Haar wavelet) of signal-processing theory. The method is very efficient for simulation of petroleum reser voirs or other strongly inhomogeneous diffusive or pressure-driven flo w systems. As we increase the number of cells N into which a sample in homogeneous two dimensional test system is divided, the method becomes faster than conventional finite-difference methods by N = 16 X 16, an d is roughly 40 times faster at N = 64 X 64; we argue that the speedup factor should asymptotically increase at least proportionally to N-2.