Dynamic renormalization-group approach to diffusive flow in heterogeneous systems

TL;DR

This paper introduces a hierarchical dynamic renormalization-group method using Walsh transforms for simulating strongly inhomogeneous diffusive systems, significantly improving efficiency over traditional methods.

Contribution

It presents a novel hierarchical approach combining renormalization-group ideas and wavelet transforms for faster simulation of complex diffusive systems.

Findings

Achieves 1.5% accuracy in a test case

25 times faster than finite difference methods

Effective for heterogeneous reservoir simulations

Abstract

Conventional methods for the simulation of diffusive systems are quite slow when applied to strongly inhomogeneous systems. We present a new hierarchical approach based on dynamic renormalization-group ideas and 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. In a test case, the hierarchical method is found to achieve 1.5% accuracy roughly 25 times faster than conventional finite difference methods.