Wavelet based solution of flow and diffusion problems in digital materials

Abstract

The computation of physical properties in a digital materials laboratory requires significant computational resources. Due to the complex nature of the media, one of the most difficult problems to solve is the multiphase flow problem, and traditional methods such as Lattice Boltzmann are not attractive as the computational demand for the solution is too high. A wavelet based algorithm reduces the amount of information required for computation. Here we solve the Poisson equation for a large three dimensional data set with a second order finite difference approximation. Constraints and fictitious domains are used to capture the complex geometry. We solve the discrete system using a discrete wavelet transform and thresholding. We show that this method is substantially faster than the original approach and has the same order of accuracy.

References

• Mark A. Knackstedt, Shane Latham, Mahyar Madadi, Adrian Sheppard, Trond Varslot, and Christoph Arns, Digital rock physics: 3D imaging of core material and correlations to acoustic and flow properties, The Leading Edge 28 (2009), no. 1, 28--33.
• Angela Kunoth, Wavelet techniques for the fictitious domain Lagrange multiplier approach, Numer Algorithms 27 (2001), 291--316, doi:10.1023/A:1011891106124
• Arthur Sakellariou, Christoph H. Arns, Adrian P. Sheppard, Rob M. Sok, Holger Averdunk, Ajay Limaye, Anthony C. Jones, Tim J. Senden, and Mark A. Knackstedt, Developing a virtual materials laboratory, Mater Today 10 (2007), no. 12, 44--51.
• Adrian P. Sheppard, Rob M. Sok, and Holger Averdunk, Techniques for image enhancement and segmentation of tomographic images of porous materials, Physica A 339 (2004), no. 1--2, 145--151.