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Analyzing Dendritic Morphology in Columns and Layers
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Hierarchical coarse-graining transform.

Vera Pancaldi1, Peter R King, Kim Christensen

  • 1Earth Science & Engineering, Imperial College London, Prince Consort Road, London SW7 2BP, United Kingdom. vera.pancaldi00@imperial.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 28, 2009
PubMed
Summary
This summary is machine-generated.

We developed a hierarchical transform for solving differential equations like Darcy's equation. This method decomposes pressure fields, enabling detailed calculations and adaptive coarse-graining for porous media flow analysis.

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Area of Science:

  • Computational fluid dynamics
  • Applied mathematics
  • Geophysics

Background:

  • Darcy's equation models single-phase flow in porous media.
  • Solving these equations often requires complex numerical methods.
  • Understanding pressure field behavior is crucial for subsurface flow analysis.

Purpose of the Study:

  • To introduce a novel hierarchical transform for Laplace-like differential equations.
  • To enable adaptive and detailed calculation of pressure fields.
  • To develop a method for localizing important features in pressure fields.

Main Methods:

  • A finite-difference discretization scheme is employed to formulate an eigenvalue problem.
  • The pressure field is decomposed into average values and multi-scale fluctuations.
  • A hierarchical transform is applied to the discretized equation.

Main Results:

  • The hierarchical transform allows pressure calculation with adjustable detail levels.
  • A procedure is presented to identify significant pressure field features using fine-scale permeability.
  • Adaptive coarse-graining is achieved based on localized features.

Conclusions:

  • The proposed hierarchical transform offers an efficient approach for solving Darcy-like equations.
  • The method facilitates adaptive analysis of porous media flow.
  • Demonstrations on synthetic problems validate the formalism and its practical applicability.