Dr. Ning Pan's Group
Effective Properties of Porous Multiphase Materials
Continuum ¨C the normal media
  • Solid and fluid, single phase continuum only approximation;

  • Conversional math and physics models

Porous and multiphase materials ¨C new challenges

From Analog to Discrete Approaches
  • Continuous cases ¨C more tedious to deal with, less accurate

    music, image, various electromagnetic signals

  • Homogenization ¨C less details, no general approach

    porous and multiphase -> continuum

  • Discretion in mathematics and physics

    - Solving equations ¨C numerical algorithms

    - PDF¡¯s ¨C Finite difference analysis, finite element analysis.

  • Discretion in physics - a few statistical and quantum models

    - Ising model, Cellular automate

    - Lattice Boltzmann method

Principles of the discrete models

Discretion of a problem- grids to digitize the system

Challenges in dealing with complex materials

Structure descriptions

  • Stochastic features of porous structure;

  • No two random structures of porous media exactly the same;

  • Statistical information for equivalent macro-behaviors;

  • Reproduced structure - the same statistical (effective) features.

Solutions of governing equations

  • Complex geometries

    Local grid refinement for traditional solvers

  • Multiphase

    Phase exchange and interface treatment

  • Conjugate boundary conditions

    Increased constrains

Prediction of thermal conductivities

Significance of this work

A robust computational method for complex materials

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