Solid and fluid, single phase continuum only approximation;
Conversional math and physics models
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
Discretion of a problem- grids to digitize the system
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
Local grid refinement for traditional solvers
Phase exchange and interface treatment
Conjugate boundary conditions
A robust computational method for complex materials
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