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Boundary Conditions, Continuum Mechanics

  1. Jul 16, 2008 #1
    Mods: I wasn't sure if I should put this here or in DE's, if you think it would be better there, feel free to move it.

    If I have a bunch of particles, which I'm modelling as a continuum, and I want to put periodic boundary conditions which reflect (completely specular reflection) some fraction of the incoming particles, how would I write this as a boundary condition equation?

    Thanks in advance.
  2. jcsd
  3. Jul 16, 2008 #2

    Andy Resnick

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    Leaving aside the question of how a collection of discrete particles are modeled as a continuum, I would think that a probabilistic equation would do just fine. What happens to the particles that are not reflected?
  4. Jul 16, 2008 #3
    If you have enough particles, you can model them as a continuous density function and velocity/momentum function.

    How would you formulate a probabilistic equation in terms of a boundary condition for a differential equation.

    The particles not reflected are transmitted.
  5. Jul 16, 2008 #4

    Andy Resnick

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    Are you using some sort of lattice Boltzmann approach?

    Shiyi Chen and Daniel Martínez, Renwei Mei
    On boundary conditions in lattice Boltzmann methods
    Phys. Fluids 8, 2527 (1996); DOI:10.1063/1.869035

    Title: Absorbing boundary and free-surface conditions in the phononic lattice solid by interpolation
    Authors: Huang, L.-J., Mora, P., & Fehler, M. C.
    Journal: Geophysical Journal International, Volume 140, Issue 1, pp. 147-157.

    Jeng-Rong Ho, , Chun-Pao Kuo and Wen-Shu Jiaung
    Study of heat transfer in multilayered structure within the framework of dual-phase-lag heat conduction model using lattice Boltzmann method
    International Journal of Heat and Mass Transfer
    Volume 46, Issue 1, January 2003, Pages 55-69

    There's plenty more, I'm sure. I'm, not an expert, those are what I was able to quickly find.
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