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发表于 2011-1-26 21:03:33
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To understand the transformation matrix in MRT, you need to understand a couple of things in linear algebra etc.: 1) linear transformation, 2) Gram-Schmidt orthogonalization procedure, 3) and project to a orthogonal basis.
In LBE, any model with n discrete velocities, you can define n moments uniquely, and these moments are physically significant. The mapping from velocities to moments is a linear one -- it is an integral transformation. If the basis is orthogonal, it is more convenient (e.g., Fourier transform) because change in one moment won't affect others. It is also more natural to execute "collision" in the space of moments (this comes from kinetic theory).
The main point I would like to stress is that MRT is not that complicated -- it's just a linear model, and lattice BGK is a special case. |
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