【求助】多松弛模型MRT问题求助

pi_scu

郭照立老师的书上介绍了一个多松弛时间模型MRT
其中，做了一个比较简单的介绍。
但是，没有对如何得到其中的变换矩阵作任何说明，然后其参考的文献我也找出来看了一下。就是一篇研究LBM
的弥散，耗散，稳定性的文章。
其中，对方法的提出做了一些说明，但是，那个由各种离散速度模型如D2Q9等得到的一个由分布函数到宏观量的
转移或者叫变换矩阵的来历没看懂。

  不知道论坛内的各位大侠有没有关注过这个东西。
  希望关注过的人能为小弟指点一二，或者推荐点文献看看。

luo@odu.edu

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.

stoneszone

原帖由 luo@odu.edu 于 2011-1-26 21:03 发表

                               
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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  ...

哇，罗老师都来回答问题了，真是荣幸。同学们，有问题还不快举手。呵呵。

yuesheng

使用MRT的变换矩阵时 是不是要求c=1 啊？

luo@odu.edu

No, you don't have to use c=1 -- it can be arbitrary. If c is not equal to 1, it has to be reflected in the transformation matrix M, which is constructed by using the Gram-Schmidt procedure in linear algebra.