update docs

This commit is contained in:
James McClure 2021-09-04 09:49:27 -04:00
parent 0b183a98ed
commit 06c01dd843
2 changed files with 13 additions and 4 deletions

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@ -140,10 +140,10 @@ terms to account for the interfacial stresses
:nowrap:
$$
f_q(\bm{x}_i + \bm{\xi}_q \delta t,t + \delta t) - f_q(\bm{x}_i,t) = \sum^{Q-1}_{k=0} M^{-1}_{qk} \lambda_{k} (m_k^{eq}-m_k) + t_q \bm{\xi}_q \cdot \frac{\bm{F}}{c_s^2} \;,
f_q(\bm{x}_i + \bm{\xi}_q \delta t,t + \delta t) - f_q(\bm{x}_i,t) = \sum^{Q-1}_{k=0} M^{-1}_{qk} \lambda_{k} (m_k^{eq}-m_k) + w_q \bm{\xi}_q \cdot \frac{\bm{F}}{c_s^2} \;,
$$
Where :math:`\bm{F}` is an external body force and :math:`c_s^2 = 1/3` is the speed of sound for the LB model.
The moments are linearly indepdendent:
.. math::

View File

@ -26,6 +26,15 @@ The essential model parameters for the color model are
- ``tau`` -- control the fluid viscosity -- :math:`0.7 < \tau < 1.5`
The kinematic viscosity is given by
.. math::
:nowrap:
$$
\nu = \frac{1}{3} \Big( \tau - \frac 12 \Big)
$$
****************************
Model Formulation
****************************
@ -37,10 +46,10 @@ velocity set, which determines the values :math:`\bm{\xi}_q`
:nowrap:
$$
f_q(\bm{x}_i + \bm{\xi}_q \delta t,t + \delta t) - f_q(\bm{x}_i,t) = \sum^{Q-1}_{k=0} M^{-1}_{qk} \lambda_{k} (m_k^{eq}-m_k) + t_q \bm{\xi}_q \cdot \frac{\bm{F}}{c_s^2} \;,
f_q(\bm{x}_i + \bm{\xi}_q \delta t,t + \delta t) - f_q(\bm{x}_i,t) = \sum^{Q-1}_{k=0} M^{-1}_{qk} \lambda_{k} (m_k^{eq}-m_k) + w_q \bm{\xi}_q \cdot \frac{\bm{F}}{c_s^2} \;,
$$
Where :math:`\bm{F}` an external body force and :math:`c_s^2 = 1/3` is the speed of sound for the LB model.
Where :math:`\bm{F}` is an external body force and :math:`c_s^2 = 1/3` is the speed of sound for the LB model.
The moments are linearly indepdendent functions of the distributions:
.. math::