working on multiline eqs in docs

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James E McClure 2021-09-02 14:06:35 -04:00
parent 7d71211f4e
commit 7c5e0f05e1

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@ -66,7 +66,36 @@ Model Formulation
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The relaxation parameters are determined from the relaxation time:
.. math::
:nowrap:
$$
\\begin{eqnarray}
\lambda_1 = \lambda_2= \lambda_9 = \lambda_{10}= \lambda_{11}= \lambda_{12}= \lambda_{13}= \lambda_{14}= \lambda_{15} = s_\nu\;, \\
\lambda_{4}= \lambda_{6}= \lambda_{8} = \lambda_{16} = \lambda_{17} = \lambda_{18}= \frac{8(2-s_\nu)}{8-s_\nu} \;,
\\end{eqnarray}
$$
The non-zero equilibrium moments are defined as
.. math::
:nowrap:
$$
\\begin{eqnarray}
m_1^{eq} &=& (j_x^2+j_y^2+j_z^2) - \alpha |\textbf{C}|, \\
m_9^{eq} &=& (2j_x^2-j_y^2-j_z^2)+ \alpha \frac{|\textbf{C}|}{2}(2n_x^2-n_y^2-n_z^2), \\
m_{11}^{eq} &=& (j_y^2-j_z^2) + \alpha \frac{|\textbf{C}|}{2}(n_y^2-n_z^2), \\
m_{13}^{eq} &=& j_x j_y + \alpha \frac{|\textbf{C}|}{2} n_x n_y\;, \\
m_{14}^{eq} &=& j_y j_z + \alpha \frac{|\textbf{C}|}{2} n_y n_z\;, \\
m_{15}^{eq} &=& j_x j_z + \alpha \frac{|\textbf{C}|}{2} n_x n_z\;,
\\end{eqnarray}
$$
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Boundary Conditions
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