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James McClure 2022-08-31 14:08:59 -04:00
parent ffe4f794de
commit e9096dbfc3
2 changed files with 69 additions and 12 deletions
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40
docs/source/userGuide/models/color/index.rst
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@ -176,42 +176,70 @@ The non-zero equilibrium moments are defined as
:nowrap:
$$
m_1^{eq} = (j_x^2+j_y^2+j_z^2) - \alpha |\textbf{C}|, \\
m_1^{eq} = 19\frac{ j_x^2+j_y^2+j_z^2}{\rho_0} - 11\rho - 19 \alpha |\textbf{C}|, \\
$$
.. math::
:nowrap:
$$
m_2^{eq} = 3\rho - \frac{11( j_x^2+j_y^2+j_z^2)}{2\rho_0}, \\
$$
.. math::
:nowrap:
$$
m_4^{eq} = -\frac{2 j_x}{3}, \\
$$
.. math::
:nowrap:
$$
m_6^{eq} = -\frac{2 j_y}{3}, \\
$$
.. math::
:nowrap:
$$
m_8^{eq} = -\frac{2 j_z}{3}, \\
$$
.. math::
:nowrap:
$$
m_9^{eq} = (2j_x^2-j_y^2-j_z^2)+ \alpha \frac{|\textbf{C}|}{2}(2n_x^2-n_y^2-n_z^2), \\
m_9^{eq} = \frac{2j_x^2-j_y^2-j_z^2}{\rho_0}+ \alpha \frac{|\textbf{C}|}{2}(2n_x^2-n_y^2-n_z^2), \\
$$
.. math::
:nowrap:
$$
m_{11}^{eq} = (j_y^2-j_z^2) + \alpha \frac{|\textbf{C}|}{2}(n_y^2-n_z^2), \\
m_{11}^{eq} = \frac{j_y^2-j_z^2}{\rho_0} + \alpha \frac{|\textbf{C}|}{2}(n_y^2-n_z^2), \\
$$
.. math::
:nowrap:
$$
m_{13}^{eq} = j_x j_y + \alpha \frac{|\textbf{C}|}{2} n_x n_y\;, \\
m_{13}^{eq} = \frac{j_x j_y}{\rho_0} + \alpha \frac{|\textbf{C}|}{2} n_x n_y\;, \\
$$
.. math::
:nowrap:
$$
m_{14}^{eq} = j_y j_z + \alpha \frac{|\textbf{C}|}{2} n_y n_z\;, \\
m_{14}^{eq} = \frac{j_y j_z}{\rho_0} + \alpha \frac{|\textbf{C}|}{2} n_y n_z\;, \\
$$
.. math::
:nowrap:
$$
m_{15}^{eq} = j_x j_z + \alpha \frac{|\textbf{C}|}{2} n_x n_z\;,
m_{15}^{eq} = \frac{j_x j_z}{\rho_0} + \alpha \frac{|\textbf{C}|}{2} n_x n_z\;.
$$
where the color gradient is determined from the phase indicator field

41
docs/source/userGuide/models/greyscaleColor/greyscaleColor.rst
View File

@ -241,46 +241,75 @@ The relaxation parameters are determined from the relaxation time:
The non-zero equilibrium moments are defined as
.. math::
:nowrap:
$$
m_1^{eq} = (j_x^2+j_y^2+j_z^2) - \alpha |\textbf{C}|, \\
m_1^{eq} = 19\frac{ j_x^2+j_y^2+j_z^2}{\rho_0} - 11\rho - 19 \alpha |\textbf{C}|, \\
$$
.. math::
:nowrap:
$$
m_2^{eq} = 3\rho - \frac{11( j_x^2+j_y^2+j_z^2)}{2\rho_0}, \\
$$
.. math::
:nowrap:
$$
m_4^{eq} = -\frac{2 j_x}{3}, \\
$$
.. math::
:nowrap:
$$
m_6^{eq} = -\frac{2 j_y}{3}, \\
$$
.. math::
:nowrap:
$$
m_8^{eq} = -\frac{2 j_z}{3}, \\
$$
.. math::
:nowrap:
$$
m_9^{eq} = (2j_x^2-j_y^2-j_z^2)+ \alpha \frac{|\textbf{C}|}{2}(2n_x^2-n_y^2-n_z^2), \\
m_9^{eq} = \frac{2j_x^2-j_y^2-j_z^2}{\rho_0}+ \alpha \frac{|\textbf{C}|}{2}(2n_x^2-n_y^2-n_z^2), \\
$$
.. math::
:nowrap:
$$
m_{11}^{eq} = (j_y^2-j_z^2) + \alpha \frac{|\textbf{C}|}{2}(n_y^2-n_z^2), \\
m_{11}^{eq} = \frac{j_y^2-j_z^2}{\rho_0} + \alpha \frac{|\textbf{C}|}{2}(n_y^2-n_z^2), \\
$$
.. math::
:nowrap:
$$
m_{13}^{eq} = j_x j_y + \alpha \frac{|\textbf{C}|}{2} n_x n_y\;, \\
m_{13}^{eq} = \frac{j_x j_y}{\rho_0} + \alpha \frac{|\textbf{C}|}{2} n_x n_y\;, \\
$$
.. math::
:nowrap:
$$
m_{14}^{eq} = j_y j_z + \alpha \frac{|\textbf{C}|}{2} n_y n_z\;, \\
m_{14}^{eq} = \frac{j_y j_z}{\rho_0} + \alpha \frac{|\textbf{C}|}{2} n_y n_z\;, \\
$$
.. math::
:nowrap:
$$
m_{15}^{eq} = j_x j_z + \alpha \frac{|\textbf{C}|}{2} n_x n_z\;,
m_{15}^{eq} = \frac{j_x j_z}{\rho_0} + \alpha \frac{|\textbf{C}|}{2} n_x n_z\;.
$$
where the color gradient is determined from the phase indicator field