MAIA bb96820c
Multiphysics at AIA
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This page currently is a place to save useful examples that can be used in Doxygen. You can get more information in the Doxygen documentation.
The section about the Markdown support is especially useful.
Empty lines are preserved.
To get a line break you have to add two spaces to the end of the line.
Like this. Otherwise, line breaks are ignored.
This is an example link to some page. If you just use the @ref command it will use the title of the page as its text: Lattice Boltzmann equation (LBE).
Here is an example of a reference to a class MAIAFvCartesianSolverXD. You just have to write the name of the class an doxygen will do the rest.
This also works for functions MAIALbSolver::noInternalCells() and variables MAIALbSolver::m_cells.
This function has the wrong input parameters MAIALbSolver::a_variable() but Doxygen still links the function.
This would be correct: MAIALbSolver::a_variable(const MInt, const MInt)
I did not find a way to specify a specific version of a function. This for example links to the wrong one: void MAIALbSolverDxQy<3, 27>::cumulant_collision_step()
You can use the \page command in the C++ code to add information about the function to a specific page. However, you have to use the very specific syntax otherwise the page will not be rendered in the order.
The auto-generated List of all collision steps of the LB solver is linked here as an example.
Doxygen takes quite a long time to parse the whole code. To quickly compile the documentation without references to the code modify the doc/Doxyfile
at line 784:
Without the \ at the end of the line and @CMAKE_SOURCE_DIR@/@SRC_DIR@
in the next line. This change is reverted when you run the configure.py
script, which may happen automatically if you git pull
.
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Some text
more text.
The particle probability distribution function (PPDF) \( f(\mv{x},\mv{\xi},t) \) represents the probability of particles to appear in momentum space at the position \( \mv{x} \) and time \( t \) with a velocity of \( \mv{\xi} \).
Macroscopic quantities such as density, velocity, or energy ( \(\rho , \mv{u}, E\)) are connected to this mesoscopic quantity \( f \) by its raw moments
\begin{align} \rho(\mv{x},t) &= \iiint f(\mv{x},\mv{\xi},t) d\mv{\xi} \,, \\ \rho(\mv{x},t)u(\mv{x},t) &= \iiint \mv{\xi} f(\mv{x},\mv{\xi},t) d\mv{\xi} \,, \text{and}\\ 2\rho(\mv{x},t)E(\mv{x},t) &= \iiint |\mv{\xi}|^2 f(\mv{x},\mv{\xi},t) d\mv{\xi} \,. \end{align}
You can go quite big:
\(A \cdot \left( \begin{array}{c} p_{200}\\ p_{020}\\ p_{002}\\ p_{110}\\ p_{101}\\ p_{011}\\ p_{100}\\ p_{010}\\ p_{001}\\ p_{000}\\ \end{array} \right) = \left( \begin{array}{c} \sum{{x_j}^2 u_{i}(x_j)}\\ \sum{{y_j}^2 u_{i}(x_j)}\\ \sum{{z_j}^2 u_{i}(x_j)}\\ \sum{x_j y_j u_{i}(x_j)}\\ \sum{x_j z_j u_{i}(x_j)}\\ \sum{y_j z_j u_{i}(x_j)}\\ \sum{x_j u_{i}(x_j)}\\ \sum{y_j u_{i}(x_j)}\\ \sum{z_j u_{i}(x_j)}\\ \sum{u_{i}(x_j)}\\ \end{array} \right)\)
with
\(A = \left( \begin{array}{cccccccccc} \sum x_j^4&\sum x_j^2 y_j^2&\sum x_j^2 z_j^2&\sum x_j^3 y_j&\sum x_j^3 z_j&\sum x_j^2 y_j z_j&\sum x_j^3&\sum x_j^2 y_j&\sum x_j^2 z_j&\sum x_j^2\\ \sum x_j^2 y_j^2&\sum y_j^4&\sum y_j^2 z_j^2&\sum x_j y_j^3&\sum x_j y_j^2 z_j&\sum y_j^3 z_j&\sum x_j y_j^2&\sum y_j^3&\sum y_j^2 z_j&\sum y_j^2\\ \sum x_j^2 z_j^2&\sum y_j^2 z_j^2&\sum z_j^4&\sum x_j y_j z_j^2&\sum x_j z_j^3&\sum y_j z_j^3&\sum x_j z_j^2&\sum y_j z_j^2&\sum z_j^3&\sum z_j^2\\ \sum x_j^3 y_j&\sum x_j y_j^3&\sum x_j y_j z_j^2&\sum x_j^2 y_j^2&\sum x_j^2 y_j z_j&\sum x_j y_j^2 z_j&\sum x_j^2 y_j&\sum x_j y_j^2&\sum x_jy_jz_j&\sum x_jy_j\\ \sum x_j^3 z_j&\sum x_j y_j^2 z_j&\sum x_j z_j^3&\sum x_j^2 y_jz_j&\sum x_j^2 z_j^2&\sum x_jy_j z_j^2&\sum x_j^2 z_j&\sum x_jy_jz_j&\sum x_j z_j^2&\sum x_jz_j\\ \sum x_j^2 y_jz_j&\sum y_j^3 z_j&\sum y_j z_j^3&\sum x_j y_j^2 z_j&\sum x_jy_jz_j^2&\sum y_j^2 z_j^2&\sum x_jy_jz_j&\sum y_j^2 z_j&\sum y_j z_j^2&\sum y_jz_j\\ \sum x_j^3&\sum x_j y_j^2&\sum x_j z_j^2&\sum x_j^2 y_j&\sum x_j^2 z_j&\sum x_jy_jz_j&\sum x_j^2&\sum x_jy_j&\sum x_jz_j&\sum x_j\\ \sum x_j^2 y_j&\sum y_j^3&\sum y_j z_j^2&\sum x_j y_j^2&\sum x_jy_jz_j&\sum y_j^2 z_j&\sum x_jy_j&\sum y_j^2&\sum y_jz_j&\sum y_j\\ \sum x_j^2 z_j&\sum y_j^2 z_j&\sum z_j^3&\sum x_jy_jz_j&\sum x_j z_j^2&\sum y_j z_j^2&\sum x_jz_j&\sum y_jz_j&\sum z_j^2&\sum z_j\\ \sum x_j^2&\sum y_j^2&\sum z_j^2&\sum x_jy_j&\sum x_jz_j&\sum y_jz_j&\sum x_j&\sum y_j&\sum z_j&N\\ \end{array} \right)\)
Some text with a citation [Bhatnagar1954]
Variable | Equation |
---|---|
Velocity | \(u^*=\frac{u}{\xi_0}\) |
Isothermal speed of sound | \(c_s^*=\frac{c_s}{\xi_0}=\sqrt{\frac{1}{3}}\) |
Molecular velocity | \(\xi_0^*=\frac{\xi_0}{\xi_0}=1\) |
Grid distance | \(\delta x^*=\frac{\delta x}{\delta x}=1\) |
Characteristic Length | \(L^*=\frac{L}{\delta x}\) |
Time step | \(\delta t^*=\frac{\delta t \cdot \xi_0}{\delta x} = 1\) |
Density | \(\rho^*=\frac{\rho}{\rho_0}\) |
Pressure | \(p^*=\frac{p}{\rho_0 \cdot \xi_0^2}\) |
Collision Operator | \(\Omega_c^* = \omega_c \cdot \delta t = \frac{2}{6 \cdot \nu^* + 1}\) |
Temperature | \(T^*=\frac{T}{T_0}\) |
Thermal diffusivity | \(\kappa^*=\frac{\nu^*}{Pr}\) |
Collision Operator (thermal) | \(\Omega_T^* = \omega_T \cdot \delta t = \frac{2}{6 \cdot \frac{\nu^*}{Pr} + 1}\) |
rankdir = "LR";