added baseics

.gitmodules

+[submodule "toucan"]
+	path = lattice-boltzmann.com/themes/toucan
+	url = https://git.42l.fr/HugoTrentesaux/toucan.git

README.md

+# Lattice Boltzmann tutorial with Futhark
+
+The aim of this tutorial is to teach a bit of lattice Boltzmann, a bit of Futhark, and produce a high porformance lattice Boltzmann code.
+
+This tutorial will be structured as follows:
+
+1. The lattice Boltzmann in dimensionless units formulation (and not is "lattice units").
+2. How to build a very simple demonstrator lattice Boltzmann code in Futhark.
+3. Build a benchmark for our code and validate it.
+4. How to make the code run faster independently of the architecture.
+5. Addition of boundary conditions.

lattice-boltzmann.com/config.toml

+# The URL the site will be built for
+base_url = "https://www.lattice-boltzmann.com"
+
+# Whether to automatically compile all Sass files in the sass directory
+compile_sass = true
+
+# Whether to build a search index to be used later on by a JavaScript library
+build_search_index = true
+
+theme = "toucan"
+
+transparent = "true"
+
+[markdown]
+# Whether to do syntax highlighting
+# Theme can be customised by setting the `highlight_theme` variable to a theme supported by Zola
+highlight_code = true
+highlight_theme = "base16-ocean-light"
+
+[extra]
+# Put all your custom variables here
+
+# Whether to do syntax highlighting
+# Theme can be customised by setting the `highlight_theme` variable to a theme supported by Zola
+title = "High performance lattice Boltzmann method"
+
+[extra.theme]
+read_more = "Read more"

lattice-boltzmann.com/content/1-dimensionless-lbm.md

++++
+title = "The dimensionless lattice Boltzmann equation"
+description = "How to write the dimensionless lattice Boltzmann equation"
+date = 2024-03-06
+slug = "dimensionless"
+
+[extra]
+katex = true
++++
+
+# Dimensionless Navier-Stokes
+
+In order to write the dimensionless lattice Boltzmann equation, we start by reminding the basis of dimensionless formulation by writing the dimensionless incompressible Navier--Stokes which are more common in the litterature.
+
+The incompressible Navier--Stokes equations reads
+
+££
+\begin{aligned}
+&\bm{\nabla}\cdot\bm{u}=0,\\\\
+&\frac{\partial}{\partial t}\bm{u}+\bm{u}\cdot\bm{\nabla}\bm{u}=-\frac{1}{\rho}\bm{\nabla}p+\nu\bm{\nabla}^2\bm{u},
+\end{aligned}
+££
+where $p$, $\rho$, $\nu$, and $\bm{u}$ are respectively the pressure, density, kinematic viscosity, and velocity of the flow.
+
+In order to transform this equation into its dimensionless form a certain amount of characteristic lengthscales must be chosen. Here we will define $U$ as the characteristic velocity of the flow and $L$ its characteristic length.
+
+We can the write all the above quantities dimensionless form
+££
+\begin{aligned}
+&\bm{u}^\ast=\frac{\bm{u}}{U}, &p^\ast=\frac{p}{\rho U^2},\\\\
+&t^\ast=\frac{U}{L}t, &\bm{x}^\ast=\frac{\bm{x}}{L},\\\\
+&\frac{\partial}{\partial t^\ast}=\frac{L}{U}\frac{\partial}{\partial t}, &\bm{\nabla}^\ast=L\bm{\nabla}
+\end{aligned}
+££
+Replacing these equations into the Navier--Stokes equations one gets
+££
+\begin{aligned}
+&\bm{\nabla}^\ast\cdot\bm{u}^\ast=0,\\\\
+&\frac{\partial}{\partial t^\ast}\bm{u}^\ast+\bm{u}^\ast\cdot\bm{\nabla}^\ast\bm{u}^\ast=\bm{\nabla}^\ast p^\ast+\frac{1}{\mathrm{Re}}\bm{\nabla}^{\ast 2}\bm{u}^\ast,
+\end{aligned}
+££
+where $\mathrm{Re}=U\cdot L/\nu$ is the _famous_ Reynolds number which represents the ratio of the .

lattice-boltzmann.com/content/_index.md

++++
+sort_by = "date"
+template = "section.html"
++++

toucan @ c8456ffe

+Subproject commit c8456ffe6d9ec321426e7f0a20bdc5f7ac14b81d