added banner and started hermite expansion

lattice-boltzmann.com/content/2-hermite-expansion.md

++++
+title = "Polynomial expansion of the BGK equation"
+description = "A possible polynomial expansion of the BGK equation"
+date = 2024-03-14
+weight = 2
+slug = "hermite"
+draft = true
+[taxonomies]
+tags = ["LBM", "Hermite", "Expansion"]
+[extra]
+math = true
+math_auto_render = true
+toc = true
++++
+
+## Macroscopic quantities
+
+In the [preceding chapter](../dimensionless) we introduced the density distribution function $f$ and its
+non-dimensional counterpart $f^\ast$. From now on, we will assume that all quantities are without dimensions
+and omit the $^\ast$. Apart from making the dimensional analysis of the Navier--Stokes and the Boltzmann equation
+we never discussed the actual link between the quantities present in each equation. It will be the aim of this
+section. Actually macroscopic quantities are related to moments of $f$ as
+$$
+\begin{align}
+\rho(\bm{x}, t)&=\int_{-\infty}^\infty f(\bm{x}, \bm{\xi}, t)\mathrm{d}\bm{\xi},\\\\
+\rho(\bm{x}, t)\bm{u}(\bm{x}, t)&=\int_{-\infty}^\infty f(\bm{x}, \bm{\xi}, t)\bm{\xi}\mathrm{d}\bm{\xi},
+\end{align}
+$$
+where the density, $\rho$, and the momentum $\rho\bm{u}$ are the zeroth and first order moment of $f$.
+
+
+
+
+
+