Add species transport theory draft

Author: TobiKattmann

_docs_v7/Theory.md

@@ -12,6 +12,7 @@ This page contains a very brief summary of the different governing equation sets
 - [Incompressible Navier-Stokes](#incompressible-navier-stokes)
 - [Incompressible Euler](#incompressible-euler)
 - [Turbulence Modeling](#turbulence-modeling)
+- [Species Transport](#species-transport)
 - [Elasticity](#elasticity)
 - [Heat Conduction](#heat-conduction)
 
@@ -169,6 +170,34 @@ Within the turbulence solvers, we discretize the equations in space using a fini
 
 ---
 
+# Species Transport #
+
+Compatible with `NAVIER_STOKES`, `RANS`, `INC_NAVIER_STOKES`, `INC_RANS`
+
+$$ \mathcal{R}(U) = \frac{\partial U}{\partial t} + \nabla \cdot \bar{F}^{c}(U) - \nabla \cdot \bar{F}^{v}(U,\nabla U)  - S = 0 $$
+
+where the conservative variables (which are also the working variables) are given by 
+
+$$U=\left\lbrace \rho Y_1, ..., \rho Y_{N-1} \right\rbrace ^\mathsf{T}$$
+
+with $$Y_i$$ $$[-]$$ being the species mass fraction. And 
+
+$$\sum_{i=0}^N Y_i = 1 \Rightarrow Y_N = 1 - \sum_{i=0}^{N-1} Y_i$$
+  
+$$S$$ is a generic source term, and the convective and viscous fluxes are
+
+$$\bar{F}^{c}(V) = \left\{\begin{array}{c} \rho Y_1 \bar{v} \\ ... \\\rho Y_{N-1} \, \bar{v} \end{array} \right\}$$
+
+$$\bar{F}^{v}(V,\nabla V) = \left\{\begin{array}{c} D \nabla Y_{1} \\ ... \\  D \nabla Y_{N-1} \end{array} \right\} $$
+
+with $$D$$ $$[m^2/s]$$ being the mass diffusion. 
+
+$$D = D_{lam} + \frac{\mu_T}{Sc_{T}}$$
+
+where $$\mu_T$$ is the eddy viscosity and $$Sc_{T}$$ $$[-]$$ the turbulent Schmidt number.
+
+---
+
 # Elasticity #
 
 | Solver | Version |