Update Inc_Combustion.md (#186)

remove density from source term in description of transport equations

Author: bigfooted

_tutorials/incompressible_flow/Inc_Combustion/Inc_Combustion.md

@@ -48,7 +48,7 @@ The `CSpeciesSolver` object in SU2 solves the controlling variables and passive
 
 $$
 \begin{equation}
-    \frac{\partial \rho \mathcal{Y}}{\partial t} + \nabla\cdot(\rho\vec{u}\mathcal{Y}) - \nabla\cdot\left(\rho D\nabla\mathcal{Y}\right) = \rho\dot{\omega}_\mathcal{Y}
+    \frac{\partial \rho \mathcal{Y}}{\partial t} + \nabla\cdot(\rho\vec{u}\mathcal{Y}) - \nabla\cdot\left(\rho D\nabla\mathcal{Y}\right) = \dot{\omega}_\mathcal{Y}
 \end{equation}
 $$
 
@@ -60,15 +60,15 @@ $$
 
 $$
 \begin{equation}
-    \frac{\partial \rho Y_j}{\partial t} + \nabla\cdot(\rho\vec{u}Y_j) - \nabla\cdot\left(\rho D\nabla Y_j\right) = \rho\dot{\omega}^+ + \rho\dot{\omega}^- Y_j
+    \frac{\partial \rho Y_j}{\partial t} + \nabla\cdot(\rho\vec{u}Y_j) - \nabla\cdot\left(\rho D\nabla Y_j\right) = \dot{\omega}^+ + \dot{\omega}^- Y_j
 \end{equation}
 $$
 
 2. partially or non-premixed, no preferential diffusion:
 
 $$
 \begin{equation}
-    \frac{\partial \rho \mathcal{Y}}{\partial t} + \nabla\cdot(\rho\vec{u}\mathcal{Y}) - \nabla\cdot\left(\rho D\nabla\mathcal{Y}\right) = \rho\dot{\omega}_\mathcal{Y}
+    \frac{\partial \rho \mathcal{Y}}{\partial t} + \nabla\cdot(\rho\vec{u}\mathcal{Y}) - \nabla\cdot\left(\rho D\nabla\mathcal{Y}\right) = \dot{\omega}_\mathcal{Y}
 \end{equation}
 $$
 
@@ -80,21 +80,21 @@ $$
 
 $$
 \begin{equation}
-    \frac{\partial \rho Z}{\partial t} + \nabla\cdot(\rho\vec{u}Z) - \nabla\cdot\left(\rho D\nabla Z\right) = \rho\dot{\omega}_\mathcal{Y}
+    \frac{\partial \rho Z}{\partial t} + \nabla\cdot(\rho\vec{u}Z) - \nabla\cdot\left(\rho D\nabla Z\right) = \dot{\omega}_\mathcal{Y}
 \end{equation}
 $$
 
 $$
 \begin{equation}
-    \frac{\partial \rho Y_j}{\partial t} + \nabla\cdot(\rho\vec{u}Y_j) - \nabla\cdot\left(\rho D\nabla Y_j\right) = \rho\dot{\omega}^+ + \rho\dot{\omega}^- Y_j
+    \frac{\partial \rho Y_j}{\partial t} + \nabla\cdot(\rho\vec{u}Y_j) - \nabla\cdot\left(\rho D\nabla Y_j\right) = \dot{\omega}^+ + \dot{\omega}^- Y_j
 \end{equation}
 $$
 
 3. pre-mixed, partially pre-mixed, non-premixed, with preferential diffusion:
 
 $$
 \begin{equation}
-    \frac{\partial \rho \mathcal{Y}}{\partial t} + \nabla\cdot(\rho\vec{u}\mathcal{Y}) - \nabla\cdot\left(\rho D\nabla\beta_\mathcal{Y}\right) = \rho\dot{\omega}_\mathcal{Y}
+    \frac{\partial \rho \mathcal{Y}}{\partial t} + \nabla\cdot(\rho\vec{u}\mathcal{Y}) - \nabla\cdot\left(\rho D\nabla\beta_\mathcal{Y}\right) = \dot{\omega}_\mathcal{Y}
 \end{equation}
 $$
 
@@ -112,7 +112,7 @@ $$
 
 $$
 \begin{equation}
-    \frac{\partial \rho Y_j}{\partial t} + \nabla\cdot(\rho\vec{u}Y_j) - \nabla\cdot\left(\rho D\nabla Y_j\right) = \rho\dot{\omega}^+ + \rho\dot{\omega}^- Y_j
+    \frac{\partial \rho Y_j}{\partial t} + \nabla\cdot(\rho\vec{u}Y_j) - \nabla\cdot\left(\rho D\nabla Y_j\right) = \dot{\omega}^+ + \dot{\omega}^- Y_j
 \end{equation}
 $$
 
@@ -175,7 +175,7 @@ Pre-mixed combustion of reactants with high hydrogen content at lean conditions
 
 $$
 \begin{equation}
-    \frac{\partial \rho \mathcal{Y}}{\partial t} + \nabla\cdot(\rho\vec{u}\mathcal{Y}) - \nabla\cdot\left(D\nabla\beta_\mathcal{Y}\right) = \rho\dot{\omega}_\mathcal{Y}
+    \frac{\partial \rho \mathcal{Y}}{\partial t} + \nabla\cdot(\rho\vec{u}\mathcal{Y}) - \nabla\cdot\left(D\nabla\beta_\mathcal{Y}\right) = \dot{\omega}_\mathcal{Y}
 \end{equation}
 $$