Species transport theory + tutorials

_data/tutorials.yml

@@ -26,6 +26,7 @@
   - Inc_Laminar_Step
   - Inc_Laminar_Cavity
   - Inc_Streamwise_Periodic
+  - Inc_Species_Transport
 
 - title: Structural Mechanics
   tutorials:
@@ -48,6 +49,7 @@
   - Inviscid_3D_Constrained_ONERAM6
   - Multi_Objective_Shape_Design
   - Unsteady_Shape_Opt_NACA0012
+  - Species_Transport
 
 - title: Event Content
   tutorials:

_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 | 

_tutorials/design_features/Inviscid_3D_Constrained_ONERAM6/Inviscid_3D_Constrained_ONERAM6.md

@@ -101,7 +101,7 @@ FFD_CONTINUITY= 2ND_DERIVATIVE
 
 As the current implementation requires each FFD box to be a quadrilaterally-faced hexahedron (6 faces, 12 edges, 8 vertices), we can simply specify the 8 corner points of the box and the polynomial degree we would like to represent along each coordinate direction (x,y,z) in order to create the complete lattice of control points. It is convenient to think of the FFD box as a small structured mesh block with (i,j,k) indices for the control points, and note that the number of control points in each direction is the specified polynomial degree plus one. 
 
-In the example above, we are creating a box with control point dimensions 11, 9, and 2 in the x-, y-, and z-directions, respectively, for a total of 198 available control points. In the `FFD_DEFINITION` option, we give a name to the box ("WING"), and then list out the x, y, and z coordinates of each corner point. The order is important, and you can use the example above to match the convention. The degree is then specified in the `FFD_DEGREE` option. A view of the box with the control points numbered is in Figure (3). Note that the numbering in the figure is 1-based just for visualization, but within SU2, the control points have 0-based indexing. For example, the (1,1,1) control point in the figure is control point (0,0,0) within SU2. This is critical for specifying the design variables in the config file.
+In the example above, we are creating a box with control point dimensions 11, 9, and 2 in the x-, y-, and z-directions, respectively, for a total of 198 available control points. In the `FFD_DEFINITION` option, we give a name to the box ("WING"), and then list out the x, y, and z coordinates of each corner point. The order is important, and you can use the example above to match the convention. Alternatively, [this tutorial](/tutorials/Species_Transport/) contains more in-depth information on how the numbering should be done. The degree is then specified in the `FFD_DEGREE` option. A view of the box with the control points numbered is in Figure (3). Note that the numbering in the figure is 1-based just for visualization, but within SU2, the control points have 0-based indexing. For example, the (1,1,1) control point in the figure is control point (0,0,0) within SU2. This is critical for specifying the design variables in the config file.
 
 ![Opt. ONERA FFD](../../tutorials_files/design_features/Inviscid_3D_Constrained_ONERAM6/images/onera_ffd_points.png)
 Figure (3): View of the control point identifying indices, which increase in value along the positive coordinate directions. Note that the numbering here is 1-based just for visualization, but within SU2, the control points have 0-based indexing.

_tutorials/design_features/Multi_Objective_Shape_Design/Multi_Objective_Shape_Design.md

@@ -71,7 +71,7 @@ OBJECTIVE_WEIGHT= -1.0E-7,1.0
 ```
 These options define a weighted sum: -1.0E-7 x (SURFACE_TOTAL_PRESSURE at the outlet) + (DRAG on the lower surface). The OBJECTIVE_FUNCTION and OBJECTIVE_WEIGHT options are set automatically during the optimization process, and are used for the calculation of the gradient. If we were starting this problem from scratch, at this point we would run the gradient method desired, in order to confirm that the gradients are being calculated as expected. In this tutorial, the discrete adjoint is used by default. When multiple objectives are specified as shown, a single adjoint solution for a 'combo' objective will be calculated, representing the gradient for the weighted sum. The upside of this is that it reduces the number of adjoint solutions required, with the downside that the contributions of different functionals to the gradient value will not be known.
 
-Next the FFD box is defined in order to provide the design variables. The mesh is provided with the FFD box information already included, however when starting from scratch a preprocessing step using SU2_MSH is required. For further detail on FFD, see the [Constrainted Optimal Shape Design Tutorial](/tutorials/Inviscid_3D_Constrained_ONERAM6/).
+Next the FFD box is defined in order to provide the design variables. The mesh is provided with the FFD box information already included, however when starting from scratch a preprocessing step using SU2_MSH is required. For further detail on FFD, see this [Unconstrained species transport tutorial](/tutorials/Species_Transport/) or [Constrainted Optimal Shape Design Tutorial](/tutorials/Inviscid_3D_Constrained_ONERAM6/).
 ```
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