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_docs/Advanced-AD-Techniques.md

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@@ -25,7 +25,7 @@ we can build an internal representation of each expression to directly compute a
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The picture below shows the computational graph for the expression `φ=cos(v1)v2` and the compile-time representation as object with `su2double` being the general datatype used throughout SU2.
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![Expression Templates](http://www.scicomp.uni-kl.de/wordpress/wp-content/uploads/2016/05/Screenshot-from-2016-05-20-15-49-59.png)
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This object can be traversed to compute and store the partial derivatives `∂φ/∂v1=cos(v1)` and `∂φ/∂v2=-sin(v1)v2` based on the derivatives of each involved unary or binary operation. If recording is enabled the traversal of the computational graph of each
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This object can be traversed to compute and store the partial derivatives `∂φ/∂v1=-sin(v1)v2` and `∂φ/∂v2=cos(v1)` based on the derivatives of each involved unary or binary operation. If recording is enabled the traversal of the computational graph of each
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expression is started as soon as it occurs on the right-hand side in a statement. Note that the partial derivatives are only stored if the corresponding argument has some dependency on the input variables set by the user. This kind of dependency or
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activity tracking is relatively easy to accomplish since every variable stores an index along with its value. A
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zero index represents passive variables while a non-zero index identifies active variables. This index will be
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### AD Tool Wrapper
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The CoDi library provides a special datatype and is automatically included
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during the compilation if AD support is requested by the user (see [[AD Build]]) . For developers of SU2 there is no need to deal
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during the compilation if AD support is requested by the user (see the build instructions for further information). For developers of SU2 there is no need to deal
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with this library explicitly which is why there are simple wrapper routines for the most important features
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available. These are for example the following:
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_docs_v7/Theory.md

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permalink: /docs_v7/Theory/
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---
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This page contains a very brief summary of the different governing equation sets that are treated in each of the solvers within SU2. The reader will be referred to other references for the full detail of the numerical implementations, but we will also describe the approaches at a high level here.
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This page contains a very brief summary of the different governing equation sets that are treated in each of the solvers within SU2. The reader will be referred to other references in some instances for the full detail of the numerical implementations, but the approaches are also described at a high level here.
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| `INC_NAVIER_STOKES`, `INC_RANS` | 7.0.0 |
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SU2 solves the incompressible Navier-Stokes equations in a general form allowing for variable density due to heat transfer through the low-Mach approximation (or incompressible ideal gas formulation). The equations can be expressed in differential form as
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SU2 solves the incompressible Navier-Stokes equations in a general form allowing for variable density due to heat transfer through the low-Mach approximation (or incompressible ideal gas formulation).
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The reader is referred to [this paper](https://arc.aiaa.org/doi/10.2514/1.J058222) for extended details on the incompressible Navier-Stokes and Euler solvers in SU2.
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The equations can be expressed in differential form as
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$$ \mathcal{R}(V) = \frac{\partial V}{\partial t} + \nabla \cdot \bar{F}^{c}(V) - \nabla \cdot \bar{F}^{v}(V,\nabla V) - S = 0 $$
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# Turbulence Modeling #
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Available for `RANS`, `INC_RANS`.
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SU2 implements several variants of the SST and SA turbulence models, for specifics of the models please see the [NASA Turbulence Modeling Resource](https://turbmodels.larc.nasa.gov/index.html) (TMR).
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For information on how to use turbulence models in SU2 see the [users guide](https://su2code.github.io/docs_v7/Physical-Definition/).
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# Species Transport #
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Compatible with `NAVIER_STOKES`, `RANS`, `INC_NAVIER_STOKES`, `INC_RANS`
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Compatible with `NAVIER_STOKES`, `RANS`, `INC_NAVIER_STOKES`, `INC_RANS`.
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$$ \mathcal{R}(U) = \frac{\partial U}{\partial t} + \nabla \cdot \bar{F}^{c}(U) - \nabla \cdot \bar{F}^{v}(U,\nabla U) - S = 0 $$
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index.html

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<div class="container">
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<!-- Begin Special Banner for temporary announcements. End the comment here to enable... --->
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<div class="row">
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<div class="col-lg-12">
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<hr>
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<center>
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<h1>3rd Annual SU2 Conference</h1>
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<h3><a href="https://www.eventbrite.com/e/3rd-annual-su2-conference-tickets-375147244507?aff=ebdsoporgprofile">Registration</a> and <a href="https://su2foundation.org/su2conference2022/">Abstract Submission</a> Open!</h3>
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<h3>Combined In-Person (<a href="https://www.google.com/maps/search/villa+monastero/@46.0084623,9.284619,17z/data=!3m1!4b1">Varenna/Italy</a>) and Virtual Event,
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September 5 - 7, 2022</h3>
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<h3>More information on abstract submission, registration etc. are posted on the <a href="https://su2foundation.org/su2conference2022/">conference website</a> and will always contain the latest updates.</h3>
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</center>
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<hr>
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</div>
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</div>
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<!-- End Special Banner -->
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<div class="row">

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