Update docs to reflect current way we comput the viscous stress

Docs/source/manual/GettingStarted.rst

@@ -24,7 +24,7 @@ Then, there are two options to obtain `PeleLM` and its dependencies:
 ^^^^^^^^^^^^^^^^^
 
 `PeleProduction` enables the user to obtain a consistent version of `PeleLM` and all its dependencies
- with a single git clone (from the user). This is the prefered option when one wants to use `PeleLM` 
+with a single git clone (from the user). This is the prefered option when one wants to use `PeleLM` 
 but do not intend to make development into the code. More information on `PeleProduction` can be found 
 on the `GitHub page <https://github.com/AMReX-Combustion/PeleProduction.git>`_.
 

Docs/source/manual/Model.rst

@@ -127,11 +127,11 @@ where  :math:`{D} \boldsymbol{\chi} = \boldsymbol{\theta}`.
 
 As can be seen, the expression for these fluxes relies upon several transport coefficients that need to be evaluated. However, in the present framework several effects are neglected, thus simplifying the fluxes evaluation.
 
+.. _sec:model:EqSets:
+
 The `PeleLM` Equation Set
 ^^^^^^^^^^^^^^^^^^^^^^^^^
 
-.. _sec:model:EqSets:
-
 The full diffusion model couples together the advance of all thermodynamics fields, including a dense matrix transport operator that is cumbersome to deal with computationally, while also being generally viewed as an overkill for most practical combustion applications -- particularly those involving turbulent fluid dynamics.  For `PeleLM`, we make the following simplifying assumptions:
 
 1. The bulk viscosity, :math:`\kappa`, is usually negligible, compared to the shear viscosity,
@@ -511,7 +511,7 @@ the time-explicit advective fluxes for :math:`U`, :math:`\rho h`, and :math:`\rh
     \frac{1}{2}\left(\nabla\cdot\tau^n
     + \nabla\cdot\tau^{n+1,*}\right) - \nabla\pi^{n-1/2} + \frac{1}{2}(F^n + F^{n+1}),
 
-where :math:`\tau^{n+1,*} = \mu^{n+1}[\nabla U^{n+1,*} +(\nabla U^{n+1,*})^T - 2\mathcal{I}\widehat S^{n+1}/3]` and 
+where :math:`\tau^{n+1,*} = \mu^{n+1}[\nabla U^{n+1,*} +(\nabla U^{n+1,*})^T - \frac{2}{3} \mathcal{I} \, \nabla \cdot U^{n+1,*}]` and 
 :math:`\rho^{n+1/2} = (\rho^n + \rho^{n+1})/2`, and :math:`F` is the velocity forcing.  This is a semi-implicit discretization for :math:`U`, requiring
 a linear solve that couples together all velocity components.  The time-centered velocity in the advective derivative,
 :math:`U^{n+1/2}`, is computed in the same way