[cig-commits] [commit] master: Clarify a statement in the manual about the adiabatic heating term. (6c2cbf8)

[cig_noreply at geodynamics.org]

Repository : https://github.com/geodynamics/aspect

On branch  : master
Link       : https://github.com/geodynamics/aspect/compare/23dc089e92ad688c53e624829e730afbd400ebca...0641d4f288912b866940d5b5fbb2491462e66122

>---------------------------------------------------------------

commit 6c2cbf8c22a579f30d189209e98b3cf6d11c207f
Author: Wolfgang Bangerth <bangerth at math.tamu.edu>
Date:   Thu Sep 4 18:14:27 2014 -0500

    Clarify a statement in the manual about the adiabatic heating term.
    
    Also bring the code comments in sync with what the code actually does.


>---------------------------------------------------------------

6c2cbf8c22a579f30d189209e98b3cf6d11c207f
 doc/manual/manual.tex        | 16 ++++++++++++----
 source/simulator/assembly.cc |  9 ++++++++-
 2 files changed, 20 insertions(+), 5 deletions(-)

diff --git a/doc/manual/manual.tex b/doc/manual/manual.tex
index ee8fa0d..e999eb3 100644
--- a/doc/manual/manual.tex
+++ b/doc/manual/manual.tex
@@ -467,12 +467,20 @@ purposes than just tracking chemical compositions. We will discuss this
 equation in more detail in Section~\ref{sec:compositional}.
 
 \subsubsection{A comment on adiabatic heating}
-In other codes and texts there is sometimes a simplification made to the adiabatic heating term in the previous equation. If you assume the pressure gradient is assumed to be small in the vertical direction, then $ -\rho \mathbf g \approx \nabla \mathbf{p} $, and we have the following relation (the negative sign is due to $\mathbf g$ pointing downwards)
-\begin{align}
+Other codes and texts sometimes make a simplification to the adiabatic heating
+term in the previous equation. If you assume the vertical component of the
+gradient of the \textit{dynamic} pressure to be small compared to the gradient
+of the \textit{total} pressure (in other words, the gradient is dominated by
+the gradient of the hydrostatic pressure), then $ -\rho \mathbf g \approx
+\nabla \mathbf{p} $, and we have the following relation (the negative sign is
+due to $\mathbf g$ pointing downwards) 
+\begin{align*}
 \alpha T \left( \mathbf u \cdot \nabla \mathbf p \right)
   & \approx -\alpha \rho T \mathbf u \cdot \mathbf g.
-  \notag
-\end{align}
+\end{align*}
+While this simplification is possible, it is not necessary if you have access
+to the total pressure. \aspect{} therefore implements the original term
+without this simplification.
 
 \subsubsection{Boundary conditions}
 Having discussed \eqref{eq:temperature}, let us come to the last one of the
diff --git a/source/simulator/assembly.cc b/source/simulator/assembly.cc
index d6f6b21..7a5b912 100644
--- a/source/simulator/assembly.cc
+++ b/source/simulator/assembly.cc
@@ -1342,9 +1342,16 @@ namespace aspect
           0)
          +
          // add the term from adiabatic compression heating
-         //   - drho/dT T (u . g)
+	 //   + alpha T (u . nabla p)
          // where we use the definition of
          //   alpha = - 1/rho drho/dT
+	 // Note: this term is often simplified using the relationship
+	 //   rho g = -nabla p
+	 // to yield
+	 //   - alpha rho T (u . g)
+	 // However, we do not use this simplification here, see the
+	 // comment in the manual in the section on the governing
+	 // equations
          (parameters.include_adiabatic_heating
           ?
           (current_u * current_grad_p) * alpha * current_T