reword step-69 slightly

diff --git a/9.2/paper.tex b/9.2/paper.tex
index 38555193a5e5f82eb8da2549805fb609ffc9c732..6b133db70b72cbec989678f9776b4addaee3bd8b 100644 (file)
--- a/9.2/paper.tex
+++ b/9.2/paper.tex
@@ -875,17 +875,26 @@ pre and post operations, which can be passed to
 to the matrix-vector product to increase data locality.
 
 \item \texttt{step-69} presents a first-order scheme solving compressible
-Euler's equations of gas dynamics using a graph-based scheme. The time-update
-at each node requires the evaluation of a right-hand side that depends
-(nonlinearly) on information from the previous time-step that spans more than
-one cell. Therefore, assembly loops operate directly on the sparsity graph in
-order to retrieve information from the entire stencil associated to each
-node. From a programming perspective, \texttt{step-69} features a number of
-techniques that are of interest for a wider audience: It discusses a hybrid
-thread and MPI parallelized scheme with efficient (MPI node) local
-numbering of degrees of freedom. It showcases how to perform asynchronous
-write-out of results using a background thread with \texttt{std::async},
-and discusses a simple but effective checkpointing and restart technique.
+Euler's equations of gas dynamics with a graph-viscosity stabilization
+technique. Beside the usual conservation properties of mass, momentum and
+total energy, the method also guarantees that the constructed solution
+obeys pointwise stability constraints (positivity of density, internal
+energy and a local minimum principle on the specific entropy). As such
+\text{step-69} is strictly speaking more a collocation-type discretization
+than a variational formulation, even though it is implemented with finite
+elements.
+
+The time-update at each node requires the evaluation of a right-hand side
+that depends (nonlinearly) on information from the previous time-step that
+spans more than one cell. Therefore, assembly loops operate directly on the
+sparsity graph in order to retrieve information from the entire stencil
+associated to each node. From a programming perspective, \texttt{step-69}
+features a number of techniques that are of interest for a wider audience:
+It discusses a hybrid thread and MPI parallelized scheme with efficient
+(MPI node) local numbering of degrees of freedom. It showcases how to
+perform asynchronous write-out of results using a background thread with
+\texttt{std::async}, and discusses a simple but effective checkpointing and
+restart technique.
 
 \item \texttt{step-70}
   \todo[inline]{Luca, please write.}