Improve wording in some comments

diff --git a/examples/step-68/doc/intro.dox b/examples/step-68/doc/intro.dox
index 52cb4381ac0d94188e129e6c1e65d2a253038aad..777a3994c03c7f0f2f0ca1035703fd41d15248c0 100644 (file)
--- a/examples/step-68/doc/intro.dox
+++ b/examples/step-68/doc/intro.dox
@@ -130,11 +130,11 @@ also be different (non-matching) from the triangulation of the background grid,
 which is useful to generate particles in particular shapes (as in this
 example), or to transfer information between two different computational grids
 (as in step-70).  Furthermore, the Particles::ParticleHandler class provides the
-Particles::ParticleHandler::insert_global_particles function() which enables the
+Particles::ParticleHandler::insert_global_particles() function which enables the
 global insertion of particles from a vector of arbitrary points and a global
 vector of bounding boxes. In the present step, we use the
 Particles::Generators::quadrature_points() function on a non-matching triangulation to
-insert particle located at positions in the shape of a disk.
+insert particles located at positions in the shape of a disk.
 
 <h4>Particle exchange</h4>
 
@@ -183,7 +183,7 @@ finite-element problems already discussed in other examples.
 <h3>The testcase</h3>
 
 In the present step, we use particles as massless tracers to illustrate
-the dynamics of a particular vortical flow: the Rayleigh-Kothe Vortex. This flow pattern
+the dynamics of a particular vortical flow: the Rayleigh--Kothe vortex. This flow pattern
 is generally used as a complex test case for interface tracking methods
 (e.g., volume-of-fluid and level set approaches) since
 it leads to strong rotation and elongation of the fluid @cite Blais2013.
@@ -191,7 +191,7 @@ it leads to strong rotation and elongation of the fluid @cite Blais2013.
 The stream function $\Psi$ of this Rayleigh-Kothe vortex is defined as:
 
 @f[
-\Psi = \frac{1}{\pi} sin^2 (\pi x) \sin^2 (\pi y) \cos \left( \pi \frac{t}{T} \right)
+\Psi = \frac{1}{\pi} \sin^2 (\pi x) \sin^2 (\pi y) \cos \left( \pi \frac{t}{T} \right)
 @f]
 where $T$ is half the period of the flow. The velocity profile in 2D ($\textbf{u}=[u,v]^T$) is :
 @f{eqnarray*}

diff --git a/examples/step-68/doc/results.dox b/examples/step-68/doc/results.dox
index a8f36323aa9a93ab3f830c0bdfe7729c210c7613..f855f4363ac3e59f3d537e5d27cf238d572bb941 100644 (file)
--- a/examples/step-68/doc/results.dox
+++ b/examples/step-68/doc/results.dox
@@ -78,7 +78,7 @@ This program highlights some of the main capabilities for handling particles in
 capacity to be used in distributed parallel simulations. However, this step could
 be extended in numerous manners:
 - High-order time integration (for example using a Runge-Kutta 4 method) could be
-used to increase the accuracy and allow for an increased time-step size.
+used to increase the accuracy or allow for larger time-step sizes with the same accuracy.
 - The full equation of motion (with inertia) could be solved for the particles. In
 this case the particles would need to have additional properties such as their mass,
 as in step-19, and if one wanted to also consider interactions with the fluid, their diameter.