add docstrings to the incompressible problems (#279)

Author: zingale

pyro/incompressible/problems/converge.py

@@ -19,7 +19,8 @@
     p(x,y,t) = -\cos(4 \pi (x - t)) - \cos(4 \pi (y - t))
 
 The numerical solution can be compared to the exact solution to
-measure the convergence rate of the algorithm.
+measure the convergence rate of the algorithm.  These initial
+conditions come from Minion 1996.
 
 """
 

pyro/incompressible/problems/shear.py

@@ -2,15 +2,18 @@
 Initialize the doubly periodic shear layer (see, for example, Martin
 and Colella, 2000, JCP, 163, 271).  This is run in a unit square
 domain, with periodic boundary conditions on all sides.  Here, the
-initial velocity is::
+initial velocity is:
 
-                 / tanh(rho_s (y-0.25))   if y <= 0.5
-   u(x,y,t=0) = <
-                 \ tanh(rho_s (0.75-y))   if y > 0.5
+.. math::
 
-   v(x,y,t=0) = delta_s sin(2 pi x)
+   u(x,y,t=0) = \begin{cases}
+                \tanh(\rho_s (y - 1/4)) &  \mbox{if}~ y \le 1/2 \\
+                \tanh(\rho_s (3/4 - y)) &  \mbox{if}~ y > 1/2
+                \end{cases}
 
+.. math::
 
+   v(x,y,t=0) = \delta_s \sin(2 \pi x)
 """
 
 

pyro/incompressible_viscous/problems/shear.py

@@ -2,15 +2,18 @@
 Initialize the doubly periodic shear layer (see, for example, Martin
 and Colella, 2000, JCP, 163, 271).  This is run in a unit square
 domain, with periodic boundary conditions on all sides.  Here, the
-initial velocity is::
+initial velocity is:
 
-                 / tanh(rho_s (y-0.25))   if y <= 0.5
-   u(x,y,t=0) = <
-                 \ tanh(rho_s (0.75-y))   if y > 0.5
+.. math::
 
-   v(x,y,t=0) = delta_s sin(2 pi x)
+   u(x,y,t=0) = \begin{cases}
+                \tanh(\rho_s (y - 1/4)) &  \mbox{if}~ y \le 1/2 \\
+                \tanh(\rho_s (3/4 - y)) &  \mbox{if}~ y > 1/2
+                \end{cases}
 
+.. math::
 
+   v(x,y,t=0) = \delta_s \sin(2 \pi x)
 """