Updated compressible solver comparison page

docs/source/compressible_compare.rst

@@ -1,5 +1,99 @@
 Compressible solver comparisons
 ===============================
 
+We run various problems run with the different compressible solvers in pyro (standard Riemann, Runge-Kutta, fourth order).
+
+
 Kelvin-Helmholtz
-----------------
+^^^^^^^^^^^^^^^^
+The McNally Kelvin-Helmholtz problem sets up a heavier fluid moving in the negative x-direction sandwiched between regions of lighter fluid moving in the positive x-direction.
+
+The image below shows the KH problem initialized with McNally's test. It ran on a 128 x 128 grid, with gamma = 1.7, and ran until t = 2.0. This is run with:
+
+.. code-block:: none
+
+  ./pyro.py compressible kh inputs.kh kh.vbulk=0
+  ./pyro.py compressible_rk kh inputs.kh kh.vbulk=0
+  ./pyro.py compressible_fv4 kh inputs.kh kh.vbulk=0
+
+.. image:: ./solver_comparisons/kh.png
+   :align: center
+
+
+We vary the velocity in the positive y-direction (vbulk) to see how effective the solvers are at preserving the initial shape.
+
+
+Sedov
+^^^^^
+The Sedov problem ran on a 128 x 128 grid, with gamma = 1.4, and until t = 0.1, which can be run as:
+
+.. code-block:: none
+
+   ./pyro.py compressible sedov inputs.sedov
+   ./pyro.py compressible_rk sedov inputs.sedov
+   ./pyro.py compressible_fv4 sedov inputs.sedov
+
+.. image:: ./solver_comparisons/sedov.png
+
+.. image:: ./solver_comparisons/sedov_rk.png
+
+.. image:: ./solver_comparisons/sedov_fv4.png
+
+Quad
+^^^^
+The quad problem ran on a 256 x 256 grid until t = 0.8, which can be run as:
+
+.. code-block:: none
+
+   ./pyro.py compressible quad inputs.quad
+   ./pyro.py compressible_rk quad inputs.quad
+   ./pyro.py compressible_fv4 quad inputs.quad
+
+.. image:: ./solver_comparisons/quad.png
+   :width: 30%
+
+.. image:: ./solver_comparisons/quad_rk.png
+   :width: 30%
+
+.. image:: ./solver_comparisons/quad_fv4.png
+   :width: 30%
+
+
+Bubble
+^^^^^^
+The bubble problem ran on a 128 x 256 grid until t = 3.0, which can be run as:
+
+.. code-block:: none
+
+   ./pyro.py compressible bubble inputs.bubble
+   ./pyro.py compressible_rk bubble inputs.bubble
+   ./pyro.py compressible_fv4 bubble inputs.bubble
+
+.. image:: ./solver_comparisons/bubble.png
+   :width: 30%
+
+.. image:: ./solver_comparisons/bubble_rk.png
+   :width: 30%
+
+.. image:: ./solver_comparisons/bubble_fv4.png
+   :width: 30%
+
+
+Rayleigh-Taylor
+^^^^^^^^^^^^^^^
+The Rayleigh-Taylor problem ran on a 64 x 192 grid until t = 3.0, which can be run as:
+
+.. code-block:: none
+
+   ./pyro.py compressible rt inputs.rt
+   ./pyro.py compressible_rk rt inputs.rt
+   ./pyro.py compressible_fv4 rt inputs.rt
+
+.. image:: ./solver_comparisons/rt.png
+   :align: center
+
+.. image:: ./solver_comparisons/rt_rk.png
+   :align: center
+
+.. image:: ./solver_comparisons/rt_fv4.png
+   :align: center