Split spatial convergence studies and update figures. (#1154)

Co-authored-by: Ann Almgren <[email protected]>

Docs/sphinx_doc/Verification.rst

@@ -22,28 +22,41 @@ second through sixth order, including the WENO 3rd and 5th order stencils. In a
 the time step was held fixed at :math:`\Delta t = 0.0000078125` to ensure that the spatial error dominates
 the temporal error.
 
-The second study, shown on the right below, tests the temporal accuracy by first setting :math:`\Delta t = 0.0005`
-and :math:`\Delta x = 1/8`, then reducing both :math:`\Delta t` and :math:`\Delta x` by a factor of two, keeping
-the ratio of :math:`\Delta t` to :math:`\Delta x` constant. These tests were run with the 6th order accurate
-spatial stencil so that the temporal error dominated the spatial error. Here we recover the expected 3rd order
-accuracy of the RK3 scheme.
-
 .. |aconv| image:: figures/conv_plot_spatial.png
  :width: 300
 
-.. |bconv| image:: figures/conv_plot_temporal.png
+.. |bconv| image:: figures/conv_plot_spatial_WENO.png
  :width: 300
 
-.. _fig:convergence
+.. _fig:convergence_spatial
 
-.. table:: Convergence studies of spatial and temporal error
+.. table:: Convergence studies of spatial error
 
  +-----------------------------------------------------+------------------------------------------------------+
  | |aconv| | |bconv| |
  +-----------------------------------------------------+------------------------------------------------------+
- | Spatial convergence study  | Temporal convergence study   |
+ | Spatial convergence study (centered/upwind) | Temporal convergence study (WENO) |
  +-----------------------------------------------------+------------------------------------------------------+
 
+The second study tests the temporal accuracy by first setting :math:`\Delta t = 0.0005`
+and :math:`\Delta x = 1/8`, then reducing both :math:`\Delta t` and :math:`\Delta x` by a factor of two, keeping
+the ratio of :math:`\Delta t` to :math:`\Delta x` constant. These tests were run with the 6th order accurate
+spatial stencil so that the temporal error dominated the spatial error. Here we recover the expected 3rd order
+accuracy of the RK3 scheme.
+
+.. |tconv| image:: figures/conv_plot_temporal.png
+ :width: 300
+
+.. _fig:convergence_temporal
+
+.. table:: Convergence studies of temporal error
+
+ +-----------------------------------------------------+
+ | |tconv| |
+ +-----------------------------------------------------+
+ | Temporal convergence study |
+ +-----------------------------------------------------+
+
 
 Nonlinear Density Current
 ---------------------------