add readme description

README.md

@@ -24,15 +24,23 @@ of transport equations with the MPDATA numerical scheme in a
 hybrid parallelisation model with both multi-threading and MPI distributed memory communication.
 PyMPDATA-MPI adapts to API of PyMPDATA offering domain decomposition logic.
 
-## Hello world example
+## Hello world examples
 
 In a minimal setup, PyMPDATA-MPI can be used to solve the following transport equation: 
 $$\partial_t (G \psi) + \nabla \cdot (Gu \psi)= 0$$
 in an environment with multiple nodes.
-In two dimensions (x,y), MPI (Message Passing Interface) is used 
-  for handling data transfers and synchronisation in the outer dimension,
-  while multi-threading (using, e.g., OpenMP via Numba) is used in the inner dimension.
-Every worker is responsible for computing its part of the decomposed domain as depicted below:
+Every node (process) is responsible for computing its part of the decomposed domain.
+
+### Spherical scenario (2D)
+
+In spherical geometry, the $$G$$ factor represents the Jacobian of coordinate transformation.
+In this example (based on a test case from [Williamson & Rasch 1989](https://doi.org/10.1175/1520-0493(1989)117<0102:TDSLTW>2.0.CO;2)),
+  domain decomposition is done cutting the sphere along meridians.
+The inner dimension uses the [`MPIPolar`](https://open-atmos.github.io/PyMPDATA-MPI/mpi_polar.html) 
+  boundary condition class, while the outer dimension uses
+  [`MPIPeriodic`](https://open-atmos.github.io/PyMPDATA-MPI/mpi_periodic.html).
+Note that the spherical animations below depict simulations without MPDATA corrective iterations,
+  i.e. only plain first-order upwind scheme is used (FIXME).
 
 ### 1 worker
 <p align="middle">
@@ -45,6 +53,14 @@ Every worker is responsible for computing its part of the decomposed domain as d
   <img src="https://github.com/open-atmos/PyMPDATA-MPI/releases/download/latest-generated-plots/n_iters.1_rank_1_size_2_c_field_.0.5.0.25.-SphericalScenario-anim.gif" width="49%" /> 
 </p>
 
+### Cartesian scenario (2D)
+
+In the carthesian example below (based on a test case from [Arabas et al. 2014](https://doi.org/10.3233/SPR-140379)),
+  a constant advector field $$u$$ is used (and $$G=1$$).
+MPI (Message Passing Interface) is used 
+  for handling data transfers and synchronisation in the outer dimension,
+  while multi-threading (using, e.g., OpenMP via Numba) is used in the inner dimension.
+
 ### 1 worker
 <p align="middle">
   <img src="https://github.com/open-atmos/PyMPDATA-MPI/releases/download/latest-generated-plots/n_iters.3_rank_0_size_1_c_field_.0.5.0.25.-CartesianScenario-anim.gif" width="49%" /> 

scenarios/spherical.py

@@ -131,13 +131,11 @@ def __init__(
         Cx_max = np.amax(
             np.abs((advector_x[1:, :] + advector_x[:-1, :]) / 2 / g_factor_z)
         )
-        print(Cx_max)
         assert Cx_max < 1
 
         Cy_max = np.amax(
             np.abs((advector_y[:, 1:] + advector_y[:, :-1]) / 2 / g_factor_z)
         )
-        print(Cy_max)
         assert Cy_max < 1
         # TODO #81: </move out>