Merge pull request #287 from opesci/con_ex

Update example to a smoother version

docs/tutorials.rst

@@ -23,6 +23,9 @@ Devito rather than pure CFD or finite difference theory.
 * `01 - Linear convection
   <http://nbviewer.jupyter.org/github/opesci/devito/blob/master/examples/cfd/test_01_convection.ipynb>`_
   - Building a linear operator with simple zero BCs.
+* `01b - Linear convection, revisisted
+  <http://nbviewer.jupyter.org/github/opesci/devito/blob/master/examples/cfd/test_01_convection_revisited.ipynb>`_
+  - The above example, with a different initial condition.
 * `02 - Nonlinear convection
   <http://nbviewer.jupyter.org/github/opesci/devito/blob/master/examples/cfd/test_02_convection_nonlinear.ipynb>`_
   - Building an operator with coupled equations and simple BCs.

examples/cfd/tools.py

@@ -48,3 +48,23 @@ def init_hat(field, dx, dy, value=2., bgvalue=1.):
     """
     field[:] = bgvalue
     field[int(.5 / dx):int(1 / dx + 1), int(.5 / dy):int(1 / dy + 1)] = value
+
+
+def gaussian(x, mu, sig):
+    return np.exp(-np.power(x - mu, 2.) / (2 * np.power(sig, 2.)))
+
+
+def fin_bump(x):
+    if x <= 0 or x >= 1:
+        return 0
+    else:
+        return 100*np.exp(-1./(x-np.power(x, 2.)))
+
+
+def init_smooth(field, dx, dy):
+    nx, ny = field.shape
+    for ix in range(nx):
+        for iy in range(ny):
+            x = ix * dx
+            y = iy * dy
+            field[ix, iy] = fin_bump(x/1.5) * fin_bump(y/1.5) + 1.