add stokes problem

examples/problems/stokes.py

@@ -0,0 +1,45 @@
+import numpy as np
+import torch
+
+from pina.problem import SpatialProblem
+from pina.operators import nabla, grad, div
+from pina import Condition, Span, LabelTensor
+
+
+class Stokes(SpatialProblem):
+
+    spatial_variables = ['x', 'y']
+    output_variables = ['ux', 'uy', 'p']
+    domain = Span({'x': [-2, 2], 'y': [-1, 1]})
+
+    def momentum(input_, output_):
+        #print(nabla(output_['ux', 'uy'], input_))
+        #print(grad(output_['p'], input_))
+        nabla_ = LabelTensor.hstack([
+            LabelTensor(nabla(output_['ux'], input_), ['x']),
+            LabelTensor(nabla(output_['uy'], input_), ['y'])])
+        #return LabelTensor(nabla_.tensor + grad(output_['p'], input_).tensor, ['x', 'y'])
+        return nabla_.tensor + grad(output_['p'], input_).tensor
+
+    def continuity(input_, output_):
+        return div(output_['ux', 'uy'], input_)
+
+    def inlet(input_, output_):
+        value = 2.0
+        return output_['ux'] - value
+
+    def outlet(input_, output_):
+        value = 0.0
+        return output_['p'] - value
+
+    def wall(input_, output_):
+        value = 0.0
+        return output_['ux', 'uy'].tensor - value
+
+    conditions = {
+        'gamma_top': Condition(Span({'x': [-2, 2], 'y':  1}), wall),
+        'gamma_bot': Condition(Span({'x': [-2, 2], 'y': -1}), wall),
+        'gamma_out': Condition(Span({'x':  2, 'y': [-1, 1]}), outlet),
+        'gamma_in':  Condition(Span({'x': -2, 'y': [-1, 1]}), inlet),
+        'D': Condition(Span({'x': [-2, 2], 'y': [-1, 1]}), [momentum, continuity]),
+    }