Added separate function to apply Dirichlet BCs to any solution in RBC (#508)

Author: brownbaerchen

pySDC/implementations/problem_classes/RayleighBenard.py

@@ -152,7 +152,7 @@ def __init__(
         )
         self.add_BC(component='T', equation='T', axis=1, x=-1, v=self.BCs['T_bottom'], kind='Dirichlet', line=-1)
         self.add_BC(component='T', equation='T', axis=1, x=1, v=self.BCs['T_top'], kind='Dirichlet', line=-2)
-        self.add_BC(component='v', equation='v', axis=1, x=1, v=self.BCs['v_bottom'], kind='Dirichlet', line=-1)
+        self.add_BC(component='v', equation='v', axis=1, x=1, v=self.BCs['v_top'], kind='Dirichlet', line=-1)
         self.add_BC(component='v', equation='v', axis=1, x=-1, v=self.BCs['v_bottom'], kind='Dirichlet', line=-2)
         self.remove_BC(component='v', equation='v', axis=1, x=-1, kind='Dirichlet', line=-2, scalar=True)
         self.add_BC(component='u', equation='u', axis=1, v=self.BCs['u_top'], x=1, kind='Dirichlet', line=-2)
@@ -257,6 +257,45 @@ def u_exact(self, t=0, noise_level=1e-3, seed=99):
         else:
             return me
 
+    def apply_BCs(self, sol):
+        """
+        Enforce the Dirichlet BCs at the top and bottom for arbitrary solution.
+        The function modifies the last two modes of u, v, and T in order to achieve this.
+        Note that the pressure is not modified here and the Nyquist mode is not altered either.
+
+        Args:
+            sol: Some solution that does not need to enforce boundary conditions
+
+        Returns:
+            Modified version of the solution that satisfies Dirichlet BCs.
+        """
+        ultraspherical = self.spectral.axes[-1]
+
+        if self.spectral_space:
+            sol_half_hat = self.itransform(sol, axes=(-2,))
+        else:
+            sol_half_hat = self.transform(sol, axes=(-1,))
+
+        BC_bottom = ultraspherical.get_BC(x=-1, kind='dirichlet')
+        BC_top = ultraspherical.get_BC(x=1, kind='dirichlet')
+
+        M = np.array([BC_top[-2:], BC_bottom[-2:]])
+        M_I = np.linalg.inv(M)
+        rhs = np.empty((2, self.nx), dtype=complex)
+        for component in ['u', 'v', 'T']:
+            i = self.index(component)
+            rhs[0] = self.BCs[f'{component}_top'] - self.xp.sum(sol_half_hat[i, :, :-2] * BC_top[:-2], axis=1)
+            rhs[1] = self.BCs[f'{component}_bottom'] - self.xp.sum(sol_half_hat[i, :, :-2] * BC_bottom[:-2], axis=1)
+
+            BC_vals = M_I @ rhs
+
+            sol_half_hat[i, :, -2:] = BC_vals.T
+
+        if self.spectral_space:
+            return self.transform(sol_half_hat, axes=(-2,))
+        else:
+            return self.itransform(sol_half_hat, axes=(-1,))
+
     def get_fig(self):  # pragma: no cover
         """
         Get a figure suitable to plot the solution of this problem

pySDC/tests/test_problems/test_RayleighBenard.py

@@ -286,10 +286,36 @@ def test_Nyquist_mode_elimination():
     assert np.allclose(u[:, Nyquist_mode_index, :], 0)
 
 
+@pytest.mark.mpi4py
+def test_apply_BCs():
+    from pySDC.implementations.problem_classes.RayleighBenard import RayleighBenard
+    import numpy as np
+
+    BCs = {
+        'u_top': np.random.rand(),
+        'u_bottom': np.random.rand(),
+        'v_top': np.random.rand(),
+        'v_bottom': np.random.rand(),
+        'T_top': np.random.rand(),
+        'T_bottom': np.random.rand(),
+    }
+    P = RayleighBenard(nx=5, nz=2**2, BCs=BCs)
+
+    u_in = P.u_init
+    u_in[...] = np.random.rand(*u_in.shape)
+    u_in_hat = P.transform(u_in)
+
+    u_hat = P.apply_BCs(u_in_hat)
+    u = P.itransform(u_hat)
+
+    P.check_BCs(u)
+
+
 if __name__ == '__main__':
     # test_eval_f(2**0, 2**2, 'z', True)
     # test_Poisson_problem(1, 'T')
-    test_Poisson_problem_v()
+    # test_Poisson_problem_v()
+    test_apply_BCs()
     # test_Nusselt_numbers(1)
     # test_buoyancy_computation()
     # test_viscous_dissipation()