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| 1 | +#! /usr/bin/env python3 |
| 2 | + |
| 3 | +from nutils import cli, mesh, function, solver, export |
| 4 | +import functools |
| 5 | +import treelog |
| 6 | +import numpy as np |
| 7 | +import precice |
| 8 | + |
| 9 | + |
| 10 | +def main(side='Dirichlet', n=10, degree=1, timestep=.1, alpha=3., beta=1.3): |
| 11 | + |
| 12 | + if side == 'Dirichlet': |
| 13 | + x_grid = np.linspace(0, 1, n) |
| 14 | + elif side == 'Neumann': |
| 15 | + x_grid = np.linspace(1, 2, n) |
| 16 | + else: |
| 17 | + raise Exception('invalid side {!r}'.format(side)) |
| 18 | + y_grid = np.linspace(0, 1, n) |
| 19 | + |
| 20 | + # define the Nutils mesh |
| 21 | + domain, geom = mesh.rectilinear([x_grid, y_grid]) |
| 22 | + coupling_boundary = domain.boundary['right' if side == 'Dirichlet' else 'left'] |
| 23 | + read_sample = coupling_boundary.sample('gauss', degree=degree * 2) |
| 24 | + |
| 25 | + # Nutils namespace |
| 26 | + ns = function.Namespace() |
| 27 | + ns.x = geom |
| 28 | + ns.basis = domain.basis('std', degree=degree) |
| 29 | + ns.alpha = alpha # parameter of problem |
| 30 | + ns.beta = beta # parameter of problem |
| 31 | + ns.u = 'basis_n ?lhs_n' # solution |
| 32 | + ns.dudt = 'basis_n (?lhs_n - ?lhs0_n) / ?dt' # time derivative |
| 33 | + ns.flux = 'basis_n ?fluxdofs_n' # heat flux |
| 34 | + ns.f = 'beta - 2 - 2 alpha' # rhs |
| 35 | + ns.uexact = '1 + x_0 x_0 + alpha x_1 x_1 + beta ?t' # analytical solution |
| 36 | + ns.readbasis = read_sample.basis() |
| 37 | + ns.readfunc = 'readbasis_n ?readdata_n' |
| 38 | + |
| 39 | + # define the weak form |
| 40 | + res = domain.integral('(basis_n dudt - basis_n f + basis_n,i u_,i) d:x' @ ns, degree=degree * 2) |
| 41 | + |
| 42 | + # set boundary conditions at non-coupling boundaries |
| 43 | + # top and bottom boundary are non-coupling for both sides |
| 44 | + sqr = domain.boundary['top,bottom,left' if side == 'Dirichlet' |
| 45 | + else 'top,bottom,right'].integral('(u - uexact)^2 d:x' @ ns, degree=degree * 2) |
| 46 | + |
| 47 | + if side == 'Dirichlet': |
| 48 | + sqr += read_sample.integral('(u - readfunc)^2 d:x' @ ns) |
| 49 | + else: |
| 50 | + res += read_sample.integral('basis_n readfunc d:x' @ ns) |
| 51 | + |
| 52 | + # preCICE setup |
| 53 | + interface = precice.Interface(side, "../precice-config.xml", 0, 1) |
| 54 | + |
| 55 | + mesh_id_read = interface.get_mesh_id("Dirichlet-Mesh" if side == "Dirichlet" else "Neumann-Mesh") |
| 56 | + mesh_id_write = interface.get_mesh_id("Neumann-Mesh" if side == "Dirichlet" else "Dirichlet-Mesh") |
| 57 | + |
| 58 | + vertex_ids_read = interface.set_mesh_vertices(mesh_id_read, read_sample.eval(ns.x)) |
| 59 | + interface.set_mesh_access_region(mesh_id_write, [.9, 1.1, -.1, 1.1]) |
| 60 | + |
| 61 | + precice_dt = interface.initialize() |
| 62 | + |
| 63 | + vertex_ids_write, coords = interface.get_mesh_vertices_and_ids(mesh_id_write) |
| 64 | + write_sample = domain.locate(ns.x, coords, eps=1e-10, tol=1e-10) |
| 65 | + precice_write = functools.partial(interface.write_block_scalar_data, interface.get_data_id( |
| 66 | + "Heat-Flux" if side == "Dirichlet" else "Temperature", mesh_id_write), vertex_ids_write) |
| 67 | + precice_read = functools.partial(interface.read_block_scalar_data, interface.get_data_id( |
| 68 | + "Temperature" if side == "Dirichlet" else "Heat-Flux", mesh_id_read), vertex_ids_read) |
| 69 | + |
| 70 | + # helper functions to project heat flux to coupling boundary |
| 71 | + if side == 'Dirichlet': |
| 72 | + # To communicate the flux to the Neumann side we should not simply |
| 73 | + # evaluate u_,i n_i as this is an unbounded term leading to suboptimal |
| 74 | + # convergence. Instead we project ∀ v: ∫_Γ v flux = ∫_Γ v u_,i n_i and |
| 75 | + # evaluate flux. While the right-hand-side contains the same unbounded |
| 76 | + # term, we can use the strong identity du/dt - u_,ii = f to rewrite it |
| 77 | + # to ∫_Ω [v (du/dt - f) + v_,i u_,i] - ∫_∂Ω\Γ v u_,k n_k, in which we |
| 78 | + # recognize the residual and an integral over the exterior boundary. |
| 79 | + # While the latter still contains the problematic unbounded term, we |
| 80 | + # can use the fact that the flux is a known value at the top and bottom |
| 81 | + # via the Dirichlet boundary condition, and impose it as constraints. |
| 82 | + right_sqr = domain.boundary['right'].integral('flux^2 d:x' @ ns, degree=degree * 2) |
| 83 | + right_cons = solver.optimize('fluxdofs', right_sqr, droptol=1e-10) |
| 84 | + # right_cons is NaN in dofs that are NOT supported on the right boundary |
| 85 | + flux_sqr = domain.boundary['right'].boundary['top,bottom'].integral( |
| 86 | + '(flux - uexact_,0)^2 d:x' @ ns, degree=degree * 2) |
| 87 | + flux_cons = solver.optimize('fluxdofs', flux_sqr, droptol=1e-10, |
| 88 | + constrain=np.choose(np.isnan(right_cons), [np.nan, 0.])) |
| 89 | + # flux_cons is NaN in dofs that are supported on ONLY the right boundary |
| 90 | + flux_res = read_sample.integral('basis_n flux d:x' @ ns) - res |
| 91 | + |
| 92 | + # write initial data |
| 93 | + if interface.is_action_required(precice.action_write_initial_data()): |
| 94 | + precice_write(write_sample.eval(0.)) |
| 95 | + interface.mark_action_fulfilled(precice.action_write_initial_data()) |
| 96 | + |
| 97 | + interface.initialize_data() |
| 98 | + |
| 99 | + t = 0. |
| 100 | + istep = 0 |
| 101 | + |
| 102 | + # initial condition |
| 103 | + sqr0 = domain.integral('(u - uexact)^2' @ ns, degree=degree * 2) |
| 104 | + lhs = solver.optimize('lhs', sqr0, arguments=dict(t=t)) |
| 105 | + bezier = domain.sample('bezier', degree * 2) |
| 106 | + |
| 107 | + while interface.is_coupling_ongoing(): |
| 108 | + |
| 109 | + # save checkpoint |
| 110 | + if interface.is_action_required(precice.action_write_iteration_checkpoint()): |
| 111 | + checkpoint = lhs, t, istep |
| 112 | + interface.mark_action_fulfilled(precice.action_write_iteration_checkpoint()) |
| 113 | + |
| 114 | + # read data from interface |
| 115 | + read_data = precice_read() |
| 116 | + |
| 117 | + # prepare next timestep |
| 118 | + lhs0 = lhs |
| 119 | + istep += 1 |
| 120 | + dt = min(timestep, precice_dt) |
| 121 | + t += dt |
| 122 | + |
| 123 | + # update (time-dependent) boundary condition |
| 124 | + cons = solver.optimize('lhs', sqr, droptol=1e-15, arguments=dict(t=t, readdata=read_data)) |
| 125 | + |
| 126 | + # solve nutils timestep |
| 127 | + lhs = solver.solve_linear('lhs', res, constrain=cons, arguments=dict(lhs0=lhs0, dt=dt, t=t, readdata=read_data)) |
| 128 | + |
| 129 | + # write data to interface |
| 130 | + if side == 'Dirichlet': |
| 131 | + fluxdofs = solver.solve_linear( |
| 132 | + 'fluxdofs', flux_res, arguments=dict( |
| 133 | + lhs0=lhs0, lhs=lhs, dt=dt, t=t), constrain=flux_cons) |
| 134 | + write_data = write_sample.eval('flux' @ ns, fluxdofs=fluxdofs) |
| 135 | + else: |
| 136 | + write_data = write_sample.eval('u' @ ns, lhs=lhs) |
| 137 | + precice_write(write_data) |
| 138 | + |
| 139 | + # do the coupling |
| 140 | + precice_dt = interface.advance(dt) |
| 141 | + |
| 142 | + # read checkpoint if required |
| 143 | + if interface.is_action_required(precice.action_read_iteration_checkpoint()): |
| 144 | + lhs, t, istep = checkpoint |
| 145 | + interface.mark_action_fulfilled(precice.action_read_iteration_checkpoint()) |
| 146 | + else: |
| 147 | + # generate output |
| 148 | + x, u, uexact = bezier.eval(['x_i', 'u', 'uexact'] @ ns, lhs=lhs, t=t) |
| 149 | + with treelog.add(treelog.DataLog()): |
| 150 | + export.vtk(side + "-" + str(istep), bezier.tri, x, Temperature=u, reference=uexact) |
| 151 | + |
| 152 | + interface.finalize() |
| 153 | + |
| 154 | + |
| 155 | +if __name__ == '__main__': |
| 156 | + cli.run(main) |
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