#!/usr/bin/env python # -*- coding: utf-8 -*- """ *********************************************************************************** tutorial_dealii_9.py DAE Tools: pyDAE module, www.daetools.com Copyright (C) Dragan Nikolic *********************************************************************************** DAE Tools is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License version 3 as published by the Free Software Foundation. DAE Tools is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with the DAE Tools software; if not, see <http://www.gnu.org/licenses/>. ************************************************************************************ """ __doc__ = """ In this example the 2D lid driven cavity problem is solved (`deal.II step-57 <https://www.dealii.org/8.5.0/doxygen/deal.II/step_57.html>`_ and `Lid-driven cavity problem <http://www.cfd-online.com/Wiki/Lid-driven_cavity_problem>`_). The problem can be described using the incompressible Navier-Stokes equations: .. code-block:: none du/dt + u div(u) + nabla(p) = 0, in Omega -div(u) = 0 in Omega The mesh is a simple square (0,1)x(0,1): .. image:: _static/square(0,1)x(0,1)-50x50.png :width: 300 px The temperature and the velocity vectors plot: .. image:: _static/tutorial_dealii_9-results.png :height: 400 px Animation: .. image:: _static/tutorial_dealii_9-animation.gif :height: 400 px """ import os, sys, numpy, json, tempfile, random from time import localtime, strftime from daetools.pyDAE import * from daetools.solvers.deal_II import * from daetools.solvers.superlu import pySuperLU as superlu # Standard variable types are defined in variable_types.py from pyUnits import m, kg, s, K, Pa, mol, J, W class WallVelocityFunction_2D(adoubleFunction_2D): def __init__(self, n_components = 1): adoubleFunction_2D.__init__(self, n_components) self.n_components = n_components def vector_value(self, point): values = [adouble(0.0)] * self.n_components values[0] = adouble(0.0) # ux component values[1] = adouble(0.0) # uy component return values # Velocity x-component: u_lid = 0.1 class LidVelocityFunction_2D(adoubleFunction_2D): def __init__(self, n_components = 1): adoubleFunction_2D.__init__(self, n_components) self.n_components = n_components def vector_value(self, point): values = [adouble(0.0)] * self.n_components values[0] = adouble(u_lid) # ux component values[1] = adouble(0.0) # uy component return values u_t = daeVariableType("u_t", unit(), 0.0, 1E20, 0, 1e-07) p_t = daeVariableType("p_t", unit(), 0.0, 1E20, 0, 1e-07) class modTutorial(daeModel): def __init__(self, Name, Parent = None, Description = ""): daeModel.__init__(self, Name, Parent, Description) FE_degree = 1 dofs = [dealiiFiniteElementDOF_2D(name = 'u', description = 'Velocity', fe = FE_Q_2D(FE_degree+1), multiplicity = 2, variableType = u_t), dealiiFiniteElementDOF_2D(name = 'p', description = 'Pressure', fe = FE_Q_2D(FE_degree), multiplicity = 1, variableType = p_t)] self.n_components = int(numpy.sum([dof.Multiplicity for dof in dofs])) meshes_dir = os.path.join(os.path.dirname(os.path.abspath(__file__)), 'meshes') mesh_file = os.path.join(meshes_dir, 'square(0,1)x(0,1)-64x64.msh') # Store the object so it does not go out of scope while still in use by daetools self.fe_system = dealiiFiniteElementSystem_2D(meshFilename = mesh_file, # path to mesh quadrature = QGauss_2D(3), # quadrature formula faceQuadrature = QGauss_1D(3), # face quadrature formula dofs = dofs) # degrees of freedom self.fe_model = daeFiniteElementModel('NavierStokes', self, 'The NavierStokes equations', self.fe_system) def DeclareEquations(self): daeModel.DeclareEquations(self) # Boundary IDs left_edge = 0 top_edge = 1 right_edge = 2 bottom_edge = 3 # Create some auxiliary objects for readability phi_p_i = phi_2D('p', fe_i, fe_q) phi_p_j = phi_2D('p', fe_j, fe_q) dphi_p_i = dphi_2D('p', fe_i, fe_q) dphi_p_j = dphi_2D('p', fe_j, fe_q) phi_vector_u_i = phi_vector_2D('u', fe_i, fe_q) phi_vector_u_j = phi_vector_2D('u', fe_j, fe_q) dphi_vector_u_i = dphi_vector_2D('u', fe_i, fe_q) dphi_vector_u_j = dphi_vector_2D('u', fe_j, fe_q) div_phi_u_i = div_phi_2D('u', fe_i, fe_q) div_phi_u_j = div_phi_2D('u', fe_j, fe_q) scalar_product = feExpression_2D.scalar_product # FE approximation of the gradient of u at the specified quadrature point (Tensor<2,dim,adouble> object) du_dof = vector_dof_gradient_approximation_2D('u', fe_q) u_dof = vector_dof_approximation_2D('u', fe_q) du_dof = vector_dof_gradient_approximation_2D('u', fe_q) normal = normal_2D(fe_q) xyz = xyz_2D(fe_q) JxW = JxW_2D(fe_q) mu = 1.0/400 dirichletBC = {} dirichletBC[left_edge] = [('p', adoubleConstantFunction_2D(adouble(0.0))), ('u', WallVelocityFunction_2D(self.n_components))] dirichletBC[top_edge] = [('p', adoubleConstantFunction_2D(adouble(0.0))), ('u', LidVelocityFunction_2D(self.n_components))] dirichletBC[right_edge] = [('p', adoubleConstantFunction_2D(adouble(0.0))), ('u', WallVelocityFunction_2D(self.n_components))] dirichletBC[bottom_edge] = [('p', adoubleConstantFunction_2D(adouble(0.0))), ('u', WallVelocityFunction_2D(self.n_components))] # Contributions from the Navie-Stokes equation: Aij_u_viscosity = mu * scalar_product(dphi_vector_u_i, dphi_vector_u_j) * JxW #Aij_u_convection = (JxW, du_dof*phi_vector_u_i, phi_vector_u_j) Aij_u_convection1 = (u_dof, phi_vector_u_i, dphi_vector_u_j * JxW) #Aij_u_convection2 = (0.5 * JxW, du_dof * phi_vector_u_i, phi_vector_u_j) Aij_p_gradient = -(div_phi_u_i * phi_p_j) * JxW # Contributions from the continuity equation: Aij_continuity = -(phi_p_i * div_phi_u_j) * JxW # Total contributions: Mij = 0 * JxW Aij = [Aij_u_viscosity + Aij_p_gradient + Aij_continuity, Aij_u_convection1] Fi = 0 * JxW weakForm = dealiiFiniteElementWeakForm_2D(Aij = Aij, Mij = Mij, Fi = Fi, functionsDirichletBC = dirichletBC) self.fe_system.WeakForm = weakForm class simTutorial(daeSimulation): def __init__(self): daeSimulation.__init__(self) self.m = modTutorial("tutorial_dealii_9") self.m.Description = __doc__ self.m.fe_model.Description = __doc__ def SetUpParametersAndDomains(self): pass def SetUpVariables(self): pass def run(**kwargs): guiRun = kwargs.get('guiRun', False) simulation = simTutorial() # Create SuperLU LA solver lasolver = pySuperLU.daeCreateSuperLUSolver() # Create and setup two data reporters: datareporter = daeDelegateDataReporter() simName = simulation.m.Name + strftime(" [%d.%m.%Y %H:%M:%S]", localtime()) if guiRun: results_folder = tempfile.mkdtemp(suffix = '-results', prefix = 'tutorial_deal_II_9-') daeQtMessage("deal.II", "The simulation results will be located in: %s" % results_folder) else: results_folder = os.path.join(os.path.dirname(os.path.abspath(__file__)), 'tutorial_deal_II_9-results') print("The simulation results will be located in: %s" % results_folder) # 1. deal.II (exports only FE DOFs in .vtk format to the specified directory) feDataReporter = simulation.m.fe_system.CreateDataReporter() datareporter.AddDataReporter(feDataReporter) if not feDataReporter.Connect(results_folder, simName): sys.exit() # 2. TCP/IP tcpipDataReporter = daeTCPIPDataReporter() datareporter.AddDataReporter(tcpipDataReporter) if not tcpipDataReporter.Connect("", simName): sys.exit() return daeActivity.simulate(simulation, reportingInterval = 1, timeHorizon = 1, lasolver = lasolver, datareporter = datareporter, **kwargs) if __name__ == "__main__": guiRun = False if (len(sys.argv) > 1 and sys.argv[1] == 'console') else True run(guiRun = guiRun)