Merge pull request #2685 from TomFischer/LineSourceTerm

Implementation of source terms for lines

Documentation/ProjectFile/prj/process_variables/process_variable/source_terms/source_term/Line/c_Line.md

+Declares a source term that is defined on a line shaped domain.

Documentation/ProjectFile/prj/process_variables/process_variable/source_terms/source_term/Line/t_parameter.md

+The name of the parameter that defines the value that should be used for the source
+term. The parameter have to defined on the line domain.
+
+The user should carefully check which physical quantity that parameter is.

ProcessLib/HeatConduction/Tests.cmake

@@ -127,3 +127,112 @@ AddTest(
         t2_1D2bt_pcs_0_ts_1500_t_3888.000000.vtu t2_1D2bt_pcs_0_ts_1500_t_3888.000000.vtu temperature temperature 10e-12 0.0
         REQUIREMENTS NOT OGS_USE_MPI
 )
+
+AddTest(
+        NAME HeatConduction_1D_LineSourceTerm
+        PATH
+        Parabolic/T/1D_line_source_term_tests/
+        EXECUTABLE ogs
+        EXECUTABLE_ARGS line_source_term.prj
+        TESTER vtkdiff
+        DIFF_DATA
+        mesh_1_line_100.vtu source_term_at_entire_line_pcs_0_ts_1_t_1.000000.vtu analytical_temperature temperature 1e-13 1e-13
+        REQUIREMENTS NOT OGS_USE_MPI
+)
+
+# tests for line source term implementation
+AddTest(
+        NAME HeatConduction_2D_LineSourceTermLeft
+        PATH Parabolic/T/2D_source_term_tests/line_source_term_left
+        EXECUTABLE ogs
+        EXECUTABLE_ARGS source_term_left.prj
+        TESTER vtkdiff
+        DIFF_DATA
+        source_term_left_pcs_0_ts_1_t_1.000000.vtu source_term_left_pcs_0_ts_1_t_1.000000.vtu temperature temperature 1e-15 0.0
+        source_term_left_pcs_0_ts_1_t_1.000000.vtu source_term_left_pcs_0_ts_1_t_1.000000.vtu heat_flux_x heat_flux_x 1e-15 0.0
+        REQUIREMENTS NOT OGS_USE_MPI
+)
+
+# For the special setup with a 'dirac' line source term at x=0.5 the
+# analytical solution in 2 dimensions is valid:
+# u(x,y) = -ln(sqrt((x-0.5)^2))/(2 * Pi)
+AddTest(
+        NAME HeatConduction_2D_LineSourceTermMiddle
+        PATH Parabolic/T/2D_source_term_tests/line_source_term_x_0.5
+        EXECUTABLE ogs
+        EXECUTABLE_ARGS line_source_term_x_0.5.prj
+        TESTER vtkdiff
+        DIFF_DATA
+        source_term_middle_pcs_0_ts_1_t_1.000000.vtu source_term_middle_pcs_0_ts_1_t_1.000000.vtu temperature temperature 4e-15 2e-14
+        source_term_middle_pcs_0_ts_1_t_1.000000.vtu source_term_middle_pcs_0_ts_1_t_1.000000.vtu heat_flux_x heat_flux_x 7e-14 0.0
+        REQUIREMENTS NOT OGS_USE_MPI
+)
+
+AddTest(
+        NAME HeatConduction_2D_LineSourceTermMiddle_Restricted
+        PATH
+        Parabolic/T/2D_source_term_tests/line_source_term_x_0.5_restricted_to_middle
+        EXECUTABLE ogs
+        EXECUTABLE_ARGS line_source_term_x_0.5.prj
+        TESTER vtkdiff
+        DIFF_DATA
+        source_term_middle_restricted_pcs_0_ts_1_t_1.000000.vtu source_term_middle_restricted_pcs_0_ts_1_t_1.000000.vtu temperature temperature 1e-15 0.0
+        source_term_middle_restricted_pcs_0_ts_1_t_1.000000.vtu source_term_middle_restricted_pcs_0_ts_1_t_1.000000.vtu heat_flux_x heat_flux_x 3e-15 4e-7
+        REQUIREMENTS NOT OGS_USE_MPI
+)
+
+# tests for line source term implementation on a cubic domain
+AddTest(
+        NAME HeatConduction_3D_LineSourceTermMiddle
+        PATH
+        Parabolic/T/3D_line_source_term_tests/3D_line_source_term_middle
+        EXECUTABLE ogs
+        EXECUTABLE_ARGS line_source_term_x_0.5_y_0.5.prj
+        TESTER vtkdiff
+        DIFF_DATA
+        3D_line_source_term_pcs_0_ts_1_t_1.000000.vtu 3D_line_source_term_pcs_0_ts_1_t_1.000000.vtu temperature temperature 1e-15 0.0
+        3D_line_source_term_pcs_0_ts_1_t_1.000000.vtu 3D_line_source_term_pcs_0_ts_1_t_1.000000.vtu heat_flux_x heat_flux_x 7e-15 7e-13
+        REQUIREMENTS NOT OGS_USE_MPI
+)
+
+# tests for line source term implementation on a cubic domain
+AddTest(
+        NAME HeatConduction_3D_LineSourceTermMiddle_Restricted
+        PATH
+        Parabolic/T/3D_line_source_term_tests/3D_line_source_term_middle_restricted
+        EXECUTABLE ogs
+        EXECUTABLE_ARGS line_source_term_x_0.5_y_0.5_restricted.prj
+        TESTER vtkdiff
+        DIFF_DATA
+        3D_line_source_term_restricted_pcs_0_ts_1_t_1.000000.vtu 3D_line_source_term_restricted_pcs_0_ts_1_t_1.000000.vtu temperature temperature 1e-15 0.0
+        3D_line_source_term_restricted_pcs_0_ts_1_t_1.000000.vtu 3D_line_source_term_restricted_pcs_0_ts_1_t_1.000000.vtu heat_flux_x heat_flux_x 1.1e-15 5e-12
+        REQUIREMENTS NOT OGS_USE_MPI
+)
+
+# tests for line source term implementation on a cylindrical domain
+# For the special setup with a line source term at position (xi, eta) the
+# analytical solution in 2 dimensions is valid:
+# u(x,y) = -ln(sqrt((x-xi)^2+(y-eta)^2))/(2 * Pi)
+AddTest(
+        NAME HeatConduction_3D_LineSourceTermInMiddleOfCylinder_49k_prisms
+        PATH
+        Parabolic/T/3D_line_source_term_tests/3D_line_source_term_in_cylinder/49k_prisms
+        EXECUTABLE ogs
+        EXECUTABLE_ARGS line_source_term_in_cylinder.prj
+        TESTER vtkdiff
+        DIFF_DATA
+        Cylinder_r_1_h_1_prism_49k.vtu 3D_line_source_term_in_cylinder_49k_pcs_0_ts_1_t_1.000000.vtu analytical_solution_temperature temperature 0.2 0.0
+        REQUIREMENTS NOT OGS_USE_MPI
+)
+
+AddTest(
+        NAME LARGE_HeatConduction_3D_LineSourceTermInMiddleOfCylinder_286k_prisms
+        PATH
+        Parabolic/T/3D_line_source_term_tests/3D_line_source_term_in_cylinder/286k_prisms
+        EXECUTABLE ogs
+        EXECUTABLE_ARGS line_source_term_in_cylinder.prj
+        TESTER vtkdiff
+        DIFF_DATA
+        Cylinder_r_1_h_1_prism_286k.vtu 3D_line_source_term_in_cylinder_286k_pcs_0_ts_1_t_1.000000.vtu analytical_solution_temperature temperature 4e-3 0.0
+        REQUIREMENTS NOT OGS_USE_MPI
+)

ProcessLib/SourceTerms/CreateLineSourceTerm.cpp

+/**
+ * \file
+ * \copyright
+ * Copyright (c) 2012-2019, OpenGeoSys Community (http://www.opengeosys.org)
+ *            Distributed under a Modified BSD License.
+ *              See accompanying file LICENSE.txt or
+ *              http://www.opengeosys.org/project/license
+ *
+ */
+
+#include "CreateLineSourceTerm.h"
+
+#include "BaseLib/ConfigTree.h"
+#include "BaseLib/FileTools.h"
+#include "MeshLib/Mesh.h"
+#include "NumLib/DOF/LocalToGlobalIndexMap.h"
+#include "ParameterLib/Utils.h"
+#include "LineSourceTerm.h"
+
+namespace ProcessLib
+{
+std::unique_ptr<SourceTerm> createLineSourceTerm(
+    BaseLib::ConfigTree const& config, unsigned const bulk_mesh_dimension,
+    MeshLib::Mesh const& source_term_mesh,
+    std::unique_ptr<NumLib::LocalToGlobalIndexMap> source_term_dof_table,
+    std::vector<std::unique_ptr<ParameterLib::ParameterBase>> const& parameters,
+    unsigned const integration_order, unsigned const shapefunction_order)
+{
+    //! \ogs_file_param{prj__process_variables__process_variable__source_terms__source_term__type}
+    config.checkConfigParameter("type", "Line");
+
+    DBUG("Constructing LineSourceTerm from config.");
+
+    // source term field name
+    auto const& line_source_term_parameter_name =
+        //! \ogs_file_param{prj__process_variables__process_variable__source_terms__source_term__Line__parameter}
+        config.getConfigParameter<std::string>("parameter");
+    auto& line_source_term = ParameterLib::findParameter<double>(
+        line_source_term_parameter_name, parameters, 1, &source_term_mesh);
+
+    DBUG("Using '%s' as line source term parameter.",
+         line_source_term.name.c_str());
+
+    return std::make_unique<LineSourceTerm>(
+        bulk_mesh_dimension, source_term_mesh, std::move(source_term_dof_table),
+        integration_order, shapefunction_order, line_source_term);
+}
+
+}  // namespace ProcessLib

ProcessLib/SourceTerms/CreateLineSourceTerm.h

+/**
+ * \file
+ * \copyright
+ * Copyright (c) 2012-2019, OpenGeoSys Community (http://www.opengeosys.org)
+ *            Distributed under a Modified BSD License.
+ *              See accompanying file LICENSE.txt or
+ *              http://www.opengeosys.org/project/license
+ *
+ */
+
+#pragma once
+
+#include <memory>
+#include <vector>
+
+namespace BaseLib
+{
+class ConfigTree;
+}
+
+namespace MeshLib
+{
+class Mesh;
+}
+
+namespace NumLib
+{
+class LocalToGlobalIndexMap;
+}
+
+namespace ParameterLib
+{
+struct ParameterBase;
+}
+
+namespace ProcessLib
+{
+class SourceTerm;
+
+std::unique_ptr<SourceTerm> createLineSourceTerm(
+    BaseLib::ConfigTree const& config, unsigned const bulk_mesh_dimension,
+    MeshLib::Mesh const& source_term_mesh,
+    std::unique_ptr<NumLib::LocalToGlobalIndexMap> source_term_dof_table,
+    std::vector<std::unique_ptr<ParameterLib::ParameterBase>> const& parameters,
+    unsigned const integration_order, unsigned const shapefunction_order);
+
+}   // namespace ProcessLib

ProcessLib/SourceTerms/CreateSourceTerm.cpp

@@ -10,6 +10,7 @@
 
 #include "CreateSourceTerm.h"
 
+#include "CreateLineSourceTerm.h"
 #include "CreateNodalSourceTerm.h"
 #include "CreateVolumetricSourceTerm.h"
 #ifdef OGS_USE_PYTHON
@@ -76,6 +77,22 @@ std::unique_ptr<SourceTerm> createSourceTerm(
             parameters);
     }
 
+    if (type == "Line")
+    {
+        std::unique_ptr<NumLib::LocalToGlobalIndexMap> dof_table_source_term(
+            dof_table_bulk.deriveBoundaryConstrainedMap(
+                variable_id, {*config.component_id},
+                std::move(source_term_mesh_subset)));
+        auto const& bulk_mesh_dimension =
+            dof_table_bulk.getMeshSubset(variable_id, *config.component_id)
+                .getMesh()
+                .getDimension();
+        return ProcessLib::createLineSourceTerm(
+            config.config, bulk_mesh_dimension, config.mesh,
+            std::move(dof_table_source_term), parameters, integration_order,
+            shapefunction_order);
+    }
+
     if (type == "Volumetric")
     {
         std::unique_ptr<NumLib::LocalToGlobalIndexMap> dof_table_source_term(

ProcessLib/SourceTerms/LineSourceTerm.cpp

+/**
+ * \file
+ * \copyright
+ * Copyright (c) 2012-2019, OpenGeoSys Community (http://www.opengeosys.org)
+ *            Distributed under a Modified BSD License.
+ *              See accompanying file LICENSE.txt or
+ *              http://www.opengeosys.org/project/license
+ *
+ */
+
+#include "LineSourceTerm.h"
+
+#include "ProcessLib/Utils/CreateLocalAssemblers.h"
+
+namespace ProcessLib
+{
+LineSourceTerm::LineSourceTerm(
+    unsigned const bulk_mesh_dimension, MeshLib::Mesh const& source_term_mesh,
+    std::unique_ptr<NumLib::LocalToGlobalIndexMap> source_term_dof_table,
+    unsigned const integration_order, unsigned const shapefunction_order,
+    ParameterLib::Parameter<double> const& line_source_term_parameter)
+    : SourceTerm(std::move(source_term_dof_table)),
+      _line_source_term_parameter(line_source_term_parameter)
+{
+    ProcessLib::createLocalAssemblers<LineSourceTermLocalAssembler>(
+        bulk_mesh_dimension, source_term_mesh.getElements(),
+        *_source_term_dof_table, shapefunction_order, _local_assemblers,
+        source_term_mesh.isAxiallySymmetric(), integration_order,
+        _line_source_term_parameter);
+}
+
+void LineSourceTerm::integrate(const double t, GlobalVector const& /*x*/,
+                               GlobalVector& b, GlobalMatrix* /*jac*/) const
+{
+    DBUG("Assemble LineSourceTerm.");
+
+    // Call global assembler for each local assembly item.
+    GlobalExecutor::executeMemberOnDereferenced(
+        &LineSourceTermLocalAssemblerInterface::integrate, _local_assemblers,
+        *_source_term_dof_table, t, b);
+}
+
+}  // namespace ProcessLib

ProcessLib/SourceTerms/LineSourceTerm.h

+/**
+ * \file
+ * \copyright
+ * Copyright (c) 2012-2019, OpenGeoSys Community (http://www.opengeosys.org)
+ *            Distributed under a Modified BSD License.
+ *              See accompanying file LICENSE.txt or
+ *              http://www.opengeosys.org/project/license
+ *
+ */
+
+#pragma once
+
+#include <memory>
+#include <vector>
+
+#include "SourceTerm.h"
+#include "LineSourceTermFEM.h"
+
+namespace ProcessLib
+{
+class LineSourceTerm final : public SourceTerm
+{
+public:
+    LineSourceTerm(
+        unsigned const bulk_mesh_dimension,
+        MeshLib::Mesh const& source_term_mesh,
+        std::unique_ptr<NumLib::LocalToGlobalIndexMap> source_term_dof_table,
+        unsigned const integration_order, unsigned const shapefunction_order,
+        ParameterLib::Parameter<double> const& line_source_term_parameter);
+
+    void integrate(const double t, GlobalVector const& x, GlobalVector& b,
+                   GlobalMatrix* jac) const override;
+
+private:
+    ParameterLib::Parameter<double> const& _line_source_term_parameter;
+    std::vector<std::unique_ptr<LineSourceTermLocalAssemblerInterface>>
+        _local_assemblers;
+};
+
+}  // namespace ProcessLib

ProcessLib/SourceTerms/LineSourceTermFEM.h

+/**
+ * \file
+ * \copyright
+ * Copyright (c) 2012-2019, OpenGeoSys Community (http://www.opengeosys.org)
+ *            Distributed under a Modified BSD License.
+ *              See accompanying file LICENSE.txt or
+ *              http://www.opengeosys.org/project/license
+ *
+ */
+
+#pragma once
+
+#include <vector>
+
+#include "MathLib/LinAlg/Eigen/EigenMapTools.h"
+#include "NumLib/DOF/DOFTableUtil.h"
+#include "NumLib/Fem/FiniteElement/TemplateIsoparametric.h"
+#include "ParameterLib/Parameter.h"
+#include "ProcessLib/LocalAssemblerTraits.h"
+#include "ProcessLib/Utils/InitShapeMatrices.h"
+
+namespace ProcessLib
+{
+class LineSourceTermLocalAssemblerInterface
+{
+public:
+    virtual void integrate(
+        std::size_t const id,
+        NumLib::LocalToGlobalIndexMap const& source_term_dof_table,
+        double const t, GlobalVector& b) = 0;
+    virtual ~LineSourceTermLocalAssemblerInterface() = default;
+};
+
+const unsigned NUM_NODAL_DOF = 1;
+
+template <typename ShapeFunction, typename IntegrationMethod,
+          unsigned GlobalDim>
+class LineSourceTermLocalAssembler final
+    : public LineSourceTermLocalAssemblerInterface
+{
+    using ShapeMatricesType = ShapeMatrixPolicyType<ShapeFunction, GlobalDim>;
+
+    using LocalAssemblerTraits = ProcessLib::LocalAssemblerTraits<
+        ShapeMatricesType, ShapeFunction::NPOINTS, NUM_NODAL_DOF, GlobalDim>;
+
+    using NodalVectorType = typename LocalAssemblerTraits::LocalVector;
+    using NodalRowVectorType = typename ShapeMatricesType::NodalRowVectorType;
+
+public:
+    LineSourceTermLocalAssembler(
+        MeshLib::Element const& element,
+        std::size_t const local_matrix_size,
+        bool const is_axially_symmetric,
+        unsigned const integration_order,
+        ParameterLib::Parameter<double> const& line_source_term_parameter)
+        : _parameter(line_source_term_parameter),
+          _integration_method(integration_order),
+          _local_rhs(local_matrix_size)
+    {
+        unsigned const n_integration_points =
+            _integration_method.getNumberOfPoints();
+
+        auto const shape_matrices =
+            initShapeMatrices<ShapeFunction, ShapeMatricesType,
+                              IntegrationMethod, GlobalDim>(
+                element, is_axially_symmetric, _integration_method);
+
+        for (unsigned ip = 0; ip < n_integration_points; ip++)
+        {
+            _ip_data.emplace_back(
+                _integration_method.getWeightedPoint(ip).getWeight() *
+                shape_matrices[ip].integralMeasure * shape_matrices[ip].detJ *
+                shape_matrices[ip].N);
+        }
+    }
+
+    void integrate(std::size_t const id,
+                   NumLib::LocalToGlobalIndexMap const& source_term_dof_table,
+                   double const t, GlobalVector& b) override
+    {
+        _local_rhs.setZero();
+
+        unsigned const n_integration_points =
+            _integration_method.getNumberOfPoints();
+
+        ParameterLib::SpatialPosition pos;
+        pos.setElementID(id);
+
+        for (unsigned ip = 0; ip < n_integration_points; ip++)
+        {
+            pos.setIntegrationPoint(ip);
+            auto const st_val = _parameter(t, pos)[0];
+
+            _local_rhs.noalias() += st_val * _ip_data[ip];
+        }
+        auto const indices = NumLib::getIndices(id, source_term_dof_table);
+        b.add(indices, _local_rhs);
+    }
+
+private:
+    ParameterLib::Parameter<double> const& _parameter;
+
+    IntegrationMethod const _integration_method;
+    std::vector<NodalRowVectorType,
+                Eigen::aligned_allocator<NodalRowVectorType>>
+        _ip_data;
+    NodalVectorType _local_rhs;
+};
+
+}  // namespace ProcessLib

Tests/Data/Parabolic/T/1D_line_source_term_tests/line_source_term.prj

+<?xml version="1.0" encoding="ISO-8859-1"?>
+<OpenGeoSysProject>
+    <meshes>
+        <mesh>mesh_1_line_100.vtu</mesh>
+        <mesh>line_1_entire_line.vtu</mesh>
+        <mesh>line_1_left.vtu</mesh>
+        <mesh>line_1_right.vtu</mesh>
+    </meshes>
+    <processes>
+        <process>
+            <name>HeatConduction</name>
+            <type>HEAT_CONDUCTION</type>
+            <integration_order>2</integration_order>
+            <thermal_conductivity>lambda</thermal_conductivity>
+            <heat_capacity>c_p</heat_capacity>
+            <density>rho</density>
+            <process_variables>
+                <process_variable>temperature</process_variable>
+            </process_variables>
+            <secondary_variables>
+                <secondary_variable type="static" internal_name="heat_flux_x" output_name="heat_flux_x"/>
+            </secondary_variables>
+        </process>
+    </processes>
+    <time_loop>
+        <processes>
+            <process ref="HeatConduction">
+                <nonlinear_solver>basic_picard</nonlinear_solver>
+                <convergence_criterion>
+                    <type>DeltaX</type>
+                    <norm_type>NORM2</norm_type>
+                    <abstol>1.e-6</abstol>
+                </convergence_criterion>
+                <time_discretization>
+                    <type>BackwardEuler</type>
+                </time_discretization>
+                <time_stepping>
+                    <type>FixedTimeStepping</type>
+                    <t_initial> 0.0 </t_initial>
+                    <t_end> 1 </t_end>
+                    <timesteps>
+                        <pair>
+                            <repeat>1</repeat>
+                            <delta_t>1</delta_t>
+                        </pair>
+                    </timesteps>
+                </time_stepping>
+            </process>
+        </processes>
+        <output>
+            <type>VTK</type>
+            <prefix>source_term_at_entire_line</prefix>
+            <timesteps>
+                <pair>
+                    <repeat> 10000 </repeat>
+                    <each_steps> 1 </each_steps>
+                </pair>
+            </timesteps>
+            <variables>
+                <variable> temperature </variable>
+                <variable> heat_flux_x </variable>
+            </variables>
+        </output>
+    </time_loop>
+    <parameters>
+        <parameter>
+            <name>lambda</name>
+            <type>Constant</type>
+            <value>1</value>
+        </parameter>
+        <parameter>
+            <name>c_p</name>
+            <type>Constant</type>
+            <value>0</value>
+        </parameter>
+        <parameter>
+            <name>rho</name>
+            <type>Constant</type>
+            <value>0</value>
+        </parameter>
+        <parameter>
+            <name>T0</name>
+            <type>Constant</type>
+            <value>0</value>
+        </parameter>
+        <parameter>
+            <name>HeatSource</name>
+            <type>Constant</type>
+            <value>1</value>
+        </parameter>
+    </parameters>
+    <process_variables>
+        <process_variable>
+            <name>temperature</name>
+            <components>1</components>
+            <order>1</order>
+            <initial_condition>T0</initial_condition>
+            <boundary_conditions>
+                <boundary_condition>
+                    <mesh>line_1_left</mesh>
+                    <type>Dirichlet</type>
+                    <parameter>T0</parameter>
+                </boundary_condition>
+                <boundary_condition>
+                    <mesh>line_1_right</mesh>
+                    <type>Dirichlet</type>
+                    <parameter>T0</parameter>
+                </boundary_condition>
+            </boundary_conditions>
+            <source_terms>
+                <source_term>
+                    <mesh>line_1_entire_line</mesh>
+                    <type>Line</type>
+                    <parameter>HeatSource</parameter>
+                </source_term>
+            </source_terms>
+        </process_variable>
+    </process_variables>
+    <nonlinear_solvers>
+        <nonlinear_solver>
+            <name>basic_picard</name>
+            <type>Picard</type>
+            <max_iter>10</max_iter>
+            <linear_solver>general_linear_solver</linear_solver>
+        </nonlinear_solver>
+    </nonlinear_solvers>
+    <linear_solvers>
+        <linear_solver>
+            <name>general_linear_solver</name>
+            <lis>-i cg -p jacobi -tol 1e-16 -maxiter 10000</lis>
+            <eigen>
+                <solver_type>CG</solver_type>
+                <precon_type>DIAGONAL</precon_type>
+                <max_iteration_step>10000</max_iteration_step>
+                <error_tolerance>1e-16</error_tolerance>
+            </eigen>
+            <petsc>
+                <prefix>gw</prefix>
+                <parameters>-gw_ksp_type cg -gw_pc_type bjacobi -gw_ksp_rtol 1e-16 -gw_ksp_max_it 10000</parameters>
+            </petsc>
+        </linear_solver>
+    </linear_solvers>
+</OpenGeoSysProject>

Tests/Data/Parabolic/T/2D_source_term_tests/line_source_term_left/source_term_left.prj

+<?xml version="1.0" encoding="ISO-8859-1"?>
+<OpenGeoSysProject>
+    <meshes>
+        <mesh>mesh.vtu</mesh>
+        <mesh>mesh_left.vtu</mesh>
+        <mesh>mesh_right.vtu</mesh>
+    </meshes>
+    <processes>
+        <process>
+            <name>HeatConduction</name>
+            <type>HEAT_CONDUCTION</type>
+            <integration_order>2</integration_order>
+            <thermal_conductivity>lambda</thermal_conductivity>
+            <heat_capacity>c_p</heat_capacity>
+            <density>rho</density>
+            <process_variables>
+                <process_variable>temperature</process_variable>
+            </process_variables>
+            <secondary_variables>
+                <secondary_variable type="static" internal_name="heat_flux_x" output_name="heat_flux_x"/>
+            </secondary_variables>
+        </process>
+    </processes>
+    <time_loop>
+        <processes>
+            <process ref="HeatConduction">
+                <nonlinear_solver>basic_picard</nonlinear_solver>
+                <convergence_criterion>
+                    <type>DeltaX</type>
+                    <norm_type>NORM2</norm_type>
+                    <abstol>1.e-6</abstol>
+                </convergence_criterion>
+                <time_discretization>
+                    <type>BackwardEuler</type>
+                </time_discretization>
+                <time_stepping>
+                    <type>FixedTimeStepping</type>
+                    <t_initial> 0.0 </t_initial>
+                    <t_end> 1 </t_end>
+                    <timesteps>
+                        <pair>
+                            <repeat>1</repeat>
+                            <delta_t>1</delta_t>
+                        </pair>
+                    </timesteps>
+                </time_stepping>
+            </process>
+        </processes>
+        <output>
+            <type>VTK</type>
+            <prefix>source_term_left</prefix>
+            <timesteps>
+                <pair>
+                    <repeat> 10000 </repeat>
+                    <each_steps> 1 </each_steps>
+                </pair>
+            </timesteps>
+            <variables>
+                <variable> temperature </variable>
+                <variable> heat_flux_x </variable>
+            </variables>
+        </output>
+    </time_loop>
+    <parameters>
+        <parameter>
+            <name>lambda</name>
+            <type>Constant</type>
+            <value>1</value>
+        </parameter>
+        <parameter>
+            <name>c_p</name>
+            <type>Constant</type>
+            <value>1</value>
+        </parameter>
+        <parameter>
+            <name>rho</name>
+            <type>Constant</type>
+            <value>1</value>
+        </parameter>
+        <parameter>
+            <name>T0</name>
+            <type>Constant</type>
+            <value>0</value>
+        </parameter>
+        <parameter>
+            <name>HeatSource</name>
+            <type>Constant</type>
+            <value>1</value>
+        </parameter>
+    </parameters>
+    <process_variables>
+        <process_variable>
+            <name>temperature</name>
+            <components>1</components>
+            <order>1</order>
+            <initial_condition>T0</initial_condition>
+            <boundary_conditions>
+                <boundary_condition>
+                    <mesh>mesh_right</mesh>
+                    <type>Dirichlet</type>
+                    <parameter>T0</parameter>
+                </boundary_condition>
+            </boundary_conditions>
+            <source_terms>
+                <source_term>
+                    <mesh>mesh_left</mesh>
+                    <type>Line</type>
+                    <parameter>HeatSource</parameter>
+                </source_term>
+            </source_terms>
+        </process_variable>
+    </process_variables>
+    <nonlinear_solvers>
+        <nonlinear_solver>
+            <name>basic_picard</name>
+            <type>Picard</type>
+            <max_iter>10</max_iter>
+            <linear_solver>general_linear_solver</linear_solver>
+        </nonlinear_solver>
+    </nonlinear_solvers>
+    <linear_solvers>
+        <linear_solver>
+            <name>general_linear_solver</name>
+            <lis>-i cg -p jacobi -tol 1e-16 -maxiter 10000</lis>
+            <eigen>
+                <solver_type>CG</solver_type>
+                <precon_type>DIAGONAL</precon_type>
+                <max_iteration_step>10000</max_iteration_step>
+                <error_tolerance>1e-16</error_tolerance>
+            </eigen>
+            <petsc>
+                <prefix>gw</prefix>
+                <parameters>-gw_ksp_type cg -gw_pc_type bjacobi -gw_ksp_rtol 1e-16 -gw_ksp_max_it 10000</parameters>
+            </petsc>
+        </linear_solver>
+    </linear_solvers>
+</OpenGeoSysProject>

Tests/Data/Parabolic/T/2D_source_term_tests/line_source_term_x_0.5/line_source_term_x_0.5.prj

+<?xml version="1.0" encoding="ISO-8859-1"?>
+<OpenGeoSysProject>
+    <meshes>
+        <mesh>mesh_1x1_quad_100x100.vtu</mesh>
+        <mesh>mesh_1x1_middle.vtu</mesh>
+        <mesh>mesh_1x1_left.vtu</mesh>
+        <mesh>mesh_1x1_right.vtu</mesh>
+    </meshes>
+    <processes>
+        <process>
+            <name>HeatConduction</name>
+            <type>HEAT_CONDUCTION</type>
+            <integration_order>2</integration_order>
+            <thermal_conductivity>lambda</thermal_conductivity>
+            <heat_capacity>c_p</heat_capacity>
+            <density>rho</density>
+            <process_variables>
+                <process_variable>temperature</process_variable>
+            </process_variables>
+            <secondary_variables>
+                <secondary_variable type="static" internal_name="heat_flux_x" output_name="heat_flux_x"/>
+            </secondary_variables>
+        </process>
+    </processes>
+    <time_loop>
+        <processes>
+            <process ref="HeatConduction">
+                <nonlinear_solver>basic_picard</nonlinear_solver>
+                <convergence_criterion>
+                    <type>DeltaX</type>
+                    <norm_type>NORM2</norm_type>
+                    <abstol>1.e-6</abstol>
+                </convergence_criterion>
+                <time_discretization>
+                    <type>BackwardEuler</type>
+                </time_discretization>
+                <time_stepping>
+                    <type>FixedTimeStepping</type>
+                    <t_initial> 0.0 </t_initial>
+                    <t_end> 1 </t_end>
+                    <timesteps>
+                        <pair>
+                            <repeat>1</repeat>
+                            <delta_t>1</delta_t>
+                        </pair>
+                    </timesteps>
+                </time_stepping>
+            </process>
+        </processes>
+        <output>
+            <type>VTK</type>
+            <prefix>source_term_middle</prefix>
+            <timesteps>
+                <pair>
+                    <repeat> 10000 </repeat>
+                    <each_steps> 1 </each_steps>
+                </pair>
+            </timesteps>
+            <variables>
+                <variable> temperature </variable>
+                <variable> heat_flux_x </variable>
+            </variables>
+        </output>
+    </time_loop>
+    <parameters>
+        <parameter>
+            <name>lambda</name>
+            <type>Constant</type>
+            <value>1</value>
+        </parameter>
+        <parameter>
+            <name>c_p</name>
+            <type>Constant</type>
+            <value>0</value>
+        </parameter>
+        <parameter>
+            <name>rho</name>
+            <type>Constant</type>
+            <value>0</value>
+        </parameter>
+        <parameter>
+            <name>T0</name>
+            <type>Constant</type>
+            <value>0</value>
+        </parameter>
+        <parameter>
+            <name>HeatSource</name>
+            <type>Constant</type>
+            <value>1</value>
+        </parameter>
+    </parameters>
+    <process_variables>
+        <process_variable>
+            <name>temperature</name>
+            <components>1</components>
+            <order>1</order>
+            <initial_condition>T0</initial_condition>
+            <boundary_conditions>
+                <boundary_condition>
+                    <mesh>mesh_1x1_left</mesh>
+                    <type>Dirichlet</type>
+                    <parameter>T0</parameter>
+                </boundary_condition>
+                <boundary_condition>
+                    <mesh>mesh_1x1_right</mesh>
+                    <type>Dirichlet</type>
+                    <parameter>T0</parameter>
+                </boundary_condition>
+            </boundary_conditions>
+            <source_terms>
+                <source_term>
+                    <mesh>mesh_1x1_middle</mesh>
+                    <type>Line</type>
+                    <parameter>HeatSource</parameter>
+                </source_term>
+            </source_terms>
+        </process_variable>
+    </process_variables>
+    <nonlinear_solvers>
+        <nonlinear_solver>
+            <name>basic_picard</name>
+            <type>Picard</type>
+            <max_iter>10</max_iter>
+            <linear_solver>general_linear_solver</linear_solver>
+        </nonlinear_solver>
+    </nonlinear_solvers>
+    <linear_solvers>
+        <linear_solver>
+            <name>general_linear_solver</name>
+            <lis>-i cg -p jacobi -tol 1e-16 -maxiter 10000</lis>
+            <eigen>
+                <solver_type>CG</solver_type>
+                <precon_type>DIAGONAL</precon_type>
+                <max_iteration_step>10000</max_iteration_step>
+                <error_tolerance>1e-16</error_tolerance>
+            </eigen>
+            <petsc>
+                <prefix>gw</prefix>
+                <parameters>-gw_ksp_type cg -gw_pc_type bjacobi -gw_ksp_rtol 1e-16 -gw_ksp_max_it 10000</parameters>
+            </petsc>
+        </linear_solver>
+    </linear_solvers>
+</OpenGeoSysProject>