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Commit 8a0f3b66 authored by Dmitri Naumov's avatar Dmitri Naumov
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Merge branch '2DRobinManufacturedSolutionTest' into 'master' 

[PL/BC] Reimplement Robin-type BC

See merge request ogs/ogs!4302
parents 4fa85ad0 7169bb13
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ProcessLib/BoundaryConditionAndSourceTerm/RobinBoundaryConditionLocalAssembler.h
+ 37
− 14
View file @ 8a0f3b66
......@@ -47,16 +47,23 @@ public:
{
}
// TODO also implement derivative for Jacobian in Newton scheme.
void assemble(std::size_t const id,
NumLib::LocalToGlobalIndexMap const& dof_table_boundary,
double const t, std::vector<GlobalVector*> const& /*x*/,
int const /*process_id*/, GlobalMatrix& K, GlobalVector& b,
GlobalMatrix* /*Jac*/) override
double const t, std::vector<GlobalVector*> const& xs,
int const process_id, GlobalMatrix& K, GlobalVector& b,
GlobalMatrix* Jac) override
{
_local_K.setZero();
_local_rhs.setZero();
auto& x = *xs[process_id];
auto const indices = NumLib::getIndices(id, dof_table_boundary);
auto const local_x = x.get(indices);
auto const u =
MathLib::toVector<Eigen::Matrix<double, ShapeFunction::NPOINTS, 1>>(
local_x, ShapeFunction::NPOINTS);
unsigned const n_integration_points =
Base::_integration_method.getNumberOfPoints();
......@@ -86,19 +93,35 @@ public:
integral_measure = (*_data.integral_measure)(t, position)[0];
}
// flux = alpha * ( u_0 - u )
// adding a alpha term to the diagonal of the stiffness matrix
// and a alpha * u_0 term to the rhs vector
_local_K.diagonal().noalias() +=
N * alpha.dot(N) * w * integral_measure;
_local_rhs.noalias() +=
N * alpha.dot(N) * u_0.dot(N) * w * integral_measure;
double const a = alpha.dot(N) * w * integral_measure;
// The local K matrix is used for both, the Newton and Picard
// methods.
_local_K.noalias() += N.transpose() * N * a;
if (Jac != nullptr)
{
_local_rhs.noalias() -= N.transpose() * (u - u_0).dot(N) * a;
}
else
{
_local_rhs.noalias() += N.transpose() * (u_0.dot(N) * a);
}
}
auto const indices = NumLib::getIndices(id, dof_table_boundary);
K.add(NumLib::LocalToGlobalIndexMap::RowColumnIndices(indices, indices),
_local_K);
b.add(indices, _local_rhs);
if (Jac != nullptr)
{
Jac->add(NumLib::LocalToGlobalIndexMap::RowColumnIndices(indices,
indices),
_local_K);
}
else
{
K.add(NumLib::LocalToGlobalIndexMap::RowColumnIndices(indices,
indices),
_local_K);
}
}
private:
......
ProcessLib/HeatConduction/Tests.cmake
+ 24
− 16
View file @ 8a0f3b66
......@@ -2,6 +2,8 @@ if (NOT OGS_USE_MPI)
OgsTest(PROJECTFILE Parabolic/T/1D_freezing_column_Stefan/Stefan_problem.prj RUNTIME 2)
OgsTest(PROJECTFILE Parabolic/T/1D_freezing_column_Stefan/Stefan_problem_homogen.prj RUNTIME 1)
OgsTest(PROJECTFILE Parabolic/T/2D_freezing_disk/circle_disk.prj RUNTIME 2)
OgsTest(PROJECTFILE Parabolic/T/2D_Robin/square_1e4_robin.prj RUNTIME 1)
OgsTest(PROJECTFILE Parabolic/T/2D_Robin/square_1e4_robin_newton.xml RUNTIME 1)
endif()
AddTest(
......@@ -128,25 +130,31 @@ AddTest(
REQUIREMENTS OGS_USE_MPI
)
# SQUARE 1x1 HEAT CONDUCTION TEST -- AXIALLY SYMMETRIC
# test results are compared to 3D simulation on a wedge-shaped domain
# The results were compared to an analytical solution (method of manufactured
# solutions). The vtkdiff comparison is against the numerical solution.
AddTest(
NAME 2D_HeatConduction_axi
PATH Parabolic/T/2D_axially_symmetric
EXECUTABLE ogs
EXECUTABLE_ARGS square_1e2_axi.prj
TESTER vtkdiff
DIFF_DATA
wedge_1e2_axi_ang_0.02_t_2s_extracted_surface.vtu square_1e2_axi_ts_2_t_2.000000.vtu temperature temperature 1.7e-5 1e-5
wedge_1e2_axi_ang_0.02_t_2s_extracted_surface.vtu square_1e2_axi_ts_2_t_2.000000.vtu heat_flux heat_flux 1.7e-5 1e-5
NAME 2D_HeatConduction_axi
PATH Parabolic/T/2D_axially_symmetric
EXECUTABLE ogs
EXECUTABLE_ARGS square_1e2_axi.prj
TESTER vtkdiff
DIFF_DATA
square_1e2_axi_ts_10_t_1.000000.vtu square_1e2_axi_ts_10_t_1.000000.vtu temperature temperature 2e-15 0
square_1e2_axi_ts_10_t_1.000000.vtu square_1e2_axi_ts_10_t_1.000000.vtu heat_flux heat_flux 1e-14 0
REQUIREMENTS NOT OGS_USE_MPI
)
# WEDGE 1x1 HEAT CONDUCTION TEST -- same setup as above test but in cartesian coordinates
AddTest(
NAME 2D_HeatConduction_wedge
PATH Parabolic/T/2D_axially_symmetric
EXECUTABLE ogs
EXECUTABLE_ARGS wedge_1e2_axi_ang_0.02.prj
TESTER vtkdiff
DIFF_DATA
wedge_ang_0.02_ts_10_t_1.000000.vtu wedge_ang_0.02_ts_10_t_1.000000.vtu temperature temperature 2e-14 0
wedge_ang_0.02_ts_10_t_1.000000.vtu wedge_ang_0.02_ts_10_t_1.000000.vtu heat_flux heat_flux 1e-13 0
REQUIREMENTS NOT OGS_USE_MPI
)
# # WEDGE 1x1 HEATCONDUCTION TEST -- computes reference results for the above test
# AddTest(
# NAME 2D_HeatConduction_wedge
# PATH Parabolic/T/2D_axially_symmetric
# EXECUTABLE ogs
# EXECUTABLE_ARGS wedge_1e2_axi_ang_0.02.prj
# )
# The 25 BHE array benchmark
# test results are compared to 2D simulation result
......
ProcessLib/SteadyStateDiffusion/Tests.cmake
+ 30
− 20
View file @ 8a0f3b66
......@@ -336,8 +336,9 @@ AddTest(
wedge_1x1x1_1e3_prism_complete_surface_specific_flux_t_1.000000.vtu wedge_1e3_surfaceflux_wedge_1x1x1_1e3_prism_complete_surface_ts_1_t_1.000000.vtu specific_flux specific_flux 2e-14 0
)
# SQUARE 1x1 GROUNDWATER FLOW TEST -- AXIALLY SYMMETRIC
# test results are compared to 3D simulation on a wedge-shaped domain
# SQUARE 1x1 GROUNDWATER FLOW TEST -- AXIALLY SYMMETRIC, 1e2
# The results were compared to an analytical solution (method of manufactured
# solutions). The vtkdiff comparison is against the numerical solution.
AddTest(
NAME SteadyStateDiffusion_square_1x1_1e2_axi
PATH Elliptic/square_1x1_SteadyStateDiffusion
......@@ -346,18 +347,23 @@ AddTest(
TESTER vtkdiff
REQUIREMENTS NOT OGS_USE_MPI
DIFF_DATA
wedge-1e2-ang-0.02-surface.vtu square_1e2_axi_ts_1_t_1.000000.vtu temperature temperature 1.6e-5 1e-5
square_1e2_axi_ts_1_t_1.000000.vtu square_1e2_axi_ts_1_t_1.000000.vtu temperature temperature 2e-15 0
)
# WEDGE 1x1 GROUNDWATER FLOW TEST -- same setup as above test but in cartesian coordinates
AddTest(
NAME SteadyStateDiffusion_wedge_1e2_ang_0.02
PATH Elliptic/square_1x1_SteadyStateDiffusion
EXECUTABLE ogs
EXECUTABLE_ARGS wedge_1e2_axi_ang_0.02.prj
TESTER vtkdiff
REQUIREMENTS NOT OGS_USE_MPI
DIFF_DATA
wedge_1e2_ang_0.02_ts_1_t_1.000000.vtu wedge_1e2_ang_0.02_ts_1_t_1.000000.vtu temperature temperature 2e-14 0
)
# # WEDGE 1x1 GROUNDWATER FLOW TEST -- computes reference results for the above test
# AddTest(
# NAME SteadyStateDiffusion_wedge_1e2_ang_0.02
# PATH Elliptic/square_1x1_SteadyStateDiffusion
# EXECUTABLE ogs
# EXECUTABLE_ARGS wedge_1e2_axi_ang_0.02.prj
# )
# SQUARE 1x1 GROUNDWATER FLOW TEST -- AXIALLY SYMMETRIC
# test results are compared to 3D simulation on a wedge-shaped domain
# SQUARE 1x1 GROUNDWATER FLOW TEST -- AXIALLY SYMMETRIC, 1e4
# The results were compared to an analytical solution (method of manufactured
# solutions). The vtkdiff comparison is against the numerical solution.
AddTest(
NAME SteadyStateDiffusion_square_1x1_1e4_axi_ang_0.02
PATH Elliptic/square_1x1_SteadyStateDiffusion
......@@ -366,15 +372,19 @@ AddTest(
TESTER vtkdiff
REQUIREMENTS NOT OGS_USE_MPI
DIFF_DATA
wedge-1e4-ang-0.02-surface.vtu square_1e4_axi_ts_1_t_1.000000.vtu temperature temperature 1.6e-5 1e-5
square_1e4_axi_ts_1_t_1.000000.vtu square_1e4_axi_ts_1_t_1.000000.vtu temperature temperature 2e-14 0
)
# WEDGE 1x1 GROUNDWATER FLOW TEST -- same setup as above test but in cartesian coordinates
AddTest(
NAME SteadyStateDiffusion_wedge_1e4_ang_0.02
PATH Elliptic/square_1x1_SteadyStateDiffusion
EXECUTABLE ogs
EXECUTABLE_ARGS wedge_1e4_axi_ang_0.02.prj
TESTER vtkdiff
REQUIREMENTS NOT OGS_USE_MPI
DIFF_DATA
wedge_1e4_axi_ang_0.02_ts_1_t_1.000000.vtu wedge_1e4_axi_ang_0.02_ts_1_t_1.000000.vtu temperature temperature 2e-14 0
)
# # WEDGE 1x1 GROUNDWATER FLOW TEST -- computes reference results for the above test
# AddTest(
# NAME SteadyStateDiffusion_wedge_1e4_ang_0.02
# PATH Elliptic/square_1x1_SteadyStateDiffusion
# EXECUTABLE ogs
# EXECUTABLE_ARGS wedge_1e4_axi_ang_0.02.prj
# )
# MPI groundwater flow tests
AddTest(
......
ProcessLib/TES/Tests.cmake
+ 14
− 7
View file @ 8a0f3b66
......@@ -44,13 +44,20 @@ AddTest(
inert-wedge-extracted-surface-t-1s.vtu tes_inert_axi_ts_4_t_1.000000.vtu temperature temperature 1e-12 2e-9
inert-wedge-extracted-surface-t-1s.vtu tes_inert_axi_ts_4_t_1.000000.vtu v_mass_frac v_mass_frac 1e-12 2e-9
)
# # WEDGE 1x1 TES TEST -- computes reference results for the above test
# AddTest(
# NAME TES_inert_wedge
# PATH Parabolic/TES/2D
# EXECUTABLE ogs
# EXECUTABLE_ARGS tes-inert-wedge.prj
# )
# WEDGE 1x1 TES TEST -- computes reference results for the above test
AddTest(
NAME TES_inert_wedge
PATH Parabolic/TES/2D
EXECUTABLE ogs
EXECUTABLE_ARGS tes-inert-wedge.prj
TESTER vtkdiff
RUNTIME 90
REQUIREMENTS NOT OGS_USE_MPI
DIFF_DATA
tes_inert_wedge_ts_4_t_1.000000.vtu tes_inert_wedge_ts_4_t_1.000000.vtu pressure pressure 1e-12 2e-9
tes_inert_wedge_ts_4_t_1.000000.vtu tes_inert_wedge_ts_4_t_1.000000.vtu temperature temperature 1e-12 2e-9
tes_inert_wedge_ts_4_t_1.000000.vtu tes_inert_wedge_ts_4_t_1.000000.vtu v_mass_frac v_mass_frac 1e-12 2e-9
)
# For PETSc/MPI
AddTest(
......
Tests/Data/Elliptic/square_1x1_SteadyStateDiffusion/square_1e2_axi.prj
+ 22
− 10
View file @ 8a0f3b66
......@@ -85,14 +85,14 @@
</linear_solvers>
<parameters>
<parameter>
<name>T0</name>
<type>Constant</type>
<value>0</value>
<name>solution</name>
<type>Function</type>
<expression>sin(2*pi*y) * x^2</expression>
</parameter>
<parameter>
<name>heat_flux_bottom</name>
<type>Constant</type>
<value>1</value>
<name>dsolution_dy</name>
<type>Function</type>
<expression>-2*pi * cos(2*pi*y) * x^2</expression>
</parameter>
<parameter>
<name>heat_transfer_coefficient</name>
......@@ -101,8 +101,13 @@
</parameter>
<parameter>
<name>ambient_temperature</name>
<type>Constant</type>
<value>0</value>
<type>Function</type>
<expression>3 * sin(2*pi*y)</expression>
</parameter>
<parameter>
<name>source_term</name>
<type>Function</type>
<expression>4 * sin(2*pi*y) * (pi^2 * x^2 - 1)</expression>
</parameter>
</parameters>
<process_variables>
......@@ -110,13 +115,13 @@
<name>temperature</name>
<components>1</components>
<order>1</order>
<initial_condition>T0</initial_condition>
<initial_condition>solution</initial_condition>
<boundary_conditions>
<boundary_condition>
<geometrical_set>geometry</geometrical_set>
<geometry>bottom</geometry>
<type>Neumann</type>
<parameter>heat_flux_bottom</parameter>
<parameter>dsolution_dy</parameter>
</boundary_condition>
<boundary_condition>
<geometrical_set>geometry</geometrical_set>
......@@ -132,6 +137,13 @@
<u_0>ambient_temperature</u_0>
</boundary_condition>
</boundary_conditions>
<source_terms>
<source_term>
<mesh>square_1x1_quad_1e2</mesh>
<type>Volumetric</type>
<parameter>source_term</parameter>
</source_term>
</source_terms>
</process_variable>
</process_variables>
</OpenGeoSysProject>
Tests/Data/Elliptic/square_1x1_SteadyStateDiffusion/square_1e2_axi_ts_1_t_1.000000.vtu 0 → 100644
+ 32
− 0
View file @ 8a0f3b66
<?xml version="1.0"?>
<VTKFile type="UnstructuredGrid" version="1.0" byte_order="LittleEndian" header_type="UInt64" compressor="vtkZLibDataCompressor">
<UnstructuredGrid>
<FieldData>
<DataArray type="Int8" Name="OGS_VERSION" NumberOfTuples="27" format="appended" RangeMin="45" RangeMax="121" offset="0" />
</FieldData>
<Piece NumberOfPoints="121" NumberOfCells="100" >
<PointData>
<DataArray type="Float64" Name="D1_left_bottom_N1_right" format="appended" RangeMin="1" RangeMax="1.6753144833" offset="92" />
<DataArray type="Float64" Name="Linear_1_to_minus1" format="appended" RangeMin="-1" RangeMax="1" offset="1236" />
<DataArray type="UInt64" Name="bulk_node_ids" format="appended" RangeMin="0" RangeMax="120" offset="1364" />
<DataArray type="Float64" Name="temperature" format="appended" RangeMin="-0.9512008155" RangeMax="0.93724397272" offset="1676" />
<DataArray type="Float64" Name="v" NumberOfComponents="2" format="appended" RangeMin="0.0008661429344" RangeMax="5.8792463601" offset="2964" />
</PointData>
<CellData>
<DataArray type="Int32" Name="MaterialIDs" format="appended" RangeMin="0" RangeMax="0" offset="5508" />
<DataArray type="UInt64" Name="bulk_element_ids" format="appended" RangeMin="0" RangeMax="99" offset="5572" />
</CellData>
<Points>
<DataArray type="Float64" Name="Points" NumberOfComponents="3" format="appended" RangeMin="0" RangeMax="1.4142135624" offset="5852" />
</Points>
<Cells>
<DataArray type="Int64" Name="connectivity" format="appended" RangeMin="" RangeMax="" offset="6388" />
<DataArray type="Int64" Name="offsets" format="appended" RangeMin="" RangeMax="" offset="7112" />
<DataArray type="UInt8" Name="types" format="appended" RangeMin="" RangeMax="" offset="7420" />
</Cells>
</Piece>
</UnstructuredGrid>
<AppendedData encoding="base64">
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Tests/Data/Elliptic/square_1x1_SteadyStateDiffusion/square_1e4_axi.prj
+ 22
− 10
View file @ 8a0f3b66
......@@ -85,14 +85,14 @@
</linear_solvers>
<parameters>
<parameter>
<name>T0</name>
<type>Constant</type>
<value>0</value>
<name>solution</name>
<type>Function</type>
<expression>sin(2*pi*y) * x^2</expression>
</parameter>
<parameter>
<name>heat_flux_bottom</name>
<type>Constant</type>
<value>1</value>
<name>dsolution_dy</name>
<type>Function</type>
<expression>-2*pi * cos(2*pi*y) * x^2</expression>
</parameter>
<parameter>
<name>heat_transfer_coefficient</name>
......@@ -101,8 +101,13 @@
</parameter>
<parameter>
<name>ambient_temperature</name>
<type>Constant</type>
<value>0</value>
<type>Function</type>
<expression>3 * sin(2*pi*y)</expression>
</parameter>
<parameter>
<name>source_term</name>
<type>Function</type>
<expression>4 * sin(2*pi*y) * (pi^2 * x^2 - 1)</expression>
</parameter>
</parameters>
<process_variables>
......@@ -110,13 +115,13 @@
<name>temperature</name>
<components>1</components>
<order>1</order>
<initial_condition>T0</initial_condition>
<initial_condition>solution</initial_condition>
<boundary_conditions>
<boundary_condition>
<geometrical_set>geometry</geometrical_set>
<geometry>bottom</geometry>
<type>Neumann</type>
<parameter>heat_flux_bottom</parameter>
<parameter>dsolution_dy</parameter>
</boundary_condition>
<boundary_condition>
<geometrical_set>geometry</geometrical_set>
......@@ -132,6 +137,13 @@
<u_0>ambient_temperature</u_0>
</boundary_condition>
</boundary_conditions>
<source_terms>
<source_term>
<mesh>square_1x1_quad_1e4</mesh>
<type>Volumetric</type>
<parameter>source_term</parameter>
</source_term>
</source_terms>
</process_variable>
</process_variables>
</OpenGeoSysProject>
Tests/Data/Elliptic/square_1x1_SteadyStateDiffusion/wedge-1e2-ang-0.02-surface.vtu deleted 100644 → 0
+ 0
− 44
View file @ 4fa85ad0
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Tests/Data/Elliptic/square_1x1_SteadyStateDiffusion/wedge-1e2-ang-0.2-surface.vtu deleted 100644 → 0
+ 0
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View file @ 4fa85ad0
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Tests/Data/Elliptic/square_1x1_SteadyStateDiffusion/wedge-1e4-ang-0.02-surface.vtu deleted 100644 → 0
+ 0
− 44
View file @ 4fa85ad0
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Tests/Data/Elliptic/square_1x1_SteadyStateDiffusion/wedge_1e2_ang_0.02_ts_1_t_1.000000.vtu 0 → 100644
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− 0
View file @ 8a0f3b66
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</AppendedData>
</VTKFile>
Tests/Data/Elliptic/square_1x1_SteadyStateDiffusion/wedge_1e2_axi_ang_0.02.prj
+ 22
− 10
View file @ 8a0f3b66
......@@ -85,14 +85,14 @@
</linear_solvers>
<parameters>
<parameter>
<name>T0</name>
<type>Constant</type>
<value>0</value>
<name>solution</name>
<type>Function</type>
<expression>sin(2*pi*z) * (x^2 + y^2)</expression>
</parameter>
<parameter>
<name>heat_flux_bottom</name>
<type>Constant</type>
<value>1</value>
<name>dsolution_dy</name>
<type>Function</type>
<expression>-2*pi * cos(2*pi*z) * (x^2 + y^2)</expression>
</parameter>
<parameter>
<name>heat_transfer_coefficient</name>
......@@ -101,8 +101,13 @@
</parameter>
<parameter>
<name>ambient_temperature</name>
<type>Constant</type>
<value>0</value>
<type>Function</type>
<expression>3 * sin(2*pi*z)</expression>
</parameter>
<parameter>
<name>source_term</name>
<type>Function</type>
<expression>4 * sin(2*pi*z) * (pi^2 * (x^2 + y^2) - 1)</expression>
</parameter>
</parameters>
<process_variables>
......@@ -110,13 +115,13 @@
<name>temperature</name>
<components>1</components>
<order>1</order>
<initial_condition>T0</initial_condition>
<initial_condition>solution</initial_condition>
<boundary_conditions>
<boundary_condition>
<geometrical_set>geometry</geometrical_set>
<geometry>bottom</geometry>
<type>Neumann</type>
<parameter>heat_flux_bottom</parameter>
<parameter>dsolution_dy</parameter>
</boundary_condition>
<boundary_condition>
<geometrical_set>geometry</geometrical_set>
......@@ -132,6 +137,13 @@
<u_0>ambient_temperature</u_0>
</boundary_condition>
</boundary_conditions>
<source_terms>
<source_term>
<mesh>wedge-1e2-ang-0.02</mesh>
<type>Volumetric</type>
<parameter>source_term</parameter>
</source_term>
</source_terms>
</process_variable>
</process_variables>
</OpenGeoSysProject>
Tests/Data/Elliptic/square_1x1_SteadyStateDiffusion/wedge_1e4_axi_ang_0.02.prj
+ 22
− 10
View file @ 8a0f3b66
......@@ -85,14 +85,14 @@
</linear_solvers>
<parameters>
<parameter>
<name>T0</name>
<type>Constant</type>
<value>0</value>
<name>solution</name>
<type>Function</type>
<expression>sin(2*pi*z) * (x^2 + y^2)</expression>
</parameter>
<parameter>
<name>heat_flux_bottom</name>
<type>Constant</type>
<value>1</value>
<name>dsolution_dy</name>
<type>Function</type>
<expression>-2*pi * cos(2*pi*z) * (x^2 + y^2)</expression>
</parameter>
<parameter>
<name>heat_transfer_coefficient</name>
......@@ -101,8 +101,13 @@
</parameter>
<parameter>
<name>ambient_temperature</name>
<type>Constant</type>
<value>0</value>
<type>Function</type>
<expression>3 * sin(2*pi*z)</expression>
</parameter>
<parameter>
<name>source_term</name>
<type>Function</type>
<expression>4 * sin(2*pi*z) * (pi^2 * (x^2 + y^2) - 1)</expression>
</parameter>
</parameters>
<process_variables>
......@@ -110,13 +115,13 @@
<name>temperature</name>
<components>1</components>
<order>1</order>
<initial_condition>T0</initial_condition>
<initial_condition>solution</initial_condition>
<boundary_conditions>
<boundary_condition>
<geometrical_set>geometry</geometrical_set>
<geometry>bottom</geometry>
<type>Neumann</type>
<parameter>heat_flux_bottom</parameter>
<parameter>dsolution_dy</parameter>
</boundary_condition>
<boundary_condition>
<geometrical_set>geometry</geometrical_set>
......@@ -132,6 +137,13 @@
<u_0>ambient_temperature</u_0>
</boundary_condition>
</boundary_conditions>
<source_terms>
<source_term>
<mesh>wedge-1e4-ang-0.02</mesh>
<type>Volumetric</type>
<parameter>source_term</parameter>
</source_term>
</source_terms>
</process_variable>
</process_variables>
</OpenGeoSysProject>
Tests/Data/Parabolic/T/2D_Robin/square_1e4_robin.prj 0 → 100644
+ 213
− 0
View file @ 8a0f3b66
<?xml version="1.0" encoding="ISO-8859-1"?>
<OpenGeoSysProject>
<mesh>square_1x1_quad_1e4.vtu</mesh>
<geometry>square_1x1.gml</geometry>
<processes>
<process>
<name>HeatConduction</name>
<type>HEAT_CONDUCTION</type>
<integration_order>2</integration_order>
<process_variables>
<process_variable>temperature</process_variable>
</process_variables>
<secondary_variables>
<secondary_variable internal_name="heat_flux" output_name="heat_flux"/>
</secondary_variables>
</process>
</processes>
<media>
<medium>
<phases/>
<properties>
<property>
<name>thermal_conductivity</name>
<type>Constant</type>
<value>1</value>
</property>
<property>
<name>specific_heat_capacity</name>
<type>Constant</type>
<value>1</value>
</property>
<property>
<name>density</name>
<type>Constant</type>
<value>1</value>
</property>
</properties>
</medium>
</media>
<time_loop>
<processes>
<process ref="HeatConduction">
<nonlinear_solver>NLS</nonlinear_solver>
<convergence_criterion>
<type>DeltaX</type>
<norm_type>NORM2</norm_type>
<reltol>1e-14</reltol>
</convergence_criterion>
<time_discretization>
<type>BackwardEuler</type>
</time_discretization>
<time_stepping>
<type>FixedTimeStepping</type>
<t_initial>0</t_initial>
<t_end>1</t_end>
<timesteps>
<pair>
<repeat>1</repeat>
<delta_t>0.1</delta_t>
</pair>
<pair>
<repeat>2</repeat>
<delta_t>0.2</delta_t>
</pair>
<pair>
<repeat>2</repeat>
<delta_t>0.25</delta_t>
</pair>
</timesteps>
</time_stepping>
</process>
</processes>
<output>
<type>VTK</type>
<prefix>{:meshname}</prefix>
<variables>
<variable>temperature</variable>
<variable>v</variable>
</variables>
<suffix>_t_{:gtime}</suffix>
<fixed_output_times>0 0.5 1</fixed_output_times>
<timesteps>
<pair>
<repeat>1</repeat>
<each_steps>100000</each_steps>
</pair>
</timesteps>
</output>
</time_loop>
<parameters>
<parameter>
<name>solution</name>
<type>Function</type>
<expression>x^2 * sin(2*pi*y) * t</expression>
</parameter>
<parameter>
<name>zero</name>
<type>Constant</type>
<value>0</value>
</parameter>
<parameter>
<name>alpha</name>
<type>Constant</type>
<value>2</value>
</parameter>
<parameter>
<name>dsolution_dx</name>
<type>Function</type>
<expression>2 * x * sin(2*pi*y) * t</expression>
</parameter>
<parameter>
<name>ambient_temperature</name>
<type>Function</type>
<!-- = 1/alpha dT/dx + T -->
<expression>2 * sin(2*pi*y) * t</expression>
</parameter>
<parameter>
<name>source_term</name>
<type>Function</type>
<!-- = dT/dt - d^2T/dx^2 - d^2T/dy^2 -->
<expression>(x^2 - 2 * t + 4 * pi^2 * x^2 * t) * sin(2*pi*y)</expression>
</parameter>
</parameters>
<process_variables>
<process_variable>
<name>temperature</name>
<order>1</order>
<components>1</components>
<initial_condition>solution</initial_condition>
<boundary_conditions>
<boundary_condition>
<geometrical_set>square_1x1_geometry</geometrical_set>
<geometry>bottom</geometry>
<type>Dirichlet</type>
<parameter>solution</parameter>
</boundary_condition>
<boundary_condition>
<geometrical_set>square_1x1_geometry</geometrical_set>
<geometry>top</geometry>
<type>Dirichlet</type>
<parameter>solution</parameter>
</boundary_condition>
<!-- Robin -->
<boundary_condition>
<geometrical_set>square_1x1_geometry</geometrical_set>
<geometry>right</geometry>
<type>Robin</type>
<alpha>alpha</alpha>
<u_0>ambient_temperature</u_0>
</boundary_condition>
<!-- Keep the alternative Neumann and Dirichlet BCs for testing. -->
<!-- Neumann -->
<!--
<boundary_condition>
<geometrical_set>square_1x1_geometry</geometrical_set>
<geometry>right</geometry>
<type>Neumann</type>
<parameter>dsolution_dx</parameter>
</boundary_condition>
-->
<!-- Dirichlet -->
<!--
<boundary_condition>
<geometrical_set>square_1x1_geometry</geometrical_set>
<geometry>right</geometry>
<type>Dirichlet</type>
<parameter>solution</parameter>
</boundary_condition>
-->
<boundary_condition>
<geometrical_set>square_1x1_geometry</geometrical_set>
<geometry>left</geometry>
<type>Neumann</type>
<parameter>dsolution_dx</parameter>
</boundary_condition>
</boundary_conditions>
<source_terms>
<source_term>
<mesh>square_1x1_quad_1e4</mesh>
<type>Volumetric</type>
<parameter>source_term</parameter>
</source_term>
</source_terms>
</process_variable>
</process_variables>
<nonlinear_solvers>
<nonlinear_solver>
<name>NLS</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>
<eigen>
<solver_type>BiCGSTAB</solver_type>
<precon_type>DIAGONAL</precon_type>
<max_iteration_step>10000</max_iteration_step>
<error_tolerance>1e-16</error_tolerance>
</eigen>
</linear_solver>
</linear_solvers>
<test_definition>
<vtkdiff>
<regex>square_1x1_quad_1e4_t_.*.vtu</regex>
<field>temperature</field>
<absolute_tolerance>2e-14</absolute_tolerance>
<relative_tolerance>0</relative_tolerance>
</vtkdiff>
</test_definition>
</OpenGeoSysProject>
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