diff --git a/ProcessLib/HT/Tests.cmake b/ProcessLib/HT/Tests.cmake
index 4892aa034b48dace21a0256422e276dff483520c..b455366f7176874ef04ed1fe25db398784f62b28 100644
--- a/ProcessLib/HT/Tests.cmake
+++ b/ProcessLib/HT/Tests.cmake
@@ -467,3 +467,17 @@ endif()
if (NOT (OGS_USE_MPI))
OgsTest(PROJECTFILE Parabolic/HT/SimpleSynthetics/deactivated_subdomain/HT_DeactivatedSubdomain.prj)
endif()
+
+AddTest(
+ NAME HT_HeatTransportInStationaryFlow
+ PATH Parabolic/HT/HeatTransportInStationaryFlow
+ EXECUTABLE ogs
+ EXECUTABLE_ARGS HeatTransportInStationaryFlow.prj
+ WRAPPER time
+ TESTER vtkdiff
+ REQUIREMENTS NOT (OGS_USE_LIS OR OGS_USE_MPI)
+ RUNTIME 17
+ DIFF_DATA
+ HT_HeatTransportInStationaryFlow_ts_50_t_50000.000000.vtu HeatTransportInStationaryFlow_ts_50_t_50000.000000.vtu temperature temperature 1.e-6 1e-10
+ HT_HeatTransportInStationaryFlow_ts_50_t_50000.000000.vtu HeatTransportInStationaryFlow_ts_50_t_50000.000000.vtu pressure pressure 1e-10 1e-10
+)
diff --git a/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/HT_HeatTransportInStationaryFlow_ts_50_t_50000.000000.vtu b/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/HT_HeatTransportInStationaryFlow_ts_50_t_50000.000000.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..8a184b0dec26d418b8905e0145edbaa44b08950f
--- /dev/null
+++ b/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/HT_HeatTransportInStationaryFlow_ts_50_t_50000.000000.vtu
@@ -0,0 +1,29 @@
+<?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="41" format="appended" RangeMin="45" RangeMax="121" offset="0" />
+ </FieldData>
+ <Piece NumberOfPoints="160" NumberOfCells="117" >
+ <PointData>
+ <DataArray type="Float64" Name="darcy_velocity" NumberOfComponents="2" format="appended" RangeMin="1e-05" RangeMax="1e-05" offset="112" />
+ <DataArray type="Float64" Name="pressure" format="appended" RangeMin="100000" RangeMax="101000" offset="1748" />
+ <DataArray type="Float64" Name="temperature" format="appended" RangeMin="0.0008171344374" RangeMax="1" offset="2664" />
+ </PointData>
+ <CellData>
+ <DataArray type="Int32" Name="MaterialIDs" format="appended" RangeMin="0" RangeMax="0" offset="3816" />
+ </CellData>
+ <Points>
+ <DataArray type="Float64" Name="Points" NumberOfComponents="3" format="appended" RangeMin="0" RangeMax="1.0049875621" offset="3880" />
+ </Points>
+ <Cells>
+ <DataArray type="Int64" Name="connectivity" format="appended" RangeMin="" RangeMax="" offset="5496" />
+ <DataArray type="Int64" Name="offsets" format="appended" RangeMin="" RangeMax="" offset="6364" />
+ <DataArray type="UInt8" Name="types" format="appended" RangeMin="" RangeMax="" offset="6700" />
+ </Cells>
+ </Piece>
+ </UnstructuredGrid>
+ <AppendedData encoding="base64">
+ 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+ </AppendedData>
+</VTKFile>
diff --git a/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/HeatTransportInStationaryFlow.prj b/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/HeatTransportInStationaryFlow.prj
new file mode 100644
index 0000000000000000000000000000000000000000..d22b2af8fdb8a21b67d8f5b7c47cae8768bb2ef4
--- /dev/null
+++ b/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/HeatTransportInStationaryFlow.prj
@@ -0,0 +1,231 @@
+<?xml version="1.0" encoding="ISO-8859-1"?>
+<OpenGeoSysProject>
+ <meshes>
+ <mesh>mesh.vtu</mesh>
+ <mesh>geometry_left.vtu</mesh>
+ <mesh>geometry_right.vtu</mesh>
+ <mesh>geometry_top.vtu</mesh>
+ <mesh>geometry_bottom.vtu</mesh>
+ </meshes>
+ <processes>
+ <process>
+ <name>HeatTransportInStationaryFlow</name>
+ <type>HT</type>
+ <integration_order>2</integration_order>
+ <process_variables>
+ <temperature>temperature</temperature>
+ <pressure>pressure</pressure>
+ </process_variables>
+ <specific_body_force>0 -0.0</specific_body_force>
+ <secondary_variables>
+ <secondary_variable internal_name="darcy_velocity" output_name="darcy_velocity"/>
+ </secondary_variables>
+ </process>
+ </processes>
+ <media>
+ <medium id="0">
+ <phases>
+ <phase>
+ <type>AqueousLiquid</type>
+ <properties>
+ <property>
+ <name>specific_heat_capacity</name>
+ <type>Constant</type>
+ <value>4182</value>
+ </property>
+ <property>
+ <name>thermal_conductivity</name>
+ <type>Constant</type>
+ <value>0.6</value>
+ </property>
+ <property>
+ <name>density</name>
+ <type>Constant</type>
+ <value>1000</value>
+ </property>
+ <property>
+ <name>viscosity</name>
+ <type>Constant</type>
+ <value>1.0e-3</value>
+ </property>
+ </properties>
+ </phase>
+ <phase>
+ <type>Solid</type>
+ <properties>
+ <property>
+ <name>storage</name>
+ <type>Constant</type>
+ <value>0.0</value>
+ </property>
+ <property>
+ <name>density</name>
+ <type>Constant</type>
+ <value>2850</value>
+ </property>
+ <property>
+ <name>thermal_conductivity</name>
+ <type>Constant</type>
+ <value>5.0</value>
+ </property>
+ <property>
+ <name>specific_heat_capacity</name>
+ <type>Constant</type>
+ <value>6000000</value>
+ </property>
+ </properties>
+ </phase>
+ </phases>
+ <properties>
+ <property>
+ <name>thermal_longitudinal_dispersivity</name>
+ <type>Constant</type>
+ <value>0</value>
+ </property>
+ <property>
+ <name>thermal_transversal_dispersivity</name>
+ <type>Constant</type>
+ <value>0</value>
+ </property>
+
+ <property>
+ <name>permeability</name>
+ <type>Constant</type>
+ <value>1.e-11</value>
+ </property>
+ <property>
+ <name>porosity</name>
+ <type>Constant</type>
+ <value>1.0</value>
+ </property>
+ </properties>
+ </medium>
+ </media>
+ <time_loop>
+ <processes>
+ <process ref="HeatTransportInStationaryFlow">
+ <nonlinear_solver>basic_picard</nonlinear_solver>
+ <convergence_criterion>
+ <type>PerComponentDeltaX</type>
+ <norm_type>NORM2</norm_type>
+ <abstols>1e-10 1e-7</abstols>
+ </convergence_criterion>
+ <time_discretization>
+ <type>BackwardEuler</type>
+ </time_discretization>
+ <time_stepping>
+ <type>FixedTimeStepping</type>
+ <t_initial> 0.0 </t_initial>
+ <t_end> 5.e+4 </t_end>
+ <timesteps>
+ <pair>
+ <repeat>250</repeat>
+ <delta_t>1000</delta_t>
+ </pair>
+ </timesteps>
+ </time_stepping>
+ </process>
+ </processes>
+ <output>
+ <type>VTK</type>
+ <prefix>HeatTransportInStationaryFlow</prefix>
+ <timesteps>
+ <pair>
+ <repeat> 1 </repeat>
+ <each_steps> 250 </each_steps>
+ </pair>
+ </timesteps>
+ <variables>
+ <variable>temperature</variable>
+ <variable>pressure</variable>
+ <variable>velocity</variable>
+ </variables>
+ <suffix>_ts_{:timestep}_t_{:time}</suffix>
+ <fixed_output_times>
+ 50000
+ 500000
+ 5000000
+ </fixed_output_times>
+ </output>
+ </time_loop>
+ <parameters>
+ <parameter>
+ <name>T0</name>
+ <type>Constant</type>
+ <value>0.0</value>
+ </parameter>
+ <parameter>
+ <name>P0</name>
+ <type>Constant</type>
+ <value>1e+5</value>
+ </parameter>
+ <parameter>
+ <name>p_left</name>
+ <type>Constant</type>
+ <value>1.01e5</value>
+ </parameter>
+ <parameter>
+ <name>p_right</name>
+ <type>Constant</type>
+ <value>1.0e5</value>
+ </parameter>
+ <parameter>
+ <name>T_left</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>geometry_left</mesh>
+ <type>Dirichlet</type>
+ <parameter>T_left</parameter>
+ </boundary_condition>
+ </boundary_conditions>
+ </process_variable>
+ <process_variable>
+ <name>pressure</name>
+ <components>1</components>
+ <order>1</order>
+ <initial_condition>P0</initial_condition>
+ <boundary_conditions>
+ <boundary_condition>
+ <mesh>geometry_left</mesh>
+ <type>Dirichlet</type>
+ <parameter>p_left</parameter>
+ </boundary_condition>
+ <boundary_condition>
+ <mesh>geometry_right</mesh>
+ <type>Dirichlet</type>
+ <parameter>p_right</parameter>
+ </boundary_condition>
+ </boundary_conditions>
+ </process_variable>
+ </process_variables>
+ <nonlinear_solvers>
+ <nonlinear_solver>
+ <name>basic_picard</name>
+ <type>Picard</type>
+ <max_iter>50</max_iter>
+ <linear_solver>general_linear_solver</linear_solver>
+ </nonlinear_solver>
+ </nonlinear_solvers>
+ <linear_solvers>
+ <linear_solver>
+ <name>general_linear_solver</name>
+ <lis>-i bicgstab -p jacobi -tol 1e-12 -maxiter 10000</lis>
+ <eigen>
+ <solver_type>BiCGSTAB</solver_type>
+ <precon_type>ILUT</precon_type>
+ <max_iteration_step>10000</max_iteration_step>
+ <error_tolerance>1e-18</error_tolerance>
+ </eigen>
+ </linear_solver>
+ </linear_solvers>
+</OpenGeoSysProject>
diff --git a/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/geometry.gml b/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/geometry.gml
new file mode 100644
index 0000000000000000000000000000000000000000..c645cfcf6cc58da26291bfd1b5e75f9893ec0852
--- /dev/null
+++ b/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/geometry.gml
@@ -0,0 +1,31 @@
+<?xml version="1.0" encoding="ISO-8859-1"?>
+<?xml-stylesheet type="text/xsl" href="OpenGeoSysGLI.xsl"?>
+
+<OpenGeoSysGLI xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:ogs="http://www.opengeosys.org">
+ <name>geometry</name>
+ <points>
+ <point id="0" x="0" y="0" z="0"/>
+ <point id="1" x="0" y="0.1" z="0"/>
+ <point id="2" x="1.0" y="0" z="0"/>
+ <point id="3" x="1.0" y="0.1" z="0"/>
+ </points>
+
+ <polylines>
+ <polyline id="0" name="left">
+ <pnt>0</pnt>
+ <pnt>1</pnt>
+ </polyline>
+ <polyline id="1" name="right">
+ <pnt>2</pnt>
+ <pnt>3</pnt>
+ </polyline>
+ <polyline id="2" name="top">
+ <pnt>1</pnt>
+ <pnt>3</pnt>
+ </polyline>
+ <polyline id="3" name="bottom">
+ <pnt>0</pnt>
+ <pnt>2</pnt>
+ </polyline>
+ </polylines>
+</OpenGeoSysGLI>
diff --git a/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/geometry_bottom.vtu b/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/geometry_bottom.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..5454b382d2dffd24c42dc57ee09f6873c50e0e78
--- /dev/null
+++ b/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/geometry_bottom.vtu
@@ -0,0 +1,30 @@
+<?xml version="1.0"?>
+<VTKFile type="UnstructuredGrid" version="1.0" byte_order="LittleEndian" header_type="UInt64">
+ <UnstructuredGrid>
+ <FieldData>
+ <DataArray type="Float64" Name="TimeValue" NumberOfTuples="1" format="appended" RangeMin="0" RangeMax="0" offset="0" />
+ </FieldData>
+ <Piece NumberOfPoints="40" NumberOfCells="39" >
+ <PointData>
+ <DataArray type="UInt64" Name="bulk_node_ids" format="appended" RangeMin="0" RangeMax="43" offset="24" />
+ <DataArray type="Int64" Name="vtkOriginalPointIds" format="appended" RangeMin="0" RangeMax="39" offset="464" />
+ </PointData>
+ <CellData>
+ <DataArray type="Int32" Name="MaterialIDs" format="appended" RangeMin="0" RangeMax="0" offset="904" />
+ <DataArray type="UInt64" Name="bulk_element_ids" format="appended" RangeMin="0" RangeMax="114" offset="1124" />
+ <DataArray type="Int64" Name="vtkOriginalCellIds" format="appended" RangeMin="0" RangeMax="115" offset="1552" />
+ </CellData>
+ <Points>
+ <DataArray type="Float64" Name="Points" NumberOfComponents="3" format="appended" RangeMin="0" RangeMax="1" offset="1980" />
+ </Points>
+ <Cells>
+ <DataArray type="Int64" Name="connectivity" format="appended" RangeMin="" RangeMax="" offset="3272" />
+ <DataArray type="Int64" Name="offsets" format="appended" RangeMin="" RangeMax="" offset="4116" />
+ <DataArray type="UInt8" Name="types" format="appended" RangeMin="" RangeMax="" offset="4544" />
+ </Cells>
+ </Piece>
+ </UnstructuredGrid>
+ <AppendedData encoding="base64">
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+ </AppendedData>
+</VTKFile>
diff --git a/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/geometry_left.vtu b/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/geometry_left.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..e6fc2865e0fb10e94688a43375178dad3db86535
--- /dev/null
+++ b/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/geometry_left.vtu
@@ -0,0 +1,30 @@
+<?xml version="1.0"?>
+<VTKFile type="UnstructuredGrid" version="1.0" byte_order="LittleEndian" header_type="UInt64">
+ <UnstructuredGrid>
+ <FieldData>
+ <DataArray type="Float64" Name="TimeValue" NumberOfTuples="1" format="appended" RangeMin="0" RangeMax="0" offset="0" />
+ </FieldData>
+ <Piece NumberOfPoints="4" NumberOfCells="3" >
+ <PointData>
+ <DataArray type="UInt64" Name="bulk_node_ids" format="appended" RangeMin="0" RangeMax="5" offset="24" />
+ <DataArray type="Int64" Name="vtkOriginalPointIds" format="appended" RangeMin="0" RangeMax="3" offset="80" />
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+ <DataArray type="Int64" Name="vtkOriginalCellIds" format="appended" RangeMin="0" RangeMax="2" offset="208" />
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+ <Points>
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+ <Cells>
+ <DataArray type="Int64" Name="connectivity" format="appended" RangeMin="" RangeMax="" offset="392" />
+ <DataArray type="Int64" Name="offsets" format="appended" RangeMin="" RangeMax="" offset="468" />
+ <DataArray type="UInt8" Name="types" format="appended" RangeMin="" RangeMax="" offset="512" />
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+ </UnstructuredGrid>
+ <AppendedData encoding="base64">
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+ </AppendedData>
+</VTKFile>
diff --git a/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/geometry_right.vtu b/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/geometry_right.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..807e84daad191f059cabd5f0db1dd767a3f1fc62
--- /dev/null
+++ b/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/geometry_right.vtu
@@ -0,0 +1,30 @@
+<?xml version="1.0"?>
+<VTKFile type="UnstructuredGrid" version="1.0" byte_order="LittleEndian" header_type="UInt64">
+ <UnstructuredGrid>
+ <FieldData>
+ <DataArray type="Float64" Name="TimeValue" NumberOfTuples="1" format="appended" RangeMin="0" RangeMax="0" offset="0" />
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+</VTKFile>
diff --git a/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/geometry_top.vtu b/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/geometry_top.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..c448d8f81cced6a95529f45c1ce223b06e2a1033
--- /dev/null
+++ b/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/geometry_top.vtu
@@ -0,0 +1,30 @@
+<?xml version="1.0"?>
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diff --git a/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/mesh.vtu b/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/mesh.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..3e11bfb37b93fdb8e63a642eef10e3e0d8a2e60a
--- /dev/null
+++ b/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/mesh.vtu
@@ -0,0 +1,23 @@
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diff --git a/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/mesh_q.vtu b/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/mesh_q.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..f63dce95f12b8f52b652fb30919af1caaa2ce41a
--- /dev/null
+++ b/Tests/Data/Parabolic/HT/HeatTransportInStationaryFlow/mesh_q.vtu
@@ -0,0 +1,23 @@
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