diff --git a/ProcessLib/LiquidFlow/Tests.cmake b/ProcessLib/LiquidFlow/Tests.cmake
index 7ff25c34ca12a51f781e58df308d60b816b19f03..0e686bad271bd56570c843bd82a0bcb4fd4e5f98 100644
--- a/ProcessLib/LiquidFlow/Tests.cmake
+++ b/ProcessLib/LiquidFlow/Tests.cmake
@@ -332,3 +332,19 @@ AddTest(
Dupuit_TestSet_01_pcs_0_ts_90_t_7776000.000000.vtu TestSet_01_pcs_0_ts_90_t_7776000.000000.vtu pressure pressure 3e-12 2e-13
Dupuit_TestSet_01_pcs_0_ts_100_t_8640000.000000.vtu TestSet_01_pcs_0_ts_100_t_8640000.000000.vtu pressure pressure 3e-12 2e-13
)
+
+AddTest(
+ NAME LiquidFlow_TimeDependentHeterogeneousDirichletBCs
+ PATH Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions
+ EXECUTABLE ogs
+ EXECUTABLE_ARGS TimeDependentHeterogeneousBoundaryConditions.prj
+ WRAPPER time
+ TESTER vtkdiff
+ REQUIREMENTS NOT OGS_USE_MPI
+ DIFF_DATA
+ time_dependent_heterogeneous_bcs_pcs_0_ts_1_t_10.000000.vtu time_dependent_heterogeneous_bcs_pcs_0_ts_1_t_10.000000.vtu pressure pressure 1e-7 1e-13
+ time_dependent_heterogeneous_bcs_pcs_0_ts_118_t_1180.000000.vtu time_dependent_heterogeneous_bcs_pcs_0_ts_118_t_1180.000000.vtu pressure pressure 1e-7 1e-13
+ time_dependent_heterogeneous_bcs_pcs_0_ts_119_t_1190.000000.vtu time_dependent_heterogeneous_bcs_pcs_0_ts_119_t_1190.000000.vtu pressure pressure 1e-7 1e-13
+ time_dependent_heterogeneous_bcs_pcs_0_ts_120_t_1200.000000.vtu time_dependent_heterogeneous_bcs_pcs_0_ts_120_t_1200.000000.vtu pressure pressure 1e-7 1e-13
+ time_dependent_heterogeneous_bcs_pcs_0_ts_200_t_2000.000000.vtu time_dependent_heterogeneous_bcs_pcs_0_ts_200_t_2000.000000.vtu pressure pressure 1e-7 1e-13
+)
diff --git a/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/TimeDependentHeterogeneousBoundaryConditions.prj b/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/TimeDependentHeterogeneousBoundaryConditions.prj
new file mode 100644
index 0000000000000000000000000000000000000000..50168fc950228543111dd2ae016e1c094496636b
--- /dev/null
+++ b/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/TimeDependentHeterogeneousBoundaryConditions.prj
@@ -0,0 +1,260 @@
+<?xml version="1.0" encoding="ISO-8859-1"?>
+<OpenGeoSysProject>
+ <meshes>
+ <mesh>mesh2D.vtu</mesh>
+ <mesh>left.vtu</mesh>
+ <mesh>right.vtu</mesh>
+ </meshes>
+ <processes>
+ <process>
+ <name>LiquidFlow</name>
+ <type>LIQUID_FLOW</type>
+ <integration_order>2</integration_order>
+ <darcy_gravity>
+ <!-- axis_id: 0, 1, or the dimension of space minus one -->
+ <axis_id>1</axis_id>
+ <!-- g>=0. g=0: non gravity term -->
+ <g>0.0</g>
+ </darcy_gravity>
+ <process_variables>
+ <process_variable>pressure</process_variable>
+ </process_variables>
+ <secondary_variables>
+ <secondary_variable type="static" internal_name="darcy_velocity" output_name="v"/>
+ </secondary_variables>
+ <material_property>
+ <fluid>
+ <density>
+ <type>Constant</type>
+ <value> 1.e3 </value>
+ </density>
+ <viscosity>
+ <type>Constant</type>
+ <value> 1.e-3 </value>
+ </viscosity>
+ </fluid>
+ <porous_medium>
+ <porous_medium id="0">
+ <permeability>
+ <permeability_tensor_entries>kappa1</permeability_tensor_entries>
+ <type>Constant</type>
+ </permeability>
+ <porosity>
+ <type>Constant</type>
+ <porosity_parameter>constant_porosity_parameter</porosity_parameter>
+ </porosity>
+ <storage>
+ <type>Constant</type>
+ <value> 1e-5 </value>
+ </storage>
+ </porous_medium>
+ </porous_medium>
+ </material_property>
+ </process>
+ </processes>
+ <time_loop>
+ <processes>
+ <process ref="LiquidFlow">
+ <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> 2000 </t_end>
+ <timesteps>
+ <pair>
+ <repeat>200</repeat>
+ <delta_t>10.0</delta_t>
+ </pair>
+ </timesteps>
+ </time_stepping>
+ </process>
+ </processes>
+ <output>
+ <type>VTK</type>
+ <prefix>time_dependent_heterogeneous_bcs</prefix>
+ <timesteps>
+ <pair>
+ <repeat> 1 </repeat>
+ <each_steps> 1 </each_steps>
+ </pair>
+ <pair>
+ <repeat> 1 </repeat>
+ <each_steps> 117 </each_steps>
+ </pair>
+ <pair>
+ <repeat> 2 </repeat>
+ <each_steps> 1 </each_steps>
+ </pair>
+ <pair>
+ <repeat> 1 </repeat>
+ <each_steps> 80 </each_steps>
+ </pair>
+ </timesteps>
+ <variables>
+ <variable> pressure </variable>
+ <variable> v </variable>
+ </variables>
+ </output>
+ </time_loop>
+ <parameters>
+ <parameter>
+ <name>p0</name>
+ <type>Constant</type>
+ <value>9.5e5</value>
+ </parameter>
+ <parameter>
+ <name>bc_left_ts1</name>
+ <type>MeshNode</type>
+ <mesh>left</mesh>
+ <field_name>p_ts1</field_name>
+ </parameter>
+ <parameter>
+ <name>bc_left_ts59</name>
+ <type>MeshNode</type>
+ <mesh>left</mesh>
+ <field_name>p_ts59</field_name>
+ </parameter>
+ <parameter>
+ <name>bc_left_ts60</name>
+ <type>MeshNode</type>
+ <mesh>left</mesh>
+ <field_name>p_ts60</field_name>
+ </parameter>
+ <parameter>
+ <name>bc_left_ts100</name>
+ <type>MeshNode</type>
+ <mesh>left</mesh>
+ <field_name>p_ts60</field_name>
+ </parameter>
+ <parameter>
+ <name>bc_right_ts1</name>
+ <type>MeshNode</type>
+ <mesh>right</mesh>
+ <field_name>p_ts1</field_name>
+ </parameter>
+ <parameter>
+ <name>bc_right_ts59</name>
+ <type>MeshNode</type>
+ <mesh>right</mesh>
+ <field_name>p_ts59</field_name>
+ </parameter>
+ <parameter>
+ <name>bc_right_ts60</name>
+ <type>MeshNode</type>
+ <mesh>right</mesh>
+ <field_name>p_ts60</field_name>
+ </parameter>
+ <parameter>
+ <name>bc_right_ts100</name>
+ <type>MeshNode</type>
+ <mesh>right</mesh>
+ <field_name>p_ts60</field_name>
+ </parameter>
+ <parameter>
+ <name>constant_porosity_parameter</name>
+ <type>Constant</type>
+ <value>0.2</value>
+ </parameter>
+ <parameter>
+ <name>kappa1</name>
+ <type>Constant</type>
+ <values>1.e-12</values>
+ </parameter>
+ <parameter>
+ <name>TimeDependentDirichlet_left</name>
+ <type>TimeDependentHeterogeneousParameter</type>
+ <time_series>
+ <pair>
+ <time>0</time>
+ <parameter_name>bc_left_ts1</parameter_name>
+ </pair>
+ <pair>
+ <time>1180</time>
+ <parameter_name>bc_left_ts59</parameter_name>
+ </pair>
+ <pair>
+ <time>1200</time>
+ <parameter_name>bc_left_ts60</parameter_name>
+ </pair>
+ <pair>
+ <time>2000</time>
+ <parameter_name>bc_left_ts100</parameter_name>
+ </pair>
+ </time_series>
+ </parameter>
+ <parameter>
+ <name>TimeDependentDirichlet_right</name>
+ <type>TimeDependentHeterogeneousParameter</type>
+ <time_series>
+ <pair>
+ <time>0</time>
+ <parameter_name>bc_right_ts1</parameter_name>
+ </pair>
+ <pair>
+ <time>1180</time>
+ <parameter_name>bc_right_ts59</parameter_name>
+ </pair>
+ <pair>
+ <time>1200</time>
+ <parameter_name>bc_right_ts60</parameter_name>
+ </pair>
+ <pair>
+ <time>2000</time>
+ <parameter_name>bc_right_ts100</parameter_name>
+ </pair>
+ </time_series>
+ </parameter>
+ </parameters>
+ <process_variables>
+ <process_variable>
+ <name>pressure</name>
+ <components>1</components>
+ <order>1</order>
+ <initial_condition>p0</initial_condition>
+ <boundary_conditions>
+ <boundary_condition>
+ <mesh>left</mesh>
+ <type>Dirichlet</type>
+ <parameter>TimeDependentDirichlet_left</parameter>
+ </boundary_condition>
+ <boundary_condition>
+ <mesh>right</mesh>
+ <type>Dirichlet</type>
+ <parameter>TimeDependentDirichlet_right</parameter>
+ </boundary_condition>
+ </boundary_conditions>
+ </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-20 -maxiter 10000</lis>
+ <eigen>
+ <solver_type>CG</solver_type>
+ <precon_type>DIAGONAL</precon_type>
+ <max_iteration_step>10000</max_iteration_step>
+ <error_tolerance>1e-20</error_tolerance>
+ </eigen>
+ <petsc>
+ <prefix>lf</prefix>
+ <parameters>-lf_ksp_type cg -lf_pc_type bjacobi -lf_ksp_rtol 1e-16 -lf_ksp_max_it 10000</parameters>
+ </petsc>
+ </linear_solver>
+ </linear_solvers>
+</OpenGeoSysProject>
diff --git a/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/left.vtu b/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/left.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..4b1400935927561cdb1d07506fe59e7979dfe55a
--- /dev/null
+++ b/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/left.vtu
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9dfa10cb45121028f8c642dc236c8ae2d9f55e84a96549dd585c0fc8bc3cfb2b
+size 4473
diff --git a/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/mesh2D.vtu b/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/mesh2D.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..9ba80c041bed1bebc910440a6a4d35edb48f72cc
--- /dev/null
+++ b/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/mesh2D.vtu
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d5d24fb327d0e8b5bb516bb6a406466e56dadee18a4766e5970f4f698dd94f74
+size 35782
diff --git a/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/right.vtu b/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/right.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..eaba8332c6d161446543326984118a7d3dae1d0a
--- /dev/null
+++ b/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/right.vtu
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:228a2083be85d765c820c2d2065f8d4f48f5a1316ff57d6c2d14471ce191415d
+size 4495
diff --git a/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/time_dependent_heterogeneous_bcs_pcs_0_ts_118_t_1180.000000.vtu b/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/time_dependent_heterogeneous_bcs_pcs_0_ts_118_t_1180.000000.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..575104efa93fee17b43f7005d2d03a85dcfb2824
--- /dev/null
+++ b/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/time_dependent_heterogeneous_bcs_pcs_0_ts_118_t_1180.000000.vtu
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:22d5dfdee5e9bb809bf96116325d582073dfd610339cecc1400669dc6af30041
+size 26794
diff --git a/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/time_dependent_heterogeneous_bcs_pcs_0_ts_119_t_1190.000000.vtu b/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/time_dependent_heterogeneous_bcs_pcs_0_ts_119_t_1190.000000.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..76d06e12f100a81f61ce03942e3e21d6159cb8f4
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+++ b/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/time_dependent_heterogeneous_bcs_pcs_0_ts_119_t_1190.000000.vtu
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
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diff --git a/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/time_dependent_heterogeneous_bcs_pcs_0_ts_120_t_1200.000000.vtu b/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/time_dependent_heterogeneous_bcs_pcs_0_ts_120_t_1200.000000.vtu
new file mode 100644
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+++ b/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/time_dependent_heterogeneous_bcs_pcs_0_ts_120_t_1200.000000.vtu
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
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diff --git a/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/time_dependent_heterogeneous_bcs_pcs_0_ts_1_t_10.000000.vtu b/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/time_dependent_heterogeneous_bcs_pcs_0_ts_1_t_10.000000.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..131f149757f2ccfa4b41318e51dab01b510bc731
--- /dev/null
+++ b/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/time_dependent_heterogeneous_bcs_pcs_0_ts_1_t_10.000000.vtu
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
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diff --git a/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/time_dependent_heterogeneous_bcs_pcs_0_ts_200_t_2000.000000.vtu b/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/time_dependent_heterogeneous_bcs_pcs_0_ts_200_t_2000.000000.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..15c3d88c12602f939e89126c73ba7a59f86c2af3
--- /dev/null
+++ b/Tests/Data/Parabolic/LiquidFlow/TimeDependentHeterogeneousBoundaryConditions/time_dependent_heterogeneous_bcs_pcs_0_ts_200_t_2000.000000.vtu
@@ -0,0 +1,3 @@
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