# Problems with HT process in 2D mesh (error in matrix)

**URL:** <https://discourse.opengeosys.org/t/problems-with-ht-process-in-2d-mesh-error-in-matrix/1692>\
**Category:** Help & Support\
**Created:** [September 13, 2025, 8:53pm UTC](https://discourse.opengeosys.org/t/problems-with-ht-process-in-2d-mesh-error-in-matrix/1692 "2025-09-13T20:53:22Z")\
**Posts on this page:** 8\
**Page:** 1

<div class="post-metadata">

**Author:** ![Ronia\_a](https://discourse.opengeosys.org/letter_avatar_proxy/v4/letter/r/9de0a6/32.png) [@Ronia\_a](https://discourse.opengeosys.org/u/Ronia_a)\
**Post date:** [September 13, 2025, 8:53pm UTC](https://discourse.opengeosys.org/t/problems-with-ht-process-in-2d-mesh-error-in-matrix/1692/1 "2025-09-13T20:53:22Z")

</div>

The following is my HT prj for 2D mesh -

```xml
<?xml version='1.0' encoding='ISO-8859-1'?>
<OpenGeoSysProject>
    <meshes>
        <mesh>2Dmesh_initialfields.vtu</mesh>
        <mesh>leftHT.vtu</mesh>
        <mesh>2DboundaryHT.vtu</mesh>
    </meshes>

     <processes>
    <process>
      <name>th_decovalex</name>
      <type>HT</type>
      <coupling_scheme>staggered</coupling_scheme>
      <integration_order>4</integration_order>
      <process_variables>
        <temperature>T</temperature>
        <pressure>p</pressure>
      </process_variables>
      <specific_body_force>0 0 -9.81</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>density</name>
                            <type>Constant</type>
                            <value>1000</value>
                        </property>
                        <property>
                            <name>viscosity</name>
                            <type>Constant</type>
                            <value>1.0e-3</value>
                        </property>
                        <property>
                            <name>specific_heat_capacity</name>
                            <type>Constant</type>
                            <value>4000</value>
                        </property>
                        <property>
                            <name>thermal_conductivity</name>
                            <type>Constant</type>
                            <value>18921600</value>
                        </property>
                    </properties>
                </phase>
                <phase>
                    <type>Solid</type>
                    <properties>
                        <property>
                            <name>storage</name>
                            <type>Constant</type>
                            <value>1e-10</value>
                        </property>
                        <property>
                            <name>density</name>
                            <type>Constant</type>
                            <value>2700</value>
                        </property>
                        <property>
                            <name>thermal_conductivity</name>
                            <type>Constant</type>
                            <value>3.0 0 0 3.0</value>
                        </property>
                        <property>
                            <name>specific_heat_capacity</name>
                            <type>Constant</type>
                            <value>900</value>
                        </property>
                    </properties>
                </phase>
            </phases>
            <properties>
                <property>
                    <name>thermal_longitudinal_dispersivity</name>
                    <type>Constant</type>
                    <value>0.0</value>
                </property>
                <property>
                    <name>thermal_transversal_dispersivity</name>
                    <type>Constant</type>
                    <value>0.0</value>
                </property>
                <property>
                    <name>permeability</name>
                    <type>Constant</type>
                    <value>1e-13 0 0 0 1e-13 0 0 0 1e-13</value>
                </property>
                <property>
                    <name>porosity</name>
                    <type>Constant</type>
                    <value>0.30</value>
                </property>
                <property>
                    <name>thermal_conductivity</name>
                    <type>EffectiveThermalConductivityPorosityMixing</type>
                </property>
            </properties>
        </medium>

        <medium id="1">
            <phases>
                <phase>
                    <type>AqueousLiquid</type>
                    <properties>
                        <property>
                            <name>density</name>
                            <type>Constant</type>
                            <value>1000</value>
                        </property>
                        <property>
                            <name>viscosity</name>
                            <type>Constant</type>
                            <value>1.0e-3</value>
                        </property>
                        <property>
                            <name>specific_heat_capacity</name>
                            <type>Constant</type>
                            <value>4000</value>
                        </property>
                        <property>
                            <name>thermal_conductivity</name>
                            <type>Constant</type>
                            <value>18921600</value>
                        </property>
                    </properties>
                </phase>
                <phase>
                    <type>Solid</type>
                    <properties>
                        <property>
                            <name>storage</name>
                            <type>Constant</type>
                            <value>1e-10</value>
                        </property>
                        <property>
                            <name>density</name>
                            <type>Constant</type>
                            <value>2160</value>
                        </property>
                        <property>
                            <name>thermal_conductivity</name>
                            <type>Constant</type>
                            <value>5.5 0 0 5.5</value>
                        </property>
                        <property>
                            <name>specific_heat_capacity</name>
                            <type>Constant</type>
                            <value>900</value>
                        </property>
                    </properties>
                </phase>
            </phases>
            <properties>
                <property>
                    <name>thermal_longitudinal_dispersivity</name>
                    <type>Constant</type>
                    <value>0.0</value>
                </property>
                <property>
                    <name>thermal_transversal_dispersivity</name>
                    <type>Constant</type>
                    <value>0.0</value>
                </property>
                <property>
                    <name>permeability</name>
                    <type>Constant</type>
                    <value>5.5e-16 0 0 0 5.5e-16 0 0 0 5.5e-16 </value>
                </property>
                <property>
                    <name>porosity</name>
                    <type>Constant</type>
                    <value>0.12</value>
                </property>
                <property>
                    <name>thermal_conductivity</name>
                    <type>EffectiveThermalConductivityPorosityMixing</type>
                </property>
            </properties>
        </medium>
    </media>
    <time_loop>
    <global_process_coupling>
      <max_iter>6</max_iter>
      <convergence_criteria>
        <convergence_criterion>
          <type>DeltaX</type>
          <norm_type>NORM2</norm_type>
          <reltol>1.e-14</reltol>
        </convergence_criterion>
        <convergence_criterion>
          <type>DeltaX</type>
          <norm_type>NORM2</norm_type>
          <reltol>1.e-14</reltol>
        </convergence_criterion>
      </convergence_criteria>
    </global_process_coupling>
    <processes>
      <process ref="th_decovalex">
        <nonlinear_solver>basic_picard_T</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>1e3</t_end>
          <timesteps>
            <pair>
              <repeat>4</repeat>
              <delta_t>0.001</delta_t>
            </pair>
            <pair>
              <repeat>1</repeat>
              <delta_t>0.006</delta_t>
            </pair>
            <pair>
              <repeat>9</repeat>
              <delta_t>0.01</delta_t>
            </pair>
            <pair>
              <repeat>9</repeat>
              <delta_t>0.1</delta_t>
            </pair>
            <pair>
              <repeat>39</repeat>
              <delta_t>1.</delta_t>
            </pair>
            <pair>
              <repeat>2</repeat>
              <delta_t>2.0</delta_t>
            </pair>
            <pair>
              <repeat>1</repeat>
              <delta_t>16.0</delta_t>
            </pair>
            <pair>
              <repeat>1</repeat>
              <delta_t>30.0</delta_t>
            </pair>
            <pair>
              <repeat>1</repeat>
              <delta_t>40.0</delta_t>
            </pair>
            <pair>
              <repeat>10</repeat>
              <delta_t>86.0</delta_t>
            </pair>
            <pair>
              <repeat>90</repeat>
              <delta_t>100.0</delta_t>
            </pair>
            <pair>
              <repeat>100</repeat>
              <delta_t>900</delta_t>
            </pair>
            <pair>
              <repeat>90</repeat>
              <delta_t>1.e4</delta_t>
            </pair>
          </timesteps>
        </time_stepping>
      </process>
      <process ref="th_decovalex">
        <nonlinear_solver>basic_picard_H</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.e3</t_end>
          <timesteps>
            <pair>
              <repeat>4</repeat>
              <delta_t>0.001</delta_t>
            </pair>
            <pair>
              <repeat>1</repeat>
              <delta_t>0.006</delta_t>
            </pair>
            <pair>
              <repeat>9</repeat>
              <delta_t>0.01</delta_t>
            </pair>
            <pair>
              <repeat>9</repeat>
              <delta_t>0.1</delta_t>
            </pair>
            <pair>
              <repeat>39</repeat>
              <delta_t>1.</delta_t>
            </pair>
            <pair>
              <repeat>2</repeat>
              <delta_t>2.0</delta_t>
            </pair>
            <pair>
              <repeat>1</repeat>
              <delta_t>16.0</delta_t>
            </pair>
            <pair>
              <repeat>1</repeat>
              <delta_t>30.0</delta_t>
            </pair>
            <pair>
              <repeat>1</repeat>
              <delta_t>40.0</delta_t>
            </pair>
            <pair>
              <repeat>10</repeat>
              <delta_t>86.0</delta_t>
            </pair>
            <pair>
              <repeat>90</repeat>
              <delta_t>100.0</delta_t>
            </pair>
            <pair>
              <repeat>100</repeat>
              <delta_t>900</delta_t>
            </pair>
            <pair>
              <repeat>90</repeat>
              <delta_t>1.e4</delta_t>
            </pair>
          </timesteps>
        </time_stepping>
      </process>
    </processes>
    <output>
      <type>VTK</type>
      <prefix>th_decovalex</prefix>
      <suffix>ts{:timestep}_t_{:time}</suffix>
      <timesteps>
        <pair>
          <repeat>1</repeat>
          <each_steps>10</each_steps>
        </pair>
      </timesteps>
      <variables>
        <variable>T</variable>
        <variable>p</variable>
        <variable>darcy_velocity</variable>
      </variables>
    </output>
    </time_loop> 
    

    <parameters>
        <parameter>
            <name>T0</name>
            <type>Constant</type>
            <value>283</value>
        </parameter>
        <parameter>
            <name>heat_source</name>
            <type>MeshNode</type>
            <field_name>t_init</field_name>
        </parameter>
        
        <parameter>
            <name>p_in</name>
            <type>Constant</type>
            <value>1.0e9</value>
        </parameter>
        <parameter>
            <name>ic</name>
            <type>MeshNode</type>
            <field_name>p_init</field_name>
        </parameter>
    </parameters>

    <process_variables>
        <process_variable>
            <name>T</name>
            <components>1</components>
            <order>1</order>
            <initial_condition>heat_source</initial_condition>
            <boundary_conditions>
                <boundary_condition>
                    <mesh>2DboundaryHT</mesh>
                    <type>Dirichlet</type>
                    <parameter>T0</parameter>
                </boundary_condition>

            </boundary_conditions>
        </process_variable>

        <process_variable>
            <name>p</name>
            <components>1</components>
            <order>1</order>

            <!-- Hydrostatic Initial Condition -->
            <initial_condition>ic</initial_condition>

            <!-- Boundary Conditions -->
            <boundary_conditions>
                <boundary_condition>
                    <mesh>leftHT</mesh>
                    <type>Neumann</type>
                    <parameter>p_in</parameter>
                </boundary_condition>
            </boundary_conditions>
        </process_variable>
    </process_variables>
    
    <nonlinear_solvers>
    <nonlinear_solver>
      <name>basic_picard_T</name>
      <type>Picard</type>
      <max_iter>10</max_iter>
      <linear_solver>linear_solver_T</linear_solver>
    </nonlinear_solver>
    <nonlinear_solver>
      <name>basic_picard_H</name>
      <type>Picard</type>
      <max_iter>10</max_iter>
      <linear_solver>linear_solver_H</linear_solver>
    </nonlinear_solver>
  </nonlinear_solvers>
  <linear_solvers>
    <linear_solver>
      <name>linear_solver_T</name>
      <lis>-i cg -p jacobi -tol 1e-20 -maxiter 10000</lis>
      <eigen>
        <solver_type>BiCGSTAB</solver_type>
        <precon_type>DIAGONAL</precon_type>
        <max_iteration_step>10000</max_iteration_step>
        <error_tolerance>1e-20</error_tolerance>
      </eigen>
      <petsc>
        <prefix>T</prefix>
        <parameters>-T_ksp_type bcgs -T_pc_type bjacobi -T_ksp_rtol 1e-16 -T_ksp_max_it 10000</parameters>
      </petsc>
    </linear_solver>
    <linear_solver>
      <name>linear_solver_H</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>H</prefix>
        <parameters>-H_ksp_type cg -H_pc_type bjacobi -H_ksp_rtol 1e-16 -H_ksp_max_it 10000</parameters>
      </petsc>
    </linear_solver>
  </linear_solvers>
</OpenGeoSysProject>

```

My error persists when I convert it into 2_2 or 3_3

```auto
info: Global coupling iteration #0 started.
info: Solve process #0 (named as not given)
info: Iteration #1 started.
critical: C:/Users/gitlab/code/ogs/ogs/MaterialLib/MPL/Utils/FormEigenTensor.cpp:57 MaterialPropertyLib::FormEigenTensor<3>::operator ()()
warning: There are still 1 global matrices in use. This might be an indicator of a possible waste of memory.
warning: There are still 2 global vectors in use. This might be an indicator of a possible waste of memory.
error: Cannot convert a 2d tensor to 3x3 matrix
error: OGS terminated with error on 2025-09-13 22:45:32+0200.

```

---

<div class="post-metadata">

**Author:** ![chleh](https://discourse.opengeosys.org/user_avatar/discourse.opengeosys.org/chleh/32/854_2.png) [@chleh](https://discourse.opengeosys.org/u/chleh)\
**Post date:** [September 15, 2025, 6:36am UTC](https://discourse.opengeosys.org/t/problems-with-ht-process-in-2d-mesh-error-in-matrix/1692/2 "2025-09-15T06:36:42Z")

</div>

Hi Ronia\_a,

I guess the problem comes from the permeability. You’ve given 9 components, which OGS will interpret as a 3x3 tensor, which it rejects in a 2D setting.

> [@Ronia\_a](#):
>
> ```xml
> <property>
> <name>permeability</name>
> <type>Constant</type>
> <value>1e-13 0 0 0 1e-13 0 0 0 1e-13</value>
> </property>
> 
> ```

In a 3D setting the 4 thermal conductivity components will likely cause problems:

```xml
                        <property>
                            <name>thermal_conductivity</name>
                            <type>Constant</type>
                            <value>3.0 0 0 3.0</value>
                        </property>

```

Best regards,  
Christoph

---

<div class="post-metadata">

**Author:** ![chleh](https://discourse.opengeosys.org/user_avatar/discourse.opengeosys.org/chleh/32/854_2.png) [@chleh](https://discourse.opengeosys.org/u/chleh)\
**Post date:** [September 15, 2025, 6:37am UTC](https://discourse.opengeosys.org/t/problems-with-ht-process-in-2d-mesh-error-in-matrix/1692/3 "2025-09-15T06:37:24Z")

</div>

Btw.: for isotropic properties a single component is sufficient.

---

<div class="post-metadata">

**Author:** ![Ronia\_a](https://discourse.opengeosys.org/letter_avatar_proxy/v4/letter/r/9de0a6/32.png) [@Ronia\_a](https://discourse.opengeosys.org/u/Ronia_a)\
**Post date:** [September 15, 2025, 9:17am UTC](https://discourse.opengeosys.org/t/problems-with-ht-process-in-2d-mesh-error-in-matrix/1692/4 "2025-09-15T09:17:59Z")

</div>

I tried with single component for permeability and thermal conductivity,  
but still the same error.  
C:\THESIS DUMP\Series1\2D\>“C:\THESIS DUMP\Series1\ogs-6.5.5.Windows-10.0.19045-python-3.13.2-utils\bin\ogs.exe” 2Drepo\_prj\_HT.prj  
info: OGS started on 2025-09-15 11:17:14+0200 in serial mode.  
info: This is OpenGeoSys-6 version 6.5.5.dirty. Log version: 2, Log level: info.  
info: Eigen use 1 threads  
info: Reading project file 2Drepo\_prj\_HT.prj.  
info: readRasters …  
info: readRasters done  
info: ConstantParameter: T0  
info: MeshNodeParameter: heat\_source  
info: ConstantParameter: p\_in  
info: MeshNodeParameter: ic  
info: No source terms for process variable ‘T’ found.  
info: No source terms for process variable ‘p’ found.  
info: The equations of the coupled processes will be solved by the staggered scheme.  
info: Initialize processes.  
info: Time step #0 started. Time: 0. Step size: 0.  
info: [time] Output of timestep 0 took 0.0029361 s.  
info: Time step #0 took 0.0316513 s.  
info: Solve processes.  
info: Time step #1 started. Time: 0.001. Step size: 0.001.  
info: Global coupling iteration #0 started.  
info: Solve process #0 (named as not given)  
info: Iteration #1 started.  
critical: C:/Users/gitlab/code/ogs/ogs/MaterialLib/MPL/Utils/FormEigenTensor.cpp:57 MaterialPropertyLib::FormEigenTensor\<3\>::operator ()()  
warning: There are still 1 global matrices in use. This might be an indicator of a possible waste of memory.  
warning: There are still 2 global vectors in use. This might be an indicator of a possible waste of memory.  
error: Cannot convert a 2d tensor to 3x3 matrix  
error: OGS terminated with error on 2025-09-15 11:17:14+0200.

---

<div class="post-metadata">

**Author:** ![dmitri.naumov](https://discourse.opengeosys.org/user_avatar/discourse.opengeosys.org/dmitri.naumov/32/561_2.png) [@dmitri.naumov](https://discourse.opengeosys.org/u/dmitri.naumov)\
**Post date:** [September 15, 2025, 1:01pm UTC](https://discourse.opengeosys.org/t/problems-with-ht-process-in-2d-mesh-error-in-matrix/1692/5 "2025-09-15T13:01:08Z")

</div>

For the isotropic thermal\_conductivity it is sufficient to give a scalar:

```xml
                        <property>
                            <name>thermal_conductivity</name>
                            <type>Constant</type>
                            <value>5.5</value>
                        </property>

```

Alternatively for a 3d mesh, you can specify all components:

```xml
                        <property>
                            <name>thermal_conductivity</name>
                            <type>Constant</type>
                            <value>5.5 0 0 0 5.5 0 0 0 5.5</value>
                        </property>

```

And same for the other thermal\_conductivity with value 3.

– d

---

<div class="post-metadata">

**Author:** ![chleh](https://discourse.opengeosys.org/user_avatar/discourse.opengeosys.org/chleh/32/854_2.png) [@chleh](https://discourse.opengeosys.org/u/chleh)\
**Post date:** [September 15, 2025, 1:05pm UTC](https://discourse.opengeosys.org/t/problems-with-ht-process-in-2d-mesh-error-in-matrix/1692/6 "2025-09-15T13:05:40Z")

</div>

Ronia, you have two media. Did you correct all occurences of thermal conductivity and permeability?

---

<div class="post-metadata">

**Author:** ![Ronia\_a](https://discourse.opengeosys.org/letter_avatar_proxy/v4/letter/r/9de0a6/32.png) [@Ronia\_a](https://discourse.opengeosys.org/u/Ronia_a)\
**Post date:** [September 16, 2025, 12:58pm UTC](https://discourse.opengeosys.org/t/problems-with-ht-process-in-2d-mesh-error-in-matrix/1692/7 "2025-09-16T12:58:30Z")

</div>

Yes I have two media, I only kept the thermal conductivity for both the media 3\*3 and rest is scalar .

Still the itartion starts and then says-  
C:\THESIS DUMP\Series1\2D\>“C:\THESIS DUMP\Series1\ogs-6.5.5.Windows-10.0.19045-python-3.13.2-utils\bin\ogs.exe” 2Drepo\_prj\_HT.prj  
info: OGS started on 2025-09-16 14:57:54+0200 in serial mode.  
info: This is OpenGeoSys-6 version 6.5.5.dirty. Log version: 2, Log level: info.  
info: Eigen use 1 threads  
info: Reading project file 2Drepo\_prj\_HT.prj.  
info: readRasters …  
info: readRasters done  
info: ConstantParameter: T0  
info: MeshNodeParameter: heat\_source  
info: ConstantParameter: p\_in  
info: MeshNodeParameter: ic  
info: No source terms for process variable ‘T’ found.  
info: No source terms for process variable ‘p’ found.  
info: The equations of the coupled processes will be solved by the staggered scheme.  
info: Initialize processes.  
info: Time step #0 started. Time: 0. Step size: 0.  
info: [time] Output of timestep 0 took 0.0058556 s.  
info: Time step #0 took 0.0161407 s.  
info: Solve processes.  
info: Time step #1 started. Time: 0.001. Step size: 0.001.  
info: Global coupling iteration #0 started.  
info: Solve process #0 (named as not given)  
info: Iteration #1 started.  
critical: C:/Users/gitlab/code/ogs/ogs/MaterialLib/MPL/Utils/FormEigenTensor.cpp:67 MaterialPropertyLib::FormEigenTensor\<2\>::operator ()()  
warning: There are still 1 global matrices in use. This might be an indicator of a possible waste of memory.  
warning: There are still 2 global vectors in use. This might be an indicator of a possible waste of memory.  
error: Cannot convert a 3d tensor to 2x2 matrix  
error: OGS terminated with error on 2025-09-16 14:57:54+0200.

NOW THE PRJ LOOKS LIKE THIS BELOW-

\<?xml version='1.0' encoding='ISO-8859-1'?\> 2Dmesh\_initialfields.vtu leftHT.vtu 2DboundaryHT.vtu 

```
 <processes>
<process>
  <name>th_decovalex</name>
  <type>HT</type>
  <coupling_scheme>staggered</coupling_scheme>
  <integration_order>4</integration_order>
  <process_variables>
    <temperature>T</temperature>
    <pressure>p</pressure>
  </process_variables>
  <specific_body_force>0 0 -9.81</specific_body_force>
  <secondary_variables>
    <secondary_variable internal_name="darcy_velocity" output_name="darcy_velocity" />
  </secondary_variables>
</process>

```

```
<media>
    <medium id="0">
        <phases>
            <phase>
                <type>AqueousLiquid</type>
                <properties>
                    <property>
                        <name>density</name>
                        <type>Constant</type>
                        <value>1000</value>
                    </property>
                    <property>
                        <name>viscosity</name>
                        <type>Constant</type>
                        <value>1.0e-3</value>
                    </property>
                    <property>
                        <name>specific_heat_capacity</name>
                        <type>Constant</type>
                        <value>4000</value>
                    </property>
                    <property>
                        <name>thermal_conductivity</name>
                        <type>Constant</type>
                        <value>18921600</value>
                    </property>
                </properties>
            </phase>
            <phase>
                <type>Solid</type>
                <properties>
                    <property>
                        <name>storage</name>
                        <type>Constant</type>
                        <value>1e-10</value>
                    </property>
                    <property>
                        <name>density</name>
                        <type>Constant</type>
                        <value>2700</value>
                    </property>
                    <property>
                        <name>thermal_conductivity</name>
                        <type>Constant</type>
                        <value>3.0 0 0 0 3.0 0 0 0 3.0</value>
                    </property>
                    <property>
                        <name>specific_heat_capacity</name>
                        <type>Constant</type>
                        <value>900</value>
                    </property>
                </properties>
            </phase>
        </phases>
        <properties>
            <property>
                <name>thermal_longitudinal_dispersivity</name>
                <type>Constant</type>
                <value>0.0</value>
            </property>
            <property>
                <name>thermal_transversal_dispersivity</name>
                <type>Constant</type>
                <value>0.0</value>
            </property>
            <property>
                <name>permeability</name>
                <type>Constant</type>
                <value>1e-13</value>
            </property>
            <property>
                <name>porosity</name>
                <type>Constant</type>
                <value>0.30</value>
            </property>
            <property>
                <name>thermal_conductivity</name>
                <type>EffectiveThermalConductivityPorosityMixing</type>
            </property>
        </properties>
    </medium>

    <medium id="1">
        <phases>
            <phase>
                <type>AqueousLiquid</type>
                <properties>
                    <property>
                        <name>density</name>
                        <type>Constant</type>
                        <value>1000</value>
                    </property>
                    <property>
                        <name>viscosity</name>
                        <type>Constant</type>
                        <value>1.0e-3</value>
                    </property>
                    <property>
                        <name>specific_heat_capacity</name>
                        <type>Constant</type>
                        <value>4000</value>
                    </property>
                    <property>
                        <name>thermal_conductivity</name>
                        <type>Constant</type>
                        <value>18921600</value>
                    </property>
                </properties>
            </phase>
            <phase>
                <type>Solid</type>
                <properties>
                    <property>
                        <name>storage</name>
                        <type>Constant</type>
                        <value>1e-10</value>
                    </property>
                    <property>
                        <name>density</name>
                        <type>Constant</type>
                        <value>2160</value>
                    </property>
                    <property>
                        <name>thermal_conductivity</name>
                        <type>Constant</type>
                        <value>5.5 0 0 0 5.5 0 0 0 5.5</value>
                    </property>
                    <property>
                        <name>specific_heat_capacity</name>
                        <type>Constant</type>
                        <value>900</value>
                    </property>
                </properties>
            </phase>
        </phases>
        <properties>
            <property>
                <name>thermal_longitudinal_dispersivity</name>
                <type>Constant</type>
                <value>0.0</value>
            </property>
            <property>
                <name>thermal_transversal_dispersivity</name>
                <type>Constant</type>
                <value>0.0</value>
            </property>
            <property>
                <name>permeability</name>
                <type>Constant</type>
                <value>1e-21</value>
            </property>
            <property>
                <name>porosity</name>
                <type>Constant</type>
                <value>0.05</value>
            </property>
            <property>
                <name>thermal_conductivity</name>
                <type>EffectiveThermalConductivityPorosityMixing</type>
            </property>
        </properties>
    </medium>
</media>
<time_loop>
<global_process_coupling>
  <max_iter>6</max_iter>
  <convergence_criteria>
    <convergence_criterion>
      <type>DeltaX</type>
      <norm_type>NORM2</norm_type>
      <reltol>1.e-14</reltol>
    </convergence_criterion>
    <convergence_criterion>
      <type>DeltaX</type>
      <norm_type>NORM2</norm_type>
      <reltol>1.e-14</reltol>
    </convergence_criterion>
  </convergence_criteria>
</global_process_coupling>
<processes>
  <process ref="th_decovalex">
    <nonlinear_solver>basic_picard_T</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>1e3</t_end>
      <timesteps>
        <pair>
          <repeat>4</repeat>
          <delta_t>0.001</delta_t>
        </pair>
        <pair>
          <repeat>1</repeat>
          <delta_t>0.006</delta_t>
        </pair>
        <pair>
          <repeat>9</repeat>
          <delta_t>0.01</delta_t>
        </pair>
        <pair>
          <repeat>9</repeat>
          <delta_t>0.1</delta_t>
        </pair>
        <pair>
          <repeat>39</repeat>
          <delta_t>1.</delta_t>
        </pair>
        <pair>
          <repeat>2</repeat>
          <delta_t>2.0</delta_t>
        </pair>
        <pair>
          <repeat>1</repeat>
          <delta_t>16.0</delta_t>
        </pair>
        <pair>
          <repeat>1</repeat>
          <delta_t>30.0</delta_t>
        </pair>
        <pair>
          <repeat>1</repeat>
          <delta_t>40.0</delta_t>
        </pair>
        <pair>
          <repeat>10</repeat>
          <delta_t>86.0</delta_t>
        </pair>
        <pair>
          <repeat>90</repeat>
          <delta_t>100.0</delta_t>
        </pair>
        <pair>
          <repeat>100</repeat>
          <delta_t>900</delta_t>
        </pair>
        <pair>
          <repeat>90</repeat>
          <delta_t>1.e4</delta_t>
        </pair>
      </timesteps>
    </time_stepping>
  </process>
  <process ref="th_decovalex">
    <nonlinear_solver>basic_picard_H</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.e3</t_end>
      <timesteps>
        <pair>
          <repeat>4</repeat>
          <delta_t>0.001</delta_t>
        </pair>
        <pair>
          <repeat>1</repeat>
          <delta_t>0.006</delta_t>
        </pair>
        <pair>
          <repeat>9</repeat>
          <delta_t>0.01</delta_t>
        </pair>
        <pair>
          <repeat>9</repeat>
          <delta_t>0.1</delta_t>
        </pair>
        <pair>
          <repeat>39</repeat>
          <delta_t>1.</delta_t>
        </pair>
        <pair>
          <repeat>2</repeat>
          <delta_t>2.0</delta_t>
        </pair>
        <pair>
          <repeat>1</repeat>
          <delta_t>16.0</delta_t>
        </pair>
        <pair>
          <repeat>1</repeat>
          <delta_t>30.0</delta_t>
        </pair>
        <pair>
          <repeat>1</repeat>
          <delta_t>40.0</delta_t>
        </pair>
        <pair>
          <repeat>10</repeat>
          <delta_t>86.0</delta_t>
        </pair>
        <pair>
          <repeat>90</repeat>
          <delta_t>100.0</delta_t>
        </pair>
        <pair>
          <repeat>100</repeat>
          <delta_t>900</delta_t>
        </pair>
        <pair>
          <repeat>90</repeat>
          <delta_t>1.e4</delta_t>
        </pair>
      </timesteps>
    </time_stepping>
  </process>
</processes>
<output>
  <type>VTK</type>
  <prefix>th_decovalex</prefix>
  <suffix>ts{:timestep}_t_{:time}</suffix>
  <timesteps>
    <pair>
      <repeat>1</repeat>
      <each_steps>10</each_steps>
    </pair>
  </timesteps>
  <variables>
    <variable>T</variable>
    <variable>p</variable>
    <variable>darcy_velocity</variable>
  </variables>
</output>
</time_loop> 

<parameters>
    <parameter>
        <name>T0</name>
        <type>Constant</type>
        <value>283</value>
    </parameter>
    <parameter>
        <name>heat_source</name>
        <type>MeshNode</type>
        <field_name>t_init</field_name>
    </parameter>
    
    <parameter>
        <name>p_in</name>
        <type>Constant</type>
        <value>1.0e9</value>
    </parameter>
    <parameter>
        <name>ic</name>
        <type>MeshNode</type>
        <field_name>p_init</field_name>
    </parameter>
</parameters>

<process_variables>
    <process_variable>
        <name>T</name>
        <components>1</components>
        <order>1</order>
        <initial_condition>heat_source</initial_condition>
        <boundary_conditions>
            <boundary_condition>
                <mesh>2DboundaryHT</mesh>
                <type>Dirichlet</type>
                <parameter>T0</parameter>
            </boundary_condition>

        </boundary_conditions>
    </process_variable>

    <process_variable>
        <name>p</name>
        <components>1</components>
        <order>1</order>

        <!-- Hydrostatic Initial Condition -->
        <initial_condition>ic</initial_condition>

        <!-- Boundary Conditions -->
        <boundary_conditions>
            <boundary_condition>
                <mesh>leftHT</mesh>
                <type>Neumann</type>
                <parameter>p_in</parameter>
            </boundary_condition>
        </boundary_conditions>
    </process_variable>
</process_variables>

<nonlinear_solvers>
<nonlinear_solver>
  <name>basic_picard_T</name>
  <type>Picard</type>
  <max_iter>10</max_iter>
  <linear_solver>linear_solver_T</linear_solver>
</nonlinear_solver>
<nonlinear_solver>
  <name>basic_picard_H</name>
  <type>Picard</type>
  <max_iter>10</max_iter>
  <linear_solver>linear_solver_H</linear_solver>
</nonlinear_solver>

```

\</nonlinear\_solvers\>  
\<linear\_solvers\>  
\<linear\_solver\>  
linear\_solver\_T  
-i cg -p jacobi -tol 1e-20 -maxiter 10000  
  
\<solver\_type\>BiCGSTAB\</solver\_type\>  
\<precon\_type\>DIAGONAL\</precon\_type\>  
\<max\_iteration\_step\>10000\</max\_iteration\_step\>  
\<error\_tolerance\>1e-20\</error\_tolerance\>  
  
  
T  
-T\_ksp\_type bcgs -T\_pc\_type bjacobi -T\_ksp\_rtol 1e-16 -T\_ksp\_max\_it 10000  
  
\</linear\_solver\>  
\<linear\_solver\>  
linear\_solver\_H  
-i cg -p jacobi -tol 1e-20 -maxiter 10000  
  
\<solver\_type\>CG\</solver\_type\>  
\<precon\_type\>DIAGONAL\</precon\_type\>  
\<max\_iteration\_step\>10000\</max\_iteration\_step\>  
\<error\_tolerance\>1e-20\</error\_tolerance\>  
  
  
H  
-H\_ksp\_type cg -H\_pc\_type bjacobi -H\_ksp\_rtol 1e-16 -H\_ksp\_max\_it 10000  
  
\</linear\_solver\>  
\</linear\_solvers\>

---

<div class="post-metadata">

**Author:** ![dmitri.naumov](https://discourse.opengeosys.org/user_avatar/discourse.opengeosys.org/dmitri.naumov/32/561_2.png) [@dmitri.naumov](https://discourse.opengeosys.org/u/dmitri.naumov)\
**Post date:** [September 16, 2025, 1:12pm UTC](https://discourse.opengeosys.org/t/problems-with-ht-process-in-2d-mesh-error-in-matrix/1692/8 "2025-09-16T13:12:22Z")

</div>

Now the conversion is from 3D to 2D. Do you try to have the same setup for 2D and 3D meshes?  
I’d start with isotropic setup first (scalar quantities), and extend it to anisotropic later, when everything is running.

From the snippets it is difficult to judge, what is happening, please upload the complete setup with meshes (as simple as possible) here or some other place, so one could take a look without guessing.

– d