docs: Tutorial examples of a vertical fault using the ALM solver by jhuang2601 · Pull Request #4082 · GEOS-DEV/GEOS

jhuang2601 · 2026-06-10T20:09:45Z

This PR

documents the analytical verification of ALM solver using a slipped vertical fault problem (shear slip for frictionless fault) in porous media
documents the analytical verification of ALM solver using a stable vertical fault problem (shear stress for friction and stable fault) in porous media
compares the results with both external (splitting fault with mesh doctor) and internal (internal surface generator) workflow
benchmarks the convergence of the relative 𝐿2-error with respect to mesh resolution
adds smoke tests for both workflows to the integratedTests

dkachuma

The two examples look quite similar. Can we possibly discuss them in the same context as a comparison?

dkachuma · 2026-06-15T17:20:47Z

+
+  inputFiles/poromechanicsFractures/Contact/AugmentedLagrangianMultipliers/ALM_verticalFault_base.xml
+  inputFiles/poromechanicsFractures/Contact/AugmentedLagrangianMultipliers/verticalFault_unstable_ISG_benchmark.xml
+


Can you please say a few words what the difference between internal and external workflow is in this instance.

dkachuma · 2026-06-15T17:23:09Z

+------------------------------------------------------------------
+
+We simulate induced stresses and shear slip along a vertical fault in a depleted reservoir and compare our results against an analytical solution.
+In conformity to the analytical set-up, the reservoir is divided into two parts by a vertical fault. The fault crosses and offsets the entire reservoir layer and well contained with the domain. The domain is infinite, homogeneous, isotropic, and elastic. The reservoir is depressurized uniformely upon depletion, and we neglect the transient effect of fluid flow. A pressure drop is applied to the reservoir layer located in the center of the domain. The overburden and underburden are impermeable, and no pressure changes occur in these layers. Due to poromechanical effects, pore pressure changes in the reservoir cause a mechanical deformation of the entire domain. This deformation leads to a stress (normal and shear) perturbation on the fault plane, potentially leading to fault reactivation. For verification, the numerical model considers plane strain deformation and the Coulomb failure criterion.


Suggested change

In conformity to the analytical set-up, the reservoir is divided into two parts by a vertical fault. The fault crosses and offsets the entire reservoir layer and well contained with the domain. The domain is infinite, homogeneous, isotropic, and elastic. The reservoir is depressurized uniformely upon depletion, and we neglect the transient effect of fluid flow. A pressure drop is applied to the reservoir layer located in the center of the domain. The overburden and underburden are impermeable, and no pressure changes occur in these layers. Due to poromechanical effects, pore pressure changes in the reservoir cause a mechanical deformation of the entire domain. This deformation leads to a stress (normal and shear) perturbation on the fault plane, potentially leading to fault reactivation. For verification, the numerical model considers plane strain deformation and the Coulomb failure criterion.

In conformity to the analytical set-up, the reservoir is divided into two parts by a vertical fault. The fault crosses and offsets the entire reservoir layer and is well contained with the domain. The domain is infinite, homogeneous, isotropic, and elastic. The reservoir is depressurized uniformly upon depletion, and we neglect the transient effect of fluid flow. A pressure drop is applied to the reservoir layer located in the center of the domain. The overburden and underburden are impermeable, and no pressure changes occur in these layers. Due to poromechanical effects, pore pressure changes in the reservoir cause a mechanical deformation of the entire domain. This deformation leads to a stress (normal and shear) perturbation on the fault plane, potentially leading to fault reactivation. For verification, the numerical model considers plane strain deformation and the Coulomb failure criterion.

dkachuma · 2026-06-15T17:29:34Z

+     <File name="ALM_verticalFault_base.xml"/>
+  </Included>
+
+  <Constitutive>


I would expect constitutive relations to be in the base file and shared between the smoke/bench and internal/external cases. Are they actually different across these models?

dkachuma · 2026-06-15T17:31:52Z

+      name="mesh1"
+      useGlobalIds="0"
+      nodesetNames="{ faultNodes }"
+      file="../../MESH/verticalFault_ISG_benchmark.vtu"/>


In these cases I have expected the internal workflow to be able to use the "domain" mesh from the external workflow. Are there differences between verticalFault_ISG_benchmark.vtu and Domain_verticalFault_benchmark.vtu?

dkachuma · 2026-06-15T17:36:18Z

+
+As demonstrated in this example, to setup a poromechanical coupling, we need to define three different solvers in the XML file:
+
+- the mechanics solver, a solver of type ``SolidMechanicsAugmentedLagrangianContact`` called here ``fractureMechSolver``, is applied to solve the frictional contact and rock deformations. In this solver, we specify ``targetRegions`` that include both the continuum region ``Region`` and the discontinuum region ``Fault``  where the solver is applied to couple rock and fracture deformations. The contact constitutive law used for the fault elements is named ``fractureContact``,  and is defined later in the ``Constitutive`` section. 


Suggested change

- the mechanics solver, a solver of type ``SolidMechanicsAugmentedLagrangianContact`` called here ``fractureMechSolver``, is applied to solve the frictional contact and rock deformations. In this solver, we specify ``targetRegions`` that include both the continuum region ``Region`` and the discontinuum region ``Fault`` where the solver is applied to couple rock and fracture deformations. The contact constitutive law used for the fault elements is named ``fractureContact``, and is defined later in the ``Constitutive`` section.

- the mechanics solver, a solver of type ``SolidMechanicsAugmentedLagrangianContact`` called here ``fractureMechSolver``, is applied to solve the frictional contact and rock deformations. In this solver, we specify ``targetRegions`` that include both the continuum region ``Region`` and the fracture region ``Fault`` where the solver is applied to couple rock and fracture deformations. The contact constitutive law used for the fault elements is named ``fractureContact``, and is defined later in the ``Constitutive`` section.

Or fault maybe.

dkachuma · 2026-06-15T17:41:07Z

+For more information on defining finite elements numerical schemes,
+please see the dedicated :ref:`FiniteElement` section.
+
+The finite volume method requires the specification of a discretization scheme.


Suggested change

The finite volume method requires the specification of a discretization scheme.

The finite volume method, for the flow solver, requires the specification of a discretization scheme.

bd713

Thanks, @jhuang2601.
Along the same lines as @dkachuma, we could probably also share the scripts (especially for the analytical solution).

bd713 · 2026-06-15T18:46:39Z

+
+**Context**
+
+In this example, the Augmented Lagrangian Method (ALM) `(Frigo et al., 2026)  <https://www.sciencedirect.com/science/article/abs/pii/S0021999126003414>`__ is applied to solve a frictional fault contact problem in a depleted reservoir. This approach employs conformal discretization where discontinuities are explicitly represented by 2D interface elements placed between 3D continuum elements. The formulation overcomes the inf-sup instability of low-order discretizations by satisfying the Babuška–Brezzi condition via displacement enrichment with bubble functions and is coupled with a Coulomb friction law. Implemented in GEOS, the model computes displacement discontinuities (fault slip unpon reactivation) along the frictionless fault, which are subsequently verified against the corresponding analytical solution `(Jansen and Meulenbroek, 2022)  <https://njgjournal.nl/index.php/njg/article/view/11453/17972>`__. This comparison confirms the accuracy of our fault contact model and coupled poroelastic formulation.


Suggested change

In this example, the Augmented Lagrangian Method (ALM) `(Frigo et al., 2026) <https://www.sciencedirect.com/science/article/abs/pii/S0021999126003414>`__ is applied to solve a frictional fault contact problem in a depleted reservoir. This approach employs conformal discretization where discontinuities are explicitly represented by 2D interface elements placed between 3D continuum elements. The formulation overcomes the inf-sup instability of low-order discretizations by satisfying the Babuška–Brezzi condition via displacement enrichment with bubble functions and is coupled with a Coulomb friction law. Implemented in GEOS, the model computes displacement discontinuities (fault slip unpon reactivation) along the frictionless fault, which are subsequently verified against the corresponding analytical solution `(Jansen and Meulenbroek, 2022) <https://njgjournal.nl/index.php/njg/article/view/11453/17972>`__. This comparison confirms the accuracy of our fault contact model and coupled poroelastic formulation.

In this example, the Augmented Lagrangian Method (ALM) `(Frigo et al., 2026) <https://www.sciencedirect.com/science/article/abs/pii/S0021999126003414>`__ is applied to solve a frictional fault contact problem in a depleted reservoir. This approach employs conformal discretization where discontinuities are explicitly represented by 2D interface elements placed between 3D continuum elements. The formulation overcomes the inf-sup instability of low-order discretizations by satisfying the Babuška–Brezzi condition via displacement enrichment with bubble functions and is coupled with a Coulomb friction law. Implemented in GEOS, the model computes displacement discontinuities (fault slip upon reactivation) along the frictionless fault, which are subsequently verified against the corresponding analytical solution `(Jansen and Meulenbroek, 2022) <https://njgjournal.nl/index.php/njg/article/view/11453/17972>`__. This comparison confirms the accuracy of our fault contact model and coupled poroelastic formulation.

bd713 · 2026-06-15T18:47:33Z

+    :start-after: <!-- SPHINX_MESH -->
+    :end-before: <!-- SPHINX_MESH_END -->
+
+The vtm file ``verticalFault_ESG_benchmark.vtm`` references two separate mesh files: the damain mesh ``Domain_verticalFault_benchmark.vtu`` and the fault mesh ``Fault_verticalFault_benchmark.vtu``, which are generated prior to running the GEOS simulation. The ``mesh doctor`` module provides a convenient way to prepare these meshes. For this case, functions ``generateFractures`` and ``generateGlobalIds`` are used (more information here: `mesh doctor  <https://geosx-geosx.readthedocs-hosted.com/projects/geosx-geospythonpackages/en/latest/mesh-doctor.html#>`__).


Suggested change

The vtm file ``verticalFault_ESG_benchmark.vtm`` references two separate mesh files: the damain mesh ``Domain_verticalFault_benchmark.vtu`` and the fault mesh ``Fault_verticalFault_benchmark.vtu``, which are generated prior to running the GEOS simulation. The ``mesh doctor`` module provides a convenient way to prepare these meshes. For this case, functions ``generateFractures`` and ``generateGlobalIds`` are used (more information here: `mesh doctor <https://geosx-geosx.readthedocs-hosted.com/projects/geosx-geospythonpackages/en/latest/mesh-doctor.html#>`__).

The vtm file ``verticalFault_ESG_benchmark.vtm`` references two separate mesh files: the domain mesh ``Domain_verticalFault_benchmark.vtu`` and the fault mesh ``Fault_verticalFault_benchmark.vtu``, which are generated prior to running the GEOS simulation. The ``mesh doctor`` module provides a convenient way to prepare these meshes. For this case, functions ``generateFractures`` and ``generateGlobalIds`` are used (more information here: `mesh doctor <https://geosx-geosx.readthedocs-hosted.com/projects/geosx-geospythonpackages/en/latest/mesh-doctor.html#>`__).

bd713 · 2026-06-15T18:48:40Z

+In this example, let us focus on the coupling solver.
+This solver (``poroFractureSolver``) uses a set of attributes that specifically describe the coupling process within a poromechanical framework.
+For instance, we must point this solver to the designated fluid solver (here: ``singlePhaseFlowSolver``) and solid solver (here: ``fractureMechSolver``).
+These solvers are forced to interact with all the constitutive models in the target regions (here, we only two, ``Region`` and ``Fault``).


Suggested change

These solvers are forced to interact with all the constitutive models in the target regions (here, we only two, ``Region`` and ``Fault``).

These solvers are forced to interact with all the constitutive models in the target regions (here, we only have two, ``Region`` and ``Fault``).

bd713 · 2026-06-15T18:52:40Z

+    :start-after: <!-- SPHINX_MESH -->
+    :end-before: <!-- SPHINX_MESH_END -->
+
+The vtm file ``verticalFault_ESG_benchmark.vtm`` references two separate mesh files: the damain mesh ``Domain_verticalFault_benchmark.vtu`` and the fault mesh ``Fault_verticalFault_benchmark.vtu``, which are generated prior to running the GEOS simulation. The ``mesh doctor`` module provides a convenient way to prepare these meshes. For this case, functions ``generateFractures`` and ``generateGlobalIds`` are used (more information here: `mesh doctor  <https://geosx-geosx.readthedocs-hosted.com/projects/geosx-geospythonpackages/en/latest/mesh-doctor.html#>`__).


Suggested change

The vtm file ``verticalFault_ESG_benchmark.vtm`` references two separate mesh files: the damain mesh ``Domain_verticalFault_benchmark.vtu`` and the fault mesh ``Fault_verticalFault_benchmark.vtu``, which are generated prior to running the GEOS simulation. The ``mesh doctor`` module provides a convenient way to prepare these meshes. For this case, functions ``generateFractures`` and ``generateGlobalIds`` are used (more information here: `mesh doctor <https://geosx-geosx.readthedocs-hosted.com/projects/geosx-geospythonpackages/en/latest/mesh-doctor.html#>`__).

The vtm file ``verticalFault_ESG_benchmark.vtm`` references two separate mesh files: the domain mesh ``Domain_verticalFault_benchmark.vtu`` and the fault mesh ``Fault_verticalFault_benchmark.vtu``, which are generated prior to running the GEOS simulation. The ``mesh doctor`` module provides a convenient way to prepare these meshes. For this case, functions ``generateFractures`` and ``generateGlobalIds`` are used (more information here: `mesh doctor <https://geosx-geosx.readthedocs-hosted.com/projects/geosx-geospythonpackages/en/latest/mesh-doctor.html#>`__).

bd713 · 2026-06-15T18:53:29Z

+In this example, let us focus on the coupling solver.
+This solver (``poroFractureSolver``) uses a set of attributes that specifically describe the coupling process within a poromechanical framework.
+For instance, we must point this solver to the designated fluid solver (here: ``singlePhaseFlowSolver``) and solid solver (here: ``fractureMechSolver``).
+These solvers are forced to interact with all the constitutive models in the target regions (here, we only two, ``Region`` and ``Fault``).


Suggested change

These solvers are forced to interact with all the constitutive models in the target regions (here, we only two, ``Region`` and ``Fault``).

These solvers are forced to interact with all the constitutive models in the target regions (here, we only have two, ``Region`` and ``Fault``).

add xml files for benchmark examples

028502d

jhuang2601 self-assigned this Jun 10, 2026

jhuang2601 mentioned this pull request Jun 10, 2026

Tutorial example for fault slippage #2958

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2 tasks

jhuang2601 added type: documentation EPIC - FF/Contact Contact mechanics labels Jun 10, 2026

jhuang2601 added 2 commits June 12, 2026 12:23

add rst file and script for slipped case

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add rst file and script for stable case

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jhuang2601 marked this pull request as ready for review June 12, 2026 18:03

jhuang2601 requested review from OmarDuran, bd713, castelletto1, dkachuma, herve-gross, joshua-white and rrsettgast as code owners June 12, 2026 18:03

jhuang2601 and others added 5 commits June 12, 2026 13:03

Merge branch 'develop' into docs/jhuang/verticalFault

bf7ae59

update keyword for Coulomb

2528327

some fix

e467d0d

update python script

d79f70f

reduce fig size

228b114

jhuang2601 changed the title ~~docs: tutorial example with a vertical fault~~ docs: Tutorial examples of a vertical fault using the ALM solver Jun 12, 2026

jhuang2601 added ci: run CUDA builds Allows to triggers (costly) CUDA jobs ci: run integrated tests Allows to run the integrated tests in GEOS CI ci: run code coverage enables running of the code coverage CI jobs labels Jun 12, 2026

add smoke tests to integratedTests

b6ef64a

dkachuma reviewed Jun 15, 2026

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bd713 reviewed Jun 15, 2026

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herve-gross approved these changes Jun 15, 2026

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		inputFiles/poromechanicsFractures/Contact/AugmentedLagrangianMultipliers/ALM_verticalFault_base.xml
		inputFiles/poromechanicsFractures/Contact/AugmentedLagrangianMultipliers/verticalFault_unstable_ISG_benchmark.xml


		As demonstrated in this example, to setup a poromechanical coupling, we need to define three different solvers in the XML file:

		- the mechanics solver, a solver of type ``SolidMechanicsAugmentedLagrangianContact`` called here ``fractureMechSolver``, is applied to solve the frictional contact and rock deformations. In this solver, we specify ``targetRegions`` that include both the continuum region ``Region`` and the discontinuum region ``Fault`` where the solver is applied to couple rock and fracture deformations. The contact constitutive law used for the fault elements is named ``fractureContact``, and is defined later in the ``Constitutive`` section.

	The finite volume method requires the specification of a discretization scheme.
	The finite volume method, for the flow solver, requires the specification of a discretization scheme.


		Context

		In this example, the Augmented Lagrangian Method (ALM) `(Frigo et al., 2026) <https://www.sciencedirect.com/science/article/abs/pii/S0021999126003414>`__ is applied to solve a frictional fault contact problem in a depleted reservoir. This approach employs conformal discretization where discontinuities are explicitly represented by 2D interface elements placed between 3D continuum elements. The formulation overcomes the inf-sup instability of low-order discretizations by satisfying the Babuška–Brezzi condition via displacement enrichment with bubble functions and is coupled with a Coulomb friction law. Implemented in GEOS, the model computes displacement discontinuities (fault slip unpon reactivation) along the frictionless fault, which are subsequently verified against the corresponding analytical solution `(Jansen and Meulenbroek, 2022) <https://njgjournal.nl/index.php/njg/article/view/11453/17972>`__. This comparison confirms the accuracy of our fault contact model and coupled poroelastic formulation.

	These solvers are forced to interact with all the constitutive models in the target regions (here, we only two, ``Region`` and ``Fault``).
	These solvers are forced to interact with all the constitutive models in the target regions (here, we only have two, ``Region`` and ``Fault``).

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jhuang2601 commented Jun 10, 2026 •

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