porepy.models.contact_mechanics_biot_model module

This is a setup class for solving the Biot equations with contact mechanics at the fractures.

The class ContactMechanicsBiot inherits from ContactMechanics, which is a model for the purely mechanical problem with contact conditions on the fractures. Here, we expand to a model where the displacement solution is coupled to a scalar variable, e.g. pressure (Biot equations) or temperature. Parameters, variables and discretizations are set in the model class, and the problem may be solved using run_biot.

class ContactMechanicsBiot(params=None)[source]

Bases: ContactMechanics

This is a shell class for poroelastic contact mechanics problems.

Setting up such problems requires a lot of boilerplate definitions of variables, parameters and discretizations. This class is intended to provide a standardized setup, with all discretizations in place and reasonable parameter and boundary values. The intended use is to inherit from this class, and do the necessary modifications and specifications for the problem to be fully defined. The minimal adjustment needed is to specify the method create_grid().

Parameters: params (Optional[Dict]) –

time_manager: Time-stepping control manager.

displacement_variable

Name assigned to the displacement variable in the highest-dimensional subdomain. Will be used throughout the simulations, including in ParaView export.

Type: str

mortar_displacement_variable

Name assigned to the displacement variable on the fracture walls. Will be used throughout the simulations, including in ParaView export.

Type: str

contact_traction_variable

Name assigned to the variable for contact forces in the fracture. Will be used throughout the simulations, including in ParaView export.

Type: str

scalar_variable

Name assigned to the scalar variable (say, temperature or pressure). Will be used throughout the simulations, including in ParaView export.

Type: str

mortar scalar_variable

Name assigned to the interface scalar variable representing flux between subdomains. Will be used throughout the simulations, including in ParaView export.

Type: str

mechanics_parameter_key

Keyword used to define parameters and discretizations for the mechanics problem.

Type: str

scalar_parameter_key

Keyword used to define parameters and discretizations for the flow problem.

Type: str

params

Dictionary of parameters used to control the solution procedure.

Type: dict

viz_folder_name

Folder for visualization export.

Type: str

mdg

Mixed-dimensional grid. Should be set by a method create_grid which should be provided by the user.

Type: pp.MixedDimensionalGrid

convergence_status

Whether the non-linear iterations have converged.

Type: bool

linear_solver

Specification of linear solver. Only known permissible value is ‘direct’

Type: str

scalar_scale

Scaling coefficient for the scalar variable. Can be used to get comparable size of the mechanical and flow problem.

Type: float

scalar_scale

Scaling coefficient for the vector variable. Can be used to get comparable size of the mechanical and flow problem.

Type: float

subtract_fracture_pressure

If True (default) the scalar variable will be interpreted as a pressure, and contribute a force to the fracture walls from the lower-dimensional grid.

Type: bool

Except from the grid, all attributes are given natural values at initialization of the class.

after_newton_convergence(solution, errors, iteration_counter)[source]

Parameters

solution (ndarray) –
errors (float) –
iteration_counter (int) –

Return type

None

after_simulation()[source]

Return type: None

before_newton_loop()[source]

Will be run before entering a Newton loop. E.g.

Discretize time-dependent quantities etc. Update time-dependent parameters (captured by assembly).

Return type: None

check_convergence(solution, prev_solution, init_solution, nl_params)[source]

Check whether the solution has converged by comparing values from the two most recent iterations.

Tailored implementation if AD is not used. Else, the generic check in AbstractModel is used.

Parameters

solution (array) – solution of current iteration.
prev_solution (array) – solution of previous iteration.
init_solution (array) – initial solution (or from beginning of time step).
nl_params (dictionary) – assumed to have the key nl_convergence_tol whose value is a float.

Return type

Tuple[float, bool, bool]

reconstruct_stress(previous_iterate=False)[source]

Compute the stress in the highest-dimensional grid based on the displacement and pressure states in that grid, adjacent interfaces and global boundary conditions.

The stress is stored in the data dictionary of the highest-dimensional grid, in [pp.STATE][‘stress’].

Parameters: previous_iterate (boolean, optional) – If True, use values from previous iteration to compute the stress. Defaults to False.
Return type: None

class ContactMechanicsBiotAdObjects[source]

Bases: ContactMechanicsAdObjects

Storage class for ad related objects.

Stored objects include variables, compound ad operators and projections.

all_subdomains: List[Grid]

codim_one_interfaces: List[MortarGrid]

flux_discretization: Union[MpfaAd, TpfaAd]

interface_flux: Variable

mortar_projections_scalar: MortarProjections

pressure: Variable

subdomain_projections_scalar: SubdomainProjections

time_step: Scalar