porepy.models.mass_and_energy_balance module

Combine single-physics models into coupled mass and energy balance equations.

class BoundaryConditionsFluidMassAndEnergy

Bases: BoundaryConditionsEnergyBalance, BoundaryConditionsSinglePhaseFlow

Combine fluid mass and energy balance boundary conditions.

domain_boundary_sides: Callable[[pp.Grid], tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray, np.ndarray, np.ndarray, np.ndarray]]

Boundary sides of the domain. Normally defined in a mixin instance of ModelGeometry.

class ConstitutiveLawFluidMassAndEnergy

Bases: FluidDensityFromPressureAndTemperature, ConstantSolidDensity, EnthalpyFromTemperature, FouriersLaw, ThermalConductivityLTE, DimensionReduction, AdvectiveFlux, DarcysLaw, FluidMobility, ConstantPorosity, ConstantPermeability, ConstantViscosity

Combine fluid mass and energy balance constitutive laws.

Fluid density dependends on pressure and temperature in the mass and energy class, respectively. Here, both dependencies are included.

fluid: pp.FluidConstants

Fluid constant object that takes care of scaling of fluid-related quantities. Normally, this is set by a mixin of instance SolutionStrategy.

perturbation_from_reference: Callable[[str, list[pp.Grid]], pp.ad.Operator]

Function that returns a perturbation from reference state. Normally provided by a mixin of instance VariableMixin.

class EquationsFluidMassAndEnergy

Bases: EnergyBalanceEquations, MassBalanceEquations

Combine fluid mass and energy balance equations.

set_equations()

Set the equations for the fluid mass and energy balance problem.

Call both parent classes’ set_equations methods.

advective_flux: Callable[[list[pp.Grid], pp.ad.Operator, pp.ad.UpwindAd, pp.ad.Operator, Callable[[list[pp.MortarGrid]], pp.ad.Operator]], pp.ad.Operator]

Ad operator representing the advective flux. Normally provided by a mixin instance of AdvectiveFlux.

basis: Callable[[Sequence[pp.GridLike], int], list[pp.ad.Matrix]]

Basis for the local coordinate system. Normally set by a mixin instance of porepy.models.geometry.ModelGeometry.

bc_values_enthalpy_flux: Callable[[list[pp.Grid]], pp.ad.Array]

Boundary condition for enthalpy flux. Normally defined in a mixin instance of BoundaryConditionsEnergyBalance.

enthalpy_keyword: str

Keyword used to identify the enthalpy flux discretization. Normally set by a mixin instance of SolutionStrategyEnergyBalance.

equation_system: pp.ad.EquationSystem

EquationSystem object for the current model. Normally defined in a mixin class defining the solution strategy.

fluid_density: Callable[[list[pp.Grid]], pp.ad.Operator]

Fluid density. Defined in a mixin class with a suitable constitutive relation.

fluid_enthalpy: Callable[[list[pp.Grid]], pp.ad.Operator]

Fluid enthalpy. Defined in a mixin class with a suitable constitutive relation.

fourier_flux: Callable[[list[pp.Grid]], pp.ad.Operator]

Fourier flux. Normally provided by a mixin instance of FouriersLaw.

interface_advective_flux: Callable[[list[pp.MortarGrid], pp.ad.Operator, pp.ad.UpwindCouplingAd], pp.ad.Operator]

Ad operator representing the advective flux on internal boundaries. Normally provided by a mixin instance of AdvectiveFlux.

interface_enthalpy_flux: Callable[[list[pp.MortarGrid]], pp.ad.MixedDimensionalVariable]

Variable for interface enthalpy flux. Normally provided by a mixin instance of VariablesEnergyBalance.

interface_fourier_flux: Callable[[list[pp.MortarGrid]], pp.ad.MixedDimensionalVariable]

Fourier flux variable on interfaces. Normally defined in a mixin instance of VariablesEnergyBalance.

interfaces_to_subdomains: Callable[[list[pp.MortarGrid]], list[pp.Grid]]

Map from interfaces to the adjacent subdomains. Normally defined in a mixin instance of ModelGeometry.

mdg: pp.MixedDimensionalGrid

Mixed dimensional grid for the current model. Normally defined in a mixin instance of ModelGeometry.

mobility: Callable[[list[pp.Grid]], pp.ad.Operator]

Fluid mobility. Normally provided by a mixin instance of FluidMobility.

nd: int

Ambient dimension of the problem. Normally set by a mixin instance of porepy.models.geometry.ModelGeometry.

porosity: Callable[[list[pp.Grid]], pp.ad.Operator]

Porosity of the rock. Normally provided by a mixin instance of ConstantPorosity or a subclass thereof.

pressure: Callable[[list[pp.Grid]], pp.ad.MixedDimensionalVariable]

Pressure variable. Normally defined in a mixin instance of VariablesSinglePhaseFlow.

solid_density: Callable[[list[pp.Grid]], pp.ad.Scalar]

Solid density. Defined in a mixin class with a suitable constitutive relation.

solid_enthalpy: Callable[[list[pp.Grid]], pp.ad.Operator]

Solid enthalpy. Defined in a mixin class with a suitable constitutive relation.

specific_volume: Callable[[list[pp.Grid]], pp.ad.Operator]

Function that returns the specific volume of a subdomain. Normally provided by a mixin of instance DimensionReduction.

subdomains_to_interfaces: Callable[[list[pp.Grid], list[int]], list[pp.MortarGrid]]

Map from subdomains to the adjacent interfaces. Normally defined in a mixin instance of ModelGeometry.

time_manager: pp.TimeManager

Time manager. Normally set by a mixin instance of porepy.models.solution_strategy.SolutionStrategy.

wrap_grid_attribute: Callable[[Sequence[pp.GridLike], str, int, bool], pp.ad.Matrix]

Wrap grid attributes as Ad operators. Normally set by a mixin instance of porepy.models.geometry.ModelGeometry.

class MassAndEnergyBalance(params=None)

Bases: EquationsFluidMassAndEnergy, VariablesFluidMassAndEnergy, ConstitutiveLawFluidMassAndEnergy, BoundaryConditionsFluidMassAndEnergy, SolutionStrategyFluidMassAndEnergy, ModelGeometry, DataSavingMixin

Combine fluid mass and energy balance models into a single class.

The equations assume single-phase flow and local thermal equilibrium.

Parameters

params (Optional[dict]) –

enthalpy_keyword: str

Keyword used to identify the enthalpy flux discretization. Normally set by a mixin instance of SolutionStrategyEnergyBalance.

equation_system: pp.ad.EquationSystem

EquationSystem object for the current model. Normally defined in a mixin class defining the solution strategy.

mdg: pp.MixedDimensionalGrid

Mixed dimensional grid for the current model. Normally defined in a mixin instance of ModelGeometry.

nd: int

Ambient dimension of the problem. Normally set by a mixin instance of porepy.models.geometry.ModelGeometry.

time_manager: pp.TimeManager

Time manager. Normally set by a mixin instance of porepy.models.solution_strategy.SolutionStrategy.

class SolutionStrategyFluidMassAndEnergy(params=None)

Bases: SolutionStrategyEnergyBalance, SolutionStrategySinglePhaseFlow

Combine fluid mass and energy balance solution strategies.

Solution strategies are proper classes (not mixins) and inherit from SolutionStrategy. Thus, overridden methods call super() by default and explicitly calling both parent classes’ methods is not necessary.

Parameters

params (Optional[dict]) –

bc_type_enthalpy: Callable[[pp.Grid], pp.BoundaryCondition]

Function that returns the boundary condition type for the enthalpy flux. Normally defined in a mixin instance of BoundaryConditionsEnergyBalance.

bc_type_fourier: Callable[[pp.Grid], pp.BoundaryCondition]

Function that returns the boundary condition type for the Fourier flux. Normally defined in a mixin instance of BoundaryConditionsEnergyBalance.

convergence_status: bool

Whether the non-linear iteration has converged.

create_variables: Callable[[], None]

Create variables. Normally provided by a mixin instance of a Variable class relevant to the model.

domain_bounds: dict

Bounding box of the domain. Will normally be set by a mixin instance of ModelGeometry.

enthalpy_keyword: str

Keyword for enthalpy flux term.

Used to access discretization parameters and store discretization matrices.

equation_system: pp.ad.EquationSystem

Equation system manager. Will be set by set_equation_system_manager().

exporter: pp.Exporter

Exporter for visualization.

finalize_data_saving: Callable[[], None]

Finalize data saving. Normally provided by a mixin instance of DataSavingMixin.

fluid: pp.FluidConstants

Fluid constants. See also set_materials().

fourier_keyword: str

Keyword for Fourier flux term.

Used to access discretization parameters and store discretization matrices.

initialize_data_saving: Callable[[], None]

Initialize data saving. Normally provided by a mixin instance of DataSavingMixin.

interface_enthalpy_flux_variable: str

Name of the primary variable representing the enthalpy flux on the interface.

interface_fourier_flux_variable: str

Name of the primary variable representing the Fourier flux on the interface.

linear_system: tuple[sps.spmatrix, np.ndarray]

The linear system to be solved in each iteration of the non-linear solver. The tuple contains the sparse matrix and the right hand side residual vector.

mdg: pp.MixedDimensionalGrid

Mixed-dimensional grid. Will normally be set by a mixin instance of ModelGeometry.

nd: int

Ambient dimension of the problem. Normally set by a mixin instance of porepy.models.geometry.ModelGeometry.

save_data_time_step: Callable[[], None]

Save data at a time step. Normally provided by a mixin instance of DataSavingMixin.

set_equations: Callable[[], None]

Set the governing equations of the model. Normally provided by the solution strategy of a specific model (i.e. a subclass of this class).

set_geometry: Callable[[], None]

Set the geometry of the model. Normally provided by a mixin instance of ModelGeometry.

solid: pp.SolidConstants

Solid constants. See also set_materials().

specific_volume: Callable[[list[pp.Grid]], pp.ad.Operator]

Function that returns the specific volume of a subdomain. Normally provided by a mixin of instance DimensionReduction.

temperature_variable: str

Name of the temperature variable.

thermal_conductivity: Callable[[list[pp.Grid]], np.ndarray]

Thermal conductivity. Normally defined in a mixin instance of ThermalConductivityLTE or a subclass.

units: pp.Units

Units of the model. See also set_units().

class VariablesFluidMassAndEnergy

Bases: VariablesEnergyBalance, VariablesSinglePhaseFlow

Combine fluid mass and energy balance variables.

create_variables()

Set the variables for the fluid mass and energy balance problem.

Call both parent classes’ set_variables methods.

Return type

None

equation_system: EquationSystem

EquationSystem object for the current model. Normally defined in a mixin class defining the solution strategy.

fluid: FluidConstants

Fluid constant object that takes care of scaling of fluid-related quantities. Normally, this is set by a mixin of instance SolutionStrategy.

interface_enthalpy_flux_variable: str

Name of the primary variable representing the enthalpy flux across an interface. Normally defined in a mixin of instance SolutionStrategyEnergyBalance.

interface_fourier_flux_variable: str

Name of the primary variable representing the Fourier flux across an interface. Normally defined in a mixin of instance SolutionStrategyEnergyBalance.

mdg: MixedDimensionalGrid

Mixed dimensional grid for the current model. Normally defined in a mixin instance of ModelGeometry.

solid: SolidConstants

Solid constant object that takes care of scaling of solid-related quantities. Normally, this is set by a mixin of instance SolutionStrategy.

temperature_variable: str

Name of the primary variable representing the temperature. Normally defined in a mixin of instance SolutionStrategyEnergyBalance.