porepy.utils.derived_discretizations.implicit_euler module

Module for extending the Upwind, MPFA and MassMatrix discretizations in PorePy to handle implicit Euler time-stepping. Flux terms are multiplied by time step and the mass term has a rhs contribution from the previous time step. See the parent discretizations for further documentation.

class ImplicitMassMatrix(keyword='flow', variable='pressure')[source]

Bases: MassMatrix

Return rhs contribution based on the previous solution, which is stored in the pp.STATE field of the data dictionary.

assemble_rhs(sd, sd_data)[source]

Overwrite MassMatrix method to return the correct rhs for an IE time discretization, e.g. of the Biot problem.

Parameters
class ImplicitMpfa(keyword)[source]

Bases: Mpfa

Multiply all contributions by the time step.

Parameters

keyword (str) –

assemble_int_bound_flux(sd, sd_data, intf, intf_data, cc, matrix, rhs, self_ind, use_secondary_proj=False)[source]

Overwrite the MPFA method to be consistent with the Biot dt convention

Parameters
Return type

None

assemble_int_bound_source(sd, sd_data, intf, intf_data, cc, matrix, rhs, self_ind)[source]

Abstract method. Assemble the contribution from an internal boundary, manifested as a source term.

The intended use is when the internal boundary is coupled to another node in a mixed-dimensional method. Specific usage depends on the interface condition between the nodes; this method will typically be used to impose flux continuity on a lower-dimensional domain.

Implementations of this method will use an interplay between the grid on the node and the mortar grid on the relevant edge.

Parameters

  • sd (pp.Grid) – Grid which the condition should be imposed on.

  • sd_data (dictionary) – Data dictionary for the node in the mixed-dimensional grid.

  • intf (pp.MortarGrid) – interface

  • intf_data (dict) – Data dictionary for the interface in the mixed-dimensional grid.

  • cc (block matrix, 3x3) – Block matrix for the coupling condition. The first and second rows and columns are identified with the primary and secondary side; the third belongs to the edge variable. The discretization of the relevant term is done in-place in cc.

  • matrix (block matrix 3x3) – Discretization matrix for the edge and the two adjacent nodes.

  • rhs (block_array 3x1) – Right hand side contribution for the edge and the two adjacent nodes.

  • self_ind (int) – Index in cc and matrix associated with this node. Should be either 1 or 2.

Return type

None

assemble_matrix_rhs(sd, sd_data)[source]

Overwrite MPFA method to be consistent with the Biot dt convention.

Parameters
class ImplicitTpfa(keyword)[source]

Bases: Tpfa

Multiply all contributions by the time step.

Implementation note: This is a copy of ImplicitMpfa, modified to inherit from Tpfa. A unified implementation would have been preferable.

Parameters

keyword (str) –

assemble_int_bound_flux(sd, sd_data, intf, intf_data, cc, matrix, rhs, self_ind, use_secondary_proj=False)[source]

Overwrite the MPFA method to be consistent with the Biot dt convention

Parameters
Return type

None

assemble_int_bound_source(sd, sd_data, intf, intf_data, cc, matrix, rhs, self_ind)[source]

Abstract method. Assemble the contribution from an internal boundary, manifested as a source term.

The intended use is when the internal boundary is coupled to another node in a mixed-dimensional method. Specific usage depends on the interface condition between the nodes; this method will typically be used to impose flux continuity on a lower-dimensional domain.

Implementations of this method will use an interplay between the grid on the node and the mortar grid on the relevant edge.

Parameters

  • sd (pp.Grid) – Grid which the condition should be imposed on.

  • sd_data (dictionary) – Data dictionary for the node in the mixed-dimensional grid.

  • intf (pp.MortarGrid) – interface

  • intf_data (dictionary) – Data dictionary for the edge in the mixed-dimensional grid.

  • cc (block matrix, 3x3) – Block matrix for the coupling condition. The first and second rows and columns are identified with the primary and secondary side; the third belongs to the edge variable. The discretization of the relevant term is done in-place in cc.

  • matrix (block matrix 3x3) – Discretization matrix for the edge and the two adjacent nodes.

  • rhs (block_array 3x1) – Right-hand side contribution for the edge and the two adjacent nodes.

  • self_ind (int) – Index in cc and matrix associated with this node. Should be either 1 or 2.

Return type

None

assemble_matrix_rhs(sd, sd_data)[source]

Overwrite MPFA method to be consistent with the Biot dt convention.

Parameters
class ImplicitUpwind(keyword='transport')[source]

Bases: Upwind

Multiply all contributions by the time step and advection weight. The latter may be a scalar or cell-wise values, in which case the upwind value is used. Note that the interior cell value is taken for BCs, regardless of the direction of the flux on the boundary.

Parameters

keyword (str) –

assemble_matrix_rhs(sd, sd_data)[source]
Parameters
Return type

tuple[scipy.sparse._base.spmatrix, numpy.ndarray]

class ImplicitUpwindCoupling(keyword)[source]

Bases: UpwindCoupling

Multiply the advective mortar fluxes by the time step and advection weight.

Parameters

keyword (str) –

assemble_matrix_rhs(sd_primary, sd_secondary, intf, sd_data_primary, sd_data_secondary, intf_data, matrix)[source]

Construct the matrix (and right-hand side) for the coupling conditions. Note: the right-hand side is not implemented now.

Parameters

  • sd_primary (pp.Grid) – grid of higher dimension

  • sd_secondary (pp.Grid) – grid of lower dimension

  • intf (pp.MortarGrid) – interface

  • sd_data_primary (dict) – dictionary which stores the data for the higher dimensional grid

  • sd_data_secondary (dict) – dictionary which stores the data for the lower dimensional grid

  • intf_data (dict) – dictionary which stores the data for the edges of the grid bucket

  • matrix (spmatrix) – Uncoupled discretization matrix.

Returns

block matrix which store the contribution of the coupling

condition. See the abstract coupling class for a more detailed description.

Return type

cc