adjust_driving_stress assemble_rhs compute_average_ice_hardness compute_driving_stress compute_nuH compute_nuH_cfbc compute_nuH_everywhere compute_residual compute_residual diagnostics_impl driving_stress fd_operator fracture_induced_softening initialize_iterations integrated_viscosity m_bc_scaling m_cell_type m_hardness m_nuH m_regional_mode m_rhs m_taud m_work SSAFDBase

fracture_induced_softening() void pism::stressbalance::SSAFDBase::fracture_induced_softening ( const array::Scalar1 &  fracture_density, double  n_glen, array::Staggered &  ice_hardness  ) protected Correct vertically-averaged hardness using a parameterization of the fracture-induced softening. See T. Albrecht, A. Levermann; Fracture-induced softening for large-scale ice dynamics; (2013), The Cryosphere Discussions 7; 4501-4544; DOI:10.5194/tcd-7-4501-2013 Note that this paper proposes an adjustment of the enhancement factor: \[E_{\text{effective}} = E \cdot (1 - (1-\epsilon) \phi)^{-n}.\] Let \(E_{\text{effective}} = E\cdot C\), where \(C\) is the factor defined by the formula above. Recall that the effective viscosity is defined by \[\nu(D) = \frac12 B D^{(1-n)/(2n)}\] and the viscosity form of the flow law is \[\sigma'_{ij} = E_{\text{effective}}^{-\frac1n}2\nu(D) D_{ij}.\] Then \[\sigma'_{ij} = E_{\text{effective}}^{-\frac1n}BD^{(1-n)/(2n)}D_{ij}.\] Using the fact that \(E_{\text{effective}} = E\cdot C\), this can be rewritten as \[\sigma'_{ij} = E^{-\frac1n} \left(C^{-\frac1n}B\right) D^{(1-n)/(2n)}D_{ij}.\] So scaling the enhancement factor by \(C\) is equivalent to scaling ice hardness \(B\) by \(C^{-\frac1n}\). Definition at line 1196 of file SSAFDBase.cc. References pism::Component::m_config, pism::Component::m_grid, and phi. Referenced by initialize_iterations().