assemble_matrix assemble_rhs compute_hardav_staggered compute_nuH_norm compute_nuH_staggered compute_nuH_staggered_cfbc diagnostics_impl fracture_induced_softening init_impl integrated_viscosity is_marginal m_A m_b m_default_pc_failure_count m_default_pc_failure_max_count m_hardness m_KSP m_nuH m_nuH_old m_nuh_viewer m_nuh_viewer_size m_scaling m_velocity_old m_view_nuh m_work pc_setup_asm pc_setup_bjacobi picard_iteration picard_manager picard_strategy_regularization solve SSAFD update_nuH_viewers write_system_petsc ~SSAFD

fracture_induced_softening() void pism::stressbalance::SSAFD::fracture_induced_softening ( const array::Scalar *  fracture_density ) protectedvirtual 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 1363 of file SSAFD.cc. References pism::Component::m_config, pism::stressbalance::ShallowStressBalance::m_flow_law, pism::Component::m_grid, m_hardness, and phi. Referenced by compute_hardav_staggered().