bed_smoother compute_3d_horizontal_velocity compute_diffusive_flux compute_diffusivity compute_I compute_surface_gradient diagnostics_impl diffusivity init interglacial m_bed_smoother m_D m_delta_0 m_delta_1 m_e_factor m_e_factor_interglacial m_eemian_end m_eemian_start m_event_sia m_h_x m_h_y m_holocene_start m_seconds_per_year m_stencil_width m_work_2d_0 m_work_2d_1 m_work_3d_0 m_work_3d_1 SIAFD surface_gradient_eta surface_gradient_haseloff surface_gradient_mahaffy surface_gradient_x surface_gradient_y update ~SIAFD

compute_diffusivity() void pism::stressbalance::SIAFD::compute_diffusivity ( bool  full_update, const Geometry &  geometry, const array::Array3D *  enthalpy, const array::Array3D *  age, const array::Staggered1 &  h_x, const array::Staggered1 &  h_y, array::Staggered1 &  result  ) protectedvirtual Compute the SIA diffusivity. If full_update, also store delta on the staggered grid. Recall that \( Q = -D \nabla h \) is the diffusive flux in the mass-continuity equation \[ \frac{\partial H}{\partial t} = M - S - \nabla \cdot (Q + \mathbf{U}_b H),\] where \(h\) is the ice surface elevation, \(M\) is the top surface accumulation/ablation rate, \(S\) is the basal mass balance and \(\mathbf{U}_b\) is the thickness-advective (in PISM: usually SSA) ice velocity. Recall also that at any particular point in the map-plane (i.e. if \(x\) and \(y\) are fixed) \[ D = 2\int_b^h F(z)P(z)(h-z)dz, \] where \(F(z)\) is a constitutive function and \(P(z)\) is the pressure at a level \(z\). By defining \[ \delta(z) = 2F(z)P(z) \] one can write \[D = \int_b^h\delta(z)(h-z)dz. \] The advantage is that it is then possible to avoid re-evaluating \(F(z)\) (which is computationally expensive) in the horizontal ice velocity (see compute_3d_horizontal_velocity()) computation. This method computes \(D\) and stores \(\delta\) in delta[0,1] if full_update is true. The trapezoidal rule is used to approximate the integral. Parameters [in] full_update the flag specitying if we're doing a "full" update. [in] h_x x-component of the surface gradient, on the staggered grid [in] h_y y-component of the surface gradient, on the staggered grid [out] result diffusivity of the SIA flow Definition at line 529 of file SIAFD.cc. References pism::Geometry::cell_type, pism::ParallelSection::check(), pism::Time::current(), pism::ParallelSection::failed(), pism::RuntimeError::formatted(), pism::array::Array3D::get_column(), pism::GlobalMax(), pism::GlobalSum(), pism::Geometry::ice_surface_elevation, pism::Geometry::ice_thickness, interglacial(), pism::k, m_bed_smoother, pism::Component::m_config, pism::stressbalance::SSB_Modifier::m_D_max, m_delta_0, m_delta_1, m_e_factor, m_e_factor_interglacial, pism::stressbalance::SSB_Modifier::m_EC, pism::stressbalance::SSB_Modifier::m_flow_law, pism::Component::m_grid, pism::Component::m_log, m_seconds_per_year, m_work_2d_0, m_work_2d_1, pism::array::max(), PISM_ERROR_LOCATION, pism::array::Array::set(), pism::array::Array3D::set_column(), pism::stressbalance::BedSmoother::smoothed_thk(), pism::array::Array::stencil_width(), pism::stressbalance::BedSmoother::theta(), pism::Component::time(), pism::grid::X_PERIODIC, and pism::grid::Y_PERIODIC. Referenced by update().