assemble_R checkReadyToSolve compute_enthalpy_CTS compute_lambda Enth Enth_s enthSystemCtx init k_from_T lambda m_B0 m_B_ks m_D0 m_D_ks m_E_e m_E_ij m_E_n m_E_s m_E_w m_EC m_Enth m_Enth3 m_Enth_s m_ice_c m_ice_density m_ice_k m_ice_thickness m_k_depends_on_T m_L_ks m_lambda m_margin_exclude_horizontal_advection m_margin_exclude_strain_heat m_margin_exclude_vertical_advection m_marginal m_nu m_p_air m_R m_R_cold m_R_factor m_R_temp m_strain_heating m_strain_heating3 m_U0 m_U_ks save_system set_basal_dirichlet_bc set_basal_heat_flux set_basal_neumann_bc set_surface_dirichlet_bc set_surface_heat_flux set_surface_neumann_bc solve ~enthSystemCtx

assemble_R() void pism::energy::enthSystemCtx::assemble_R ( ) protected Assemble the R array. The R value switches at the CTS. In a simple abstract diffusion \[ \frac{\partial u}{\partial t} = D \frac{\partial^2 u}{\partial z^2}, \] with time steps \(\Delta t\) and spatial steps \(\Delta z\) we define \[ R = \frac{D \Delta t}{\Delta z^2}. \] This is used in an implicit method to write each line in the linear system, for example [MortonMayers]: \[ -R U_{j-1}^{n+1} + (1+2R) U_j^{n+1} - R U_{j+1}^{n+1} = U_j^n. \] In the case of conservation of energy [AschwandenBuelerKhroulevBlatter], \[ u=E \qquad \text{ and } \qquad D = \frac{K}{\rho} \qquad \text{ and } \qquad K = \frac{k}{c}. \] Thus \[ R = \frac{k \Delta t}{\rho c \Delta z^2}. \] Definition at line 393 of file enthSystem.cc. References pism::k, k_from_T(), pism::columnSystemCtx::m_dz, m_EC, m_Enth, m_Enth_s, m_ice_k, m_ice_thickness, m_k_depends_on_T, pism::columnSystemCtx::m_ks, m_R, m_R_cold, m_R_factor, and m_R_temp. Referenced by init().