AccessType Aglen albers_conical_equal_area_to_proj apply args_string average_water_column_pressure axis_type_from_string AxisType azimuthal_equidistant_to_proj backend_to_string bedrock_surface_temperature blatter_xy_exact blatter_xy_source blatter_xz_cfbc_base blatter_xz_cfbc_exact blatter_xz_cfbc_source blatter_xz_cfbc_surface blatter_xz_exact blatter_xz_halfar_exact blatter_xz_halfar_source blatter_xz_halfar_source_base blatter_xz_halfar_source_lateral blatter_xz_halfar_source_surface blatter_xz_source blatter_xz_source_bed blatter_xz_source_surface blatter_xz_vanderveen_beta blatter_xz_vanderveen_exact blatter_xz_vanderveen_source_lateral blatter_xz_vanderveen_source_surface blatter_xz_vanderveen_thickness Box c1 c2 calendar calendar_from_file cf_to_proj check_c_call check_consistency_epsg check_forcing_duration check_input check_petsc_call choose_backend clear_fftw_array clip combine common_flags compute_area compute_cell_areas compute_coordinates compute_corrective_velocity compute_grounded_cell_fraction compute_horizontal_grid_size compute_horizontal_spacing compute_interface_velocity compute_lat_bounds compute_latitude compute_lon_bounds compute_lon_lat compute_lon_lat_bounds compute_longitude compute_node_types compute_strain_heating_errors computeSurfaceVelocityErrors config_from_options config_from_options config_metadata ConfigSettingFlag contains_epsg context_from_config context_from_options convert_vec convert_vec copy_fftw_array count_CFL_violations create_backend create_restriction criticalW DiagnosticList DiagnosticReport Direction dx_estimate dx_min dy_estimate dy_min effective_change end_time ends_with enthalpy_from_temperature_cold epsg_to_cf exactFG exactP exactP_list F F fftfreq filename_add_suffix finalize fletcher64 floating_ice_sheet_area_fraction_name flux_limiter flux_limiter format_attributes funcP g generate_mound_topography generate_trough_topography get_ get_proj_parameters get_real_part get_shared_ get_time getsb getW GlobalMax GlobalMax GlobalMax GlobalMax GlobalMin GlobalMin GlobalReduce GlobalReduce GlobalSum GlobalSum GlobalSum GlobalSum GlobalSum Grid_FromFile grid_name grid_subset grid_transpose grid_z grounded_area_fraction grounded_ice_sheet_area_fraction_name h0 handle_fatal_errors ice_area ice_area_floating ice_area_grounded ice_bottom_surface ice_flow_rate_across_grounding_line ice_volume ice_volume_not_displacing_seawater IceModelTerminationReason increment_date init_interpolation_indexes init_step initialconditionW InitializationType initialize initialize initialize_options integration_weights integration_weights InterpolationType intersect_ab intersect_ac intersect_bc invalid is_increasing join join_impl k label_components_impl lambert_azimuthal_equal_area_to_proj lambert_conformal_conic_to_proj lambert_cylindrical_equal_area_to_proj land_ice_area_fraction_name lapse_rate_correction latitude_longitude_to_proj limit_advective_flux limit_diffusive_flux LoggerLevel LonLat m0 make_nonnegative_preserving mapping_info_from_file MaskValue max_timestep_cfl_2d max_timestep_cfl_3d max_timestep_diffusivity maybe_show_usage member mercator_to_proj Metadata nc_type_to_pism_type netcdf_version NodeType operator* operator< operator< operator== operator> orthographic_to_proj p3 p4 parse_date parse_epsg parse_integer parse_integer_list parse_number parse_number_list part_grid_threshold_thickness pism_is_valid_calendar_name pism_type_to_nc_type polar_stereographic_to_proj print_checksum print_config print_diagnostics print_diagnostics_json print_unused_parameters print_vector print_vector printf process_input_options process_ts_shortcuts process_variable_list_shortcuts psteady R1 reference_date reference_date_from_file remove_narrow_tongues replace_character report_range reportErrors reporting_max_timestep restrict_data rhoi rhow rotated_latitude_longitude_to_proj s_pism_finalize_mpi same scalar_diag_metadata sea_level_rise_potential secondInvariant_2D ServerActions set_config_from_options set_flag_from_option set_integer_from_option set_join set_keyword_from_option set_member set_no_model_strip set_no_model_yield_stress set_number_from_option set_parameter_from_options set_real_part set_split set_string_from_option set_union setInitStateF setup_level show_usage SNESScalarProblem SNESVectorProblem spatial_diag_metadata special_parameter SperA split square start_time step step stereographic_to_proj string_is_false string_is_true string_strip string_to_backend subset_start_and_count TEMPORARY_STRING_LENGTH timestamp total_grounding_line_flux transverse_mercator_to_proj triangle_area TSDiagnosticList UNOType upwind username_prefix v0 validate_format_string vector_max vector_member vector_min version vertical_perspective_to_proj volume_flow_rate_from_land_to_water wall_clock_hours warn_about_missing weights_piecewise_constant weights_piecewise_linear Wr write

flux_limiter() [2/2] double pism::flux_limiter ( double  F, double  F_out_c, double  F_out_n, double  x_c, double  x_n  ) Smolarkiewicz-Zalesak flux limiter (equation 10 in [Smolarkiewicz1989]) Parameters [in] F total flux across a boundary between two cells ("c" and "n") over the course of a time step [in] F_out_c total flux leaving the "current" cell over the course of a time step [in] F_out_n total flux leaving the "neighbor" cell over the course of a time step [in] x_c value at the "current" cell (non-negative) [in] x_n value at the "neighbor" cell (non-negative) Returns the limited total flux over the course of a time step Notes: Equation 10 contains the fraction pp(F) / F_out_c, so we need to avoid division by zero. Note that F_out_c >= 0 by construction. Also, if pp(F) > 0 then F_out_c > 0 because F_out_c contains a term pp(F) * dt / delta where delta is grid spacing (dx or dy). This implies that if F_out_c == 0 then pp(F) == 0 (equivalently, F <= 0). But if pp(F) == 0 then F is a flux into the cell "c" and it cannot make the value x_c negative, so we don't need to limit it using the value of x_c. This implies that the term pp(F) / F_out_c * x_c should be replaced by 0. Equation 10 also contains the fraction -np(F) / F_out_n, so we need to avoid division by zero here as well. Note that F_out_n >= 0 by construction. Also, if np(F) > 0 then F_out_n > 0 because F_out_n contains a term np(F) * dt / delta` where delta is grid spacing (dx or dy). This implies that if F_out_n == 0 then np(F) == 0 (equivalently, F >= 0). But if np(F) == 0 then F is a flux into the cell "n" and it cannot make the value x_n negative, so we don't need to limit it using the value of x_n. This implies that the term -np(F) / F_out_n * x_n should be replaced by 0. Definition at line 107 of file flux_limiter.cc. References F(), pism::details::np(), and pism::details::pp(). Referenced by flux_limiter(), and make_nonnegative_preserving().