Improve and document 'recycling fraction' example inputs

examples/recycling-fraction/README.md

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+'Recycling fraction' examples
+=============================
+
+The input files in this directory are for a 1D1V example with a central source
+of plasma particles and energy, and a recycling fraction of 0.5 at the walls
+providing a source of neutrals. Plasma and neutrals are coupled by charge
+exchange and ionization, with ad-hoc constant rates chosen to give a
+penetration depth of neutrals into the domain that is similar to the size of
+the domain (to avoid as much as possible very steep gradients near the sheath
+entrances).
+
+On the numerical side, these examples use a compressed grid near the target -
+to provide better resolution of steep gradients near the sheath entrance - and
+adaptive, explicit timestepping.
+
+Running the examples
+--------------------
+
+To minimise the computer time needed to reach steady state solutions, there is
+an input file for an initialisation drift-kinetic run with lower-order finite
+elements, which provides a good initial condition for higher resolution runs.
+Drift kinetic runs allow longer timesteps, and the 'split2' case (with
+separately evolved density and parallel flow) is slightly closer to the steady
+state of the full moment-kinetic 'split3' case (with separately evolved
+density, parallel flow, and parallel pressure), so provides a better initial
+guess. The suggested sequence for runs is:
+```julia
+julia> using moment_kinetics
+julia> run_moment_kinetics("examples/recycling-fraction/wall-bc_recyclefraction0.5-init.toml")
+julia> run_moment_kinetics("examples/recycling-fraction/wall-bc_recyclefraction0.5.toml"; restart="runs/wall-bc_recyclefraction0.5-init/wall-bc_recyclefraction0.5-init.dfns.h5")
+julia> run_moment_kinetics("examples/recycling-fraction/wall-bc_recyclefraction0.5_split1.toml"; restart="runs/wall-bc_recyclefraction0.5/wall-bc_recyclefraction0.5.dfns.h5")
+julia> run_moment_kinetics("examples/recycling-fraction/wall-bc_recyclefraction0.5_split2.toml"; restart="runs/wall-bc_recyclefraction0.5/wall-bc_recyclefraction0.5.dfns.h5")
+julia> run_moment_kinetics("examples/recycling-fraction/wall-bc_recyclefraction0.5_split3.toml"; restart="runs/wall-bc_recyclefraction0.5_split2/wall-bc_recyclefraction0.5_split2.dfns.h5")
+```
+The full moment-kinetic run 'split3' is still quite slow, ~6.5hrs on 8 cores.
+
+Remember that runs can be paused by doing `touch stop` in the output directory, and restarted with, e.g.
+```julia
+julia> run_moment_kinetics("examples/recycling-fraction/wall-bc_recyclefraction0.5_split3.toml"; restart=true)
+```
+
+There are several other input files in this directory that use different
+Runge-Kutta timestepping schemes for the full moment-kinetic 'split3' case, but
+unless you are experimenting with timestepping schemes the `"Fekete4(3)"` used
+for all the runs mentioned above seems to be a reasonable choice.

examples/recycling-fraction/wall-bc_recyclefraction0.5-init.toml

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+n_ion_species = 1
+n_neutral_species = 1
+evolve_moments_density = false
+evolve_moments_parallel_flow = false
+evolve_moments_parallel_pressure = false
+evolve_moments_conservation = false
+recycling_fraction = 0.5
+T_e = 0.2 # 1.0
+T_wall = 0.1
+initial_density1 = 1.0
+initial_temperature1 = 1.0
+z_IC_option1 = "gaussian"
+z_IC_density_amplitude1 = 0.001
+z_IC_density_phase1 = 0.0
+z_IC_upar_amplitude1 = 1.0
+z_IC_upar_phase1 = 0.0
+z_IC_temperature_amplitude1 = 0.0
+z_IC_temperature_phase1 = 0.0
+vpa_IC_option1 = "gaussian"
+vpa_IC_density_amplitude1 = 1.0
+vpa_IC_density_phase1 = 0.0
+vpa_IC_upar_amplitude1 = 0.0
+vpa_IC_upar_phase1 = 0.0
+vpa_IC_temperature_amplitude1 = 0.0
+vpa_IC_temperature_phase1 = 0.0
+initial_density2 = 1.0
+initial_temperature2 = 1.0
+z_IC_option2 = "gaussian"
+z_IC_density_amplitude2 = 0.001
+z_IC_density_phase2 = 0.0
+z_IC_upar_amplitude2 = -1.0
+z_IC_upar_phase2 = 0.0
+z_IC_temperature_amplitude2 = 0.0
+z_IC_temperature_phase2 = 0.0
+vpa_IC_option2 = "gaussian"
+vpa_IC_density_amplitude2 = 1.0
+vpa_IC_density_phase2 = 0.0
+vpa_IC_upar_amplitude2 = 0.0
+vpa_IC_upar_phase2 = 0.0
+vpa_IC_temperature_amplitude2 = 0.0
+vpa_IC_temperature_phase2 = 0.0
+charge_exchange_frequency = 0.75
+ionization_frequency = 0.5
+constant_ionization_rate = false
+r_ngrid = 1
+r_nelement = 1
+z_ngrid = 5
+z_nelement = 32
+z_nelement_local = 16
+z_bc = "wall"
+z_discretization = "chebyshev_pseudospectral"
+z_element_spacing_option = "sqrt"
+vpa_ngrid = 6
+vpa_nelement = 63
+vpa_L = 36.0
+vpa_bc = "zero"
+vpa_discretization = "chebyshev_pseudospectral"
+vz_ngrid = 6
+vz_nelement = 63
+vz_L = 36.0
+vz_bc = "zero"
+vz_discretization = "chebyshev_pseudospectral"
+
+[timestepping]
+type = "Fekete4(3)"
+nstep = 10000000
+dt = 1.0e-5
+minimum_dt = 1.0e-6
+nwrite = 10000
+nwrite_dfns = 10000
+split_operators = false
+steady_state_residual = true
+converged_residual_value = 1.0e-3
+
+[krook_collisions]
+use_krook = true
+
+[ion_source]
+active = true
+z_profile = "gaussian"
+z_width = 0.125
+source_strength = 2.0
+source_T = 2.0
+
+[ion_numerical_dissipation]
+#vpa_dissipation_coefficient = 1.0e-1
+#vpa_dissipation_coefficient = 1.0e-2
+#vpa_dissipation_coefficient = 1.0e-3
+
+[neutral_numerical_dissipation]
+#vz_dissipation_coefficient = 1.0e-1
+#vz_dissipation_coefficient = 1.0e-2
+#vz_dissipation_coefficient = 1.0e-3

examples/recycling-fraction/wall-bc_recyclefraction0.5.toml

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+n_ion_species = 1
+n_neutral_species = 1
+evolve_moments_density = false
+evolve_moments_parallel_flow = false
+evolve_moments_parallel_pressure = false
+evolve_moments_conservation = false
+recycling_fraction = 0.5
+T_e = 0.2 # 1.0
+T_wall = 0.1
+initial_density1 = 1.0
+initial_temperature1 = 1.0
+z_IC_option1 = "gaussian"
+z_IC_density_amplitude1 = 0.001
+z_IC_density_phase1 = 0.0
+z_IC_upar_amplitude1 = 1.0
+z_IC_upar_phase1 = 0.0
+z_IC_temperature_amplitude1 = 0.0
+z_IC_temperature_phase1 = 0.0
+vpa_IC_option1 = "gaussian"
+vpa_IC_density_amplitude1 = 1.0
+vpa_IC_density_phase1 = 0.0
+vpa_IC_upar_amplitude1 = 0.0
+vpa_IC_upar_phase1 = 0.0
+vpa_IC_temperature_amplitude1 = 0.0
+vpa_IC_temperature_phase1 = 0.0
+initial_density2 = 1.0
+initial_temperature2 = 1.0
+z_IC_option2 = "gaussian"
+z_IC_density_amplitude2 = 0.001
+z_IC_density_phase2 = 0.0
+z_IC_upar_amplitude2 = -1.0
+z_IC_upar_phase2 = 0.0
+z_IC_temperature_amplitude2 = 0.0
+z_IC_temperature_phase2 = 0.0
+vpa_IC_option2 = "gaussian"
+vpa_IC_density_amplitude2 = 1.0
+vpa_IC_density_phase2 = 0.0
+vpa_IC_upar_amplitude2 = 0.0
+vpa_IC_upar_phase2 = 0.0
+vpa_IC_temperature_amplitude2 = 0.0
+vpa_IC_temperature_phase2 = 0.0
+charge_exchange_frequency = 0.75
+ionization_frequency = 0.5
+constant_ionization_rate = false
+r_ngrid = 1
+r_nelement = 1
+z_ngrid = 9
+z_nelement = 32
+z_nelement_local = 16
+z_bc = "wall"
+z_discretization = "chebyshev_pseudospectral"
+z_element_spacing_option = "sqrt"
+vpa_ngrid = 10
+vpa_nelement = 63
+vpa_L = 36.0
+vpa_bc = "zero"
+vpa_discretization = "chebyshev_pseudospectral"
+vz_ngrid = 10
+vz_nelement = 63
+vz_L = 36.0
+vz_bc = "zero"
+vz_discretization = "chebyshev_pseudospectral"
+
+[timestepping]
+type = "Fekete4(3)"
+#nstep = 50000
+nstep = 1000000
+dt = 1.0e-5
+#minimum_dt = 1.0e-8
+minimum_dt = 1.0e-6
+step_update_prefactor = 0.5
+atol = 1.0e-10
+#atol = 1.0e-9
+nwrite = 10000
+nwrite_dfns = 10000
+split_operators = false
+steady_state_residual = true
+converged_residual_value = 1.0e-3
+
+[krook_collisions]
+use_krook = true
+
+[ion_source]
+active = true
+z_profile = "gaussian"
+z_width = 0.125
+source_strength = 2.0
+source_T = 2.0
+
+[ion_numerical_dissipation]
+#vpa_dissipation_coefficient = 1.0e-1
+#vpa_dissipation_coefficient = 1.0e-2
+#vpa_dissipation_coefficient = 1.0e-3
+
+[neutral_numerical_dissipation]
+#vz_dissipation_coefficient = 1.0e-1
+#vz_dissipation_coefficient = 1.0e-2
+#vz_dissipation_coefficient = 1.0e-3

examples/recycling-fraction/wall-bc_recyclefraction0.5_split1.toml

@@ -0,0 +1,98 @@
+n_ion_species = 1
+n_neutral_species = 1
+evolve_moments_density = true
+evolve_moments_parallel_flow = false
+evolve_moments_parallel_pressure = false
+evolve_moments_conservation = true
+recycling_fraction = 0.5
+T_e = 0.2 # 1.0
+T_wall = 0.1
+initial_density1 = 1.0
+initial_temperature1 = 1.0
+z_IC_option1 = "gaussian"
+z_IC_density_amplitude1 = 0.001
+z_IC_density_phase1 = 0.0
+z_IC_upar_amplitude1 = 1.0
+z_IC_upar_phase1 = 0.0
+z_IC_temperature_amplitude1 = 0.0
+z_IC_temperature_phase1 = 0.0
+vpa_IC_option1 = "gaussian"
+vpa_IC_density_amplitude1 = 1.0
+vpa_IC_density_phase1 = 0.0
+vpa_IC_upar_amplitude1 = 0.0
+vpa_IC_upar_phase1 = 0.0
+vpa_IC_temperature_amplitude1 = 0.0
+vpa_IC_temperature_phase1 = 0.0
+initial_density2 = 1.0
+initial_temperature2 = 1.0
+z_IC_option2 = "gaussian"
+z_IC_density_amplitude2 = 0.001
+z_IC_density_phase2 = 0.0
+z_IC_upar_amplitude2 = -1.0
+z_IC_upar_phase2 = 0.0
+z_IC_temperature_amplitude2 = 0.0
+z_IC_temperature_phase2 = 0.0
+vpa_IC_option2 = "gaussian"
+vpa_IC_density_amplitude2 = 1.0
+vpa_IC_density_phase2 = 0.0
+vpa_IC_upar_amplitude2 = 0.0
+vpa_IC_upar_phase2 = 0.0
+vpa_IC_temperature_amplitude2 = 0.0
+vpa_IC_temperature_phase2 = 0.0
+charge_exchange_frequency = 0.75
+ionization_frequency = 0.5
+constant_ionization_rate = false
+r_ngrid = 1
+r_nelement = 1
+z_ngrid = 9
+z_nelement = 32
+z_nelement_local = 16
+z_bc = "wall"
+z_discretization = "chebyshev_pseudospectral"
+z_element_spacing_option = "sqrt"
+vpa_ngrid = 10
+vpa_nelement = 63
+vpa_L = 36.0
+vpa_bc = "zero"
+vpa_discretization = "chebyshev_pseudospectral"
+vz_ngrid = 10
+vz_nelement = 63
+vz_L = 36.0
+vz_bc = "zero"
+vz_discretization = "chebyshev_pseudospectral"
+
+[timestepping]
+type = "Fekete4(3)"
+#nstep = 50000
+nstep = 1000000
+dt = 1.0e-5
+#minimum_dt = 1.0e-8
+minimum_dt = 1.0e-6
+step_update_prefactor = 0.5
+atol = 1.0e-10
+#atol = 1.0e-9
+nwrite = 10000
+nwrite_dfns = 10000
+split_operators = false
+steady_state_residual = true
+converged_residual_value = 1.0e-3
+
+[krook_collisions]
+use_krook = true
+
+[ion_source]
+active = true
+z_profile = "gaussian"
+z_width = 0.125
+source_strength = 2.0
+source_T = 2.0
+
+[ion_numerical_dissipation]
+#vpa_dissipation_coefficient = 1.0e-1
+#vpa_dissipation_coefficient = 1.0e-2
+#vpa_dissipation_coefficient = 1.0e-3
+
+[neutral_numerical_dissipation]
+#vz_dissipation_coefficient = 1.0e-1
+#vz_dissipation_coefficient = 1.0e-2
+#vz_dissipation_coefficient = 1.0e-3

examples/recycling-fraction/wall-bc_recyclefraction0.5_split3_fekete43.toml → examples/recycling-fraction/wall-bc_recyclefraction0.5_split2.toml

@@ -1,13 +1,10 @@
-
 n_ion_species = 1
 n_neutral_species = 1
-boltzmann_electron_response = true
 evolve_moments_density = true
 evolve_moments_parallel_flow = true
-evolve_moments_parallel_pressure = true
+evolve_moments_parallel_pressure = false
 evolve_moments_conservation = true
 recycling_fraction = 0.5
-krook_collisions_option = "reference_parameters"
 T_e = 0.2 # 1.0
 T_wall = 0.1
 initial_density1 = 1.0
@@ -80,6 +77,9 @@ split_operators = false
 steady_state_residual = true
 converged_residual_value = 1.0e-3
 
+[krook_collisions]
+use_krook = true
+
 [ion_source]
 active = true
 z_profile = "gaussian"

examples/recycling-fraction/wall-bc_recyclefraction0.5_split3-init.toml

@@ -1,13 +1,10 @@
-#runtime_plots = true
 n_ion_species = 1
 n_neutral_species = 1
-boltzmann_electron_response = true
 evolve_moments_density = true
 evolve_moments_parallel_flow = true
 evolve_moments_parallel_pressure = true
 evolve_moments_conservation = true
 recycling_fraction = 0.5
-krook_collisions_option = "reference_parameters"
 T_e = 0.2 # 1.0
 T_wall = 0.1
 initial_density1 = 1.0
@@ -65,15 +62,19 @@ vz_bc = "zero"
 vz_discretization = "chebyshev_pseudospectral"
 
 [timestepping]
-#nstep = 50000
-nstep = 1000000
-dt = 1.0e-6
+type = "Fekete4(3)"
+nstep = 100000
+dt = 1.0e-5
+minimum_dt = 1.0e-6
 nwrite = 1000
 nwrite_dfns = 1000
 split_operators = false
 steady_state_residual = true
 converged_residual_value = 1.0e-3
 
+[krook_collisions]
+use_krook = true
+
 [ion_source]
 active = true
 z_profile = "gaussian"