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variables_turbulence_rans Module Reference

Define variables associated to the turbulence models. More...

Data Types

type  t_rans_ibc_initializer_item
 

Variables

logical is_rans_fully_explicit = .false.
 
double precision n_v2f = 1d0
 
Variables associated to the RANS models
integer rans_model = rans_model_k_omega
 RANS model choice.
 
logical rans_is_k_omega_sst = .false.
 RANS SST option of k omega (false by default)
 
logical rans_is_v2_f_coupled = .true.
 RANS coupled option of v2-f (true by default)
 
double precision rans_time_step = 0d0
 Current time step.
 
double precision rans_time_step_n = 0d0
 Previous time step.
 
double precision rans_time_step_nm1 = 0d0
 Ante previous time step.
 
integer rans_time_order_discretization = time_order_1
 Time order discretization.
 
integer rans_explicit_time_order_discretization = time_order_nssp32
 Explicit time order discretization.
 
logical rans_use_explicit_terms_accumulator = .false.
 A switch for when to use explicit accumulator.
 
Boundary condition RANS variables
type(t_boundary_conditionturbulent_kinetic_energy_boundary_condition
 Boundary conditions.
 
type(t_boundary_conditionspecific_dissipation_rate_boundary_condition
 
type(t_boundary_conditionturbulence_dissipation_boundary_condition
 
type(t_boundary_conditionmean_squared_velocity_boundary_condition
 
type(t_boundary_conditionf_22_boundary_condition
 
Initializer
class(t_scalar_initializer), pointer turbulent_kinetic_energy_initializer => null()
 Initial condition initializer.
 
class(t_scalar_initializer), pointer specific_dissipation_rate_initializer => null()
 
class(t_scalar_initializer), pointer turbulence_dissipation_initializer => null()
 
class(t_scalar_initializer), pointer mean_squared_velocity_initializer => null()
 
class(t_scalar_initializer), pointer f_22_initializer => null()
 
class(t_cell_bc_initializer), pointer turbulent_kinetic_energy_bc_initializer => null()
 Boundary conditions initializer.
 
class(t_cell_bc_initializer), pointer specific_dissipation_rate_bc_initializer => null()
 
class(t_cell_bc_initializer), pointer turbulence_dissipation_bc_initializer => null()
 
class(t_cell_bc_initializer), pointer mean_squared_velocity_bc_initializer => null()
 
class(t_cell_bc_initializer), pointer f_22_bc_initializer => null()
 
class(t_rans_ibc_initializer_item), dimension(:), allocatable turbulent_kinetic_energy_ibc_initializer
 Immersed boundary conditions initializers.
 
class(t_rans_ibc_initializer_item), dimension(:), allocatable specific_dissipation_rate_ibc_initializer
 
class(t_rans_ibc_initializer_item), dimension(:), allocatable turbulence_dissipation_ibc_initializer
 
class(t_rans_ibc_initializer_item), dimension(:), allocatable mean_squared_velocity_ibc_initializer
 
class(t_rans_ibc_initializer_item), dimension(:), allocatable f_22_ibc_initializer
 
class(t_scalar_initializer), pointer turbulent_kinetic_energy_source_term_initializer => null()
 Source term initializer.
 
class(t_scalar_initializer), pointer specific_dissipation_rate_source_term_initializer => null()
 
class(t_scalar_initializer), pointer turbulence_dissipation_source_term_initializer => null()
 
class(t_scalar_initializer), pointer mean_squared_velocity_source_term_initializer => null()
 
class(t_scalar_initializer), pointer f_22_source_term_initializer => null()
 
class(t_scalar_initializer), pointer turbulent_kinetic_energy_linear_term_initializer => null()
 Linear term initializer.
 
class(t_scalar_initializer), pointer specific_dissipation_rate_linear_term_initializer => null()
 
class(t_scalar_initializer), pointer turbulence_dissipation_linear_term_initializer => null()
 
class(t_scalar_initializer), pointer mean_squared_velocity_linear_term_initializer => null()
 
class(t_scalar_initializer), pointer f_22_linear_term_initializer => null()
 
Logical list to activate terms of the RANS equation
logical turbulent_kinetic_energy_has_source_term = .false.
 Has source term?
 
logical specific_dissipation_rate_has_source_term = .false.
 
logical turbulence_dissipation_has_source_term = .true.
 
logical mean_squared_velocity_has_source_term = .false.
 
logical f_22_has_source_term = .false.
 
logical rans_has_advection_term = .true.
 Has advection term? Unique variable for (k,omega)
 
logical k_omega_sst_has_advection_term = .true.
 
logical v2_f_has_advection_term = .true.
 
logical rans_has_diffusion_term = .true.
 Has diffusion term? Unique variable for (k,omega)
 
logical k_omega_sst_has_diffusion_term = .true.
 
logical v2_f_has_diffusion_term = .true.
 
logical k_omega_sst_has_div_u_advection_term = .false.
 Has \( div(\mathbf{u}) \) advection term? Unique variable for (k,omega)
 
logical v2_f_has_div_u_advection_term = .true.
 
logical k_omega_sst_has_temporal_term = .true.
 Has temporal term? Unique variable for (k,omega)
 
logical v2_f_has_temporal_term = .true.
 
logical turbulent_kinetic_energy_has_linear_term = .false.
 Has linear term?
 
logical specific_dissipation_rate_has_linear_term = .false.
 
logical turbulence_dissipation_has_linear_term = .true.
 
logical mean_squared_velocity_has_linear_term = .false.
 
logical f_22_has_linear_term = .false.
 
Variables related to immersed boundaries
logical rans_ib_has_one_sided_inner_discretization
 One sided discretization close to immersed boundaries.
 
integer, dimension(:), allocatable rans_ib_inner_discretization_order
 
Variables associated to the discretization of the advection term
integer rans_advection_term_discretization_type = implicit_discretization
 Advection term discretization type (implicit or explicit)
 
integer rans_advection_term_scheme = cell_centered_o2_advection_scheme
 Advection term scheme.
 
integer rans_advection_term_splitting_scheme = lie_trotter_splitting
 Advection term: Splitting Method for Lax-Wendroff TVD Superbee.
 
double precision, dimension(3) rans_splitting_time_coeff =1d0
 
logical rans_advection_term_dir_split = .false.
 Advection term: directional splitting option.
 
logical is_rans_specify_advection_scheme_stability_factor = .false.
 Specify a CFL factor for explicit sub iterations.
 
double precision rans_advection_scheme_stability_factor = -1d0
 CFL used for explicit sub iterations (if is_rans_specify_advection_scheme_stability_factor, otherwize, using default values)
 
type(t_fv_flux), parameter default_rans_advection_explicit_flux = default_flux_godunov
 Fluxes type The default explicit cell advection flux.
 
type(t_fv_fluxrans_advection_explicit_flux = default_rans_advection_explicit_flux
 Fluxes type The effective explicit cell advection flux.
 
integer rans_diffusion_term_discretization_type = implicit_discretization
 Diffusion term discretization type (implicit or explicit)
 
integer rans_diffusion_term_scheme = cell_centered_o2_diffusion_scheme
 Diffusion term scheme.
 
integer rans_diffusion_explicit_time_order_discretization
 
Miscellaneous variables
logical rans_has_ghost_boundary_cells = .false.
 Ghost boudary cell choice.
 
type(t_cell_stencilrans_stencil
 Stencil of the energy equation.
 
integer rans_enforced_stencil = -1
 Enforced stencil.
 
Linear system solver variables
type(t_ls_maprans_ls_map
 Mapping variables.
 
class(t_linear_solver), allocatable rans_solver
 Linear system solver.
 
double precision, parameter min_turbulent_kinetic_energy = 1d-12
 Numerical thresholds.
 
double precision, parameter min_specific_dissipation_rate = 1d-12
 
double precision, parameter min_turbulence_dissipation = 1d-12
 
double precision, parameter min_mean_squared_velocity = 1d-12
 
double precision, parameter min_f_22 = 1d-12
 
k-omega limiters
integer k_omega_sst_production_term_limiter = production_term_limiter_menter
 
k-omega SST constants
double precision sst_sigma_k1 = 0.85d0
 
double precision sst_sigma_omega1 = 0.5d0
 
double precision sst_beta1 = 0.075d0
 
double precision sst_gamma1 = 0.553166667d0
 
double precision sst_sigma_k2 = 1d0
 
double precision sst_sigma_omega2 = 0.856d0
 
double precision sst_beta2 = 0.0828d0
 
double precision sst_gamma2 = 0.440354667d0
 
double precision sst_beta_star = 0.09d0
 
double precision sst_kappa = 0.41d0
 
double precision sst_a1 = 0.31d0
 
k-omega constants
double precision beta_star = 0.09d0
 
double precision clim = 0.875d0
 
double precision sigma_star = 0.6d0
 
double precision sigma = 0.5d0
 
double precision alpha = 0.52d0
 
double precision beta_0 = 0.0708d0
 
double precision sigma_d0 = 0.125d0
 
v2_f model constants
double precision v2_f_sigma_k = 1d0
 
double precision v2_f_sigma_e = 1.3d0
 
double precision v2_f_c_mu = 0.22d0
 
double precision v2_f_c_e_2 = 1.9d0
 
double precision v2_f_c_1 = 1.4d0
 
double precision v2_f_c_2 = 0.3d0
 
double precision v2_f_c_l = 0.25d0
 
double precision v2_f_c_eta = 85d0
 

Detailed Description

Define variables associated to the turbulence models.

Variable Documentation

◆ alpha

double precision variables_turbulence_rans::alpha = 0.52d0

◆ beta_0

double precision variables_turbulence_rans::beta_0 = 0.0708d0

◆ beta_star

double precision variables_turbulence_rans::beta_star = 0.09d0

◆ clim

double precision variables_turbulence_rans::clim = 0.875d0

◆ default_rans_advection_explicit_flux

type(t_fv_flux), parameter variables_turbulence_rans::default_rans_advection_explicit_flux = default_flux_godunov

Fluxes type The default explicit cell advection flux.

◆ f_22_bc_initializer

class(t_cell_bc_initializer), pointer variables_turbulence_rans::f_22_bc_initializer => null()

◆ f_22_boundary_condition

type(t_boundary_condition) variables_turbulence_rans::f_22_boundary_condition

◆ f_22_has_linear_term

logical variables_turbulence_rans::f_22_has_linear_term = .false.

◆ f_22_has_source_term

logical variables_turbulence_rans::f_22_has_source_term = .false.

◆ f_22_ibc_initializer

class(t_rans_ibc_initializer_item), dimension(:), allocatable variables_turbulence_rans::f_22_ibc_initializer

◆ f_22_initializer

class(t_scalar_initializer), pointer variables_turbulence_rans::f_22_initializer => null()

◆ f_22_linear_term_initializer

class(t_scalar_initializer), pointer variables_turbulence_rans::f_22_linear_term_initializer => null()

◆ f_22_source_term_initializer

class(t_scalar_initializer), pointer variables_turbulence_rans::f_22_source_term_initializer => null()

◆ is_rans_fully_explicit

logical variables_turbulence_rans::is_rans_fully_explicit = .false.

◆ is_rans_specify_advection_scheme_stability_factor

logical variables_turbulence_rans::is_rans_specify_advection_scheme_stability_factor = .false.

Specify a CFL factor for explicit sub iterations.

◆ k_omega_sst_has_advection_term

logical variables_turbulence_rans::k_omega_sst_has_advection_term = .true.

◆ k_omega_sst_has_diffusion_term

logical variables_turbulence_rans::k_omega_sst_has_diffusion_term = .true.

◆ k_omega_sst_has_div_u_advection_term

logical variables_turbulence_rans::k_omega_sst_has_div_u_advection_term = .false.

Has \( div(\mathbf{u}) \) advection term? Unique variable for (k,omega)

◆ k_omega_sst_has_temporal_term

logical variables_turbulence_rans::k_omega_sst_has_temporal_term = .true.

Has temporal term? Unique variable for (k,omega)

◆ k_omega_sst_production_term_limiter

integer variables_turbulence_rans::k_omega_sst_production_term_limiter = production_term_limiter_menter

◆ mean_squared_velocity_bc_initializer

class(t_cell_bc_initializer), pointer variables_turbulence_rans::mean_squared_velocity_bc_initializer => null()

◆ mean_squared_velocity_boundary_condition

type(t_boundary_condition) variables_turbulence_rans::mean_squared_velocity_boundary_condition

◆ mean_squared_velocity_has_linear_term

logical variables_turbulence_rans::mean_squared_velocity_has_linear_term = .false.

◆ mean_squared_velocity_has_source_term

logical variables_turbulence_rans::mean_squared_velocity_has_source_term = .false.

◆ mean_squared_velocity_ibc_initializer

class(t_rans_ibc_initializer_item), dimension(:), allocatable variables_turbulence_rans::mean_squared_velocity_ibc_initializer

◆ mean_squared_velocity_initializer

class(t_scalar_initializer), pointer variables_turbulence_rans::mean_squared_velocity_initializer => null()

◆ mean_squared_velocity_linear_term_initializer

class(t_scalar_initializer), pointer variables_turbulence_rans::mean_squared_velocity_linear_term_initializer => null()

◆ mean_squared_velocity_source_term_initializer

class(t_scalar_initializer), pointer variables_turbulence_rans::mean_squared_velocity_source_term_initializer => null()

◆ min_f_22

double precision, parameter variables_turbulence_rans::min_f_22 = 1d-12

◆ min_mean_squared_velocity

double precision, parameter variables_turbulence_rans::min_mean_squared_velocity = 1d-12

◆ min_specific_dissipation_rate

double precision, parameter variables_turbulence_rans::min_specific_dissipation_rate = 1d-12

◆ min_turbulence_dissipation

double precision, parameter variables_turbulence_rans::min_turbulence_dissipation = 1d-12

◆ min_turbulent_kinetic_energy

double precision, parameter variables_turbulence_rans::min_turbulent_kinetic_energy = 1d-12

Numerical thresholds.

◆ n_v2f

double precision variables_turbulence_rans::n_v2f = 1d0

◆ rans_advection_explicit_flux

type(t_fv_flux) variables_turbulence_rans::rans_advection_explicit_flux = default_rans_advection_explicit_flux

Fluxes type The effective explicit cell advection flux.

◆ rans_advection_scheme_stability_factor

double precision variables_turbulence_rans::rans_advection_scheme_stability_factor = -1d0

CFL used for explicit sub iterations (if is_rans_specify_advection_scheme_stability_factor, otherwize, using default values)

◆ rans_advection_term_dir_split

logical variables_turbulence_rans::rans_advection_term_dir_split = .false.

Advection term: directional splitting option.

◆ rans_advection_term_discretization_type

integer variables_turbulence_rans::rans_advection_term_discretization_type = implicit_discretization

Advection term discretization type (implicit or explicit)

◆ rans_advection_term_scheme

integer variables_turbulence_rans::rans_advection_term_scheme = cell_centered_o2_advection_scheme

Advection term scheme.

◆ rans_advection_term_splitting_scheme

integer variables_turbulence_rans::rans_advection_term_splitting_scheme = lie_trotter_splitting

Advection term: Splitting Method for Lax-Wendroff TVD Superbee.

◆ rans_diffusion_explicit_time_order_discretization

integer variables_turbulence_rans::rans_diffusion_explicit_time_order_discretization

◆ rans_diffusion_term_discretization_type

integer variables_turbulence_rans::rans_diffusion_term_discretization_type = implicit_discretization

Diffusion term discretization type (implicit or explicit)

◆ rans_diffusion_term_scheme

integer variables_turbulence_rans::rans_diffusion_term_scheme = cell_centered_o2_diffusion_scheme

Diffusion term scheme.

◆ rans_enforced_stencil

integer variables_turbulence_rans::rans_enforced_stencil = -1

Enforced stencil.

◆ rans_explicit_time_order_discretization

integer variables_turbulence_rans::rans_explicit_time_order_discretization = time_order_nssp32

Explicit time order discretization.

◆ rans_has_advection_term

logical variables_turbulence_rans::rans_has_advection_term = .true.

Has advection term? Unique variable for (k,omega)

◆ rans_has_diffusion_term

logical variables_turbulence_rans::rans_has_diffusion_term = .true.

Has diffusion term? Unique variable for (k,omega)

◆ rans_has_ghost_boundary_cells

logical variables_turbulence_rans::rans_has_ghost_boundary_cells = .false.

Ghost boudary cell choice.

◆ rans_ib_has_one_sided_inner_discretization

logical variables_turbulence_rans::rans_ib_has_one_sided_inner_discretization

One sided discretization close to immersed boundaries.

◆ rans_ib_inner_discretization_order

integer, dimension(:), allocatable variables_turbulence_rans::rans_ib_inner_discretization_order

◆ rans_is_k_omega_sst

logical variables_turbulence_rans::rans_is_k_omega_sst = .false.

RANS SST option of k omega (false by default)

◆ rans_is_v2_f_coupled

logical variables_turbulence_rans::rans_is_v2_f_coupled = .true.

RANS coupled option of v2-f (true by default)

◆ rans_ls_map

type(t_ls_map) variables_turbulence_rans::rans_ls_map

Mapping variables.

◆ rans_model

integer variables_turbulence_rans::rans_model = rans_model_k_omega

RANS model choice.

◆ rans_solver

class(t_linear_solver), allocatable variables_turbulence_rans::rans_solver

Linear system solver.

◆ rans_splitting_time_coeff

double precision, dimension (3) variables_turbulence_rans::rans_splitting_time_coeff =1d0

◆ rans_stencil

type(t_cell_stencil) variables_turbulence_rans::rans_stencil

Stencil of the energy equation.

◆ rans_time_order_discretization

integer variables_turbulence_rans::rans_time_order_discretization = time_order_1

Time order discretization.

◆ rans_time_step

double precision variables_turbulence_rans::rans_time_step = 0d0

Current time step.

◆ rans_time_step_n

double precision variables_turbulence_rans::rans_time_step_n = 0d0

Previous time step.

◆ rans_time_step_nm1

double precision variables_turbulence_rans::rans_time_step_nm1 = 0d0

Ante previous time step.

◆ rans_use_explicit_terms_accumulator

logical variables_turbulence_rans::rans_use_explicit_terms_accumulator = .false.

A switch for when to use explicit accumulator.

◆ sigma

double precision variables_turbulence_rans::sigma = 0.5d0

◆ sigma_d0

double precision variables_turbulence_rans::sigma_d0 = 0.125d0

◆ sigma_star

double precision variables_turbulence_rans::sigma_star = 0.6d0

◆ specific_dissipation_rate_bc_initializer

class(t_cell_bc_initializer), pointer variables_turbulence_rans::specific_dissipation_rate_bc_initializer => null()

◆ specific_dissipation_rate_boundary_condition

type(t_boundary_condition) variables_turbulence_rans::specific_dissipation_rate_boundary_condition

◆ specific_dissipation_rate_has_linear_term

logical variables_turbulence_rans::specific_dissipation_rate_has_linear_term = .false.

◆ specific_dissipation_rate_has_source_term

logical variables_turbulence_rans::specific_dissipation_rate_has_source_term = .false.

◆ specific_dissipation_rate_ibc_initializer

class(t_rans_ibc_initializer_item), dimension(:), allocatable variables_turbulence_rans::specific_dissipation_rate_ibc_initializer

◆ specific_dissipation_rate_initializer

class(t_scalar_initializer), pointer variables_turbulence_rans::specific_dissipation_rate_initializer => null()

◆ specific_dissipation_rate_linear_term_initializer

class(t_scalar_initializer), pointer variables_turbulence_rans::specific_dissipation_rate_linear_term_initializer => null()

◆ specific_dissipation_rate_source_term_initializer

class(t_scalar_initializer), pointer variables_turbulence_rans::specific_dissipation_rate_source_term_initializer => null()

◆ sst_a1

double precision variables_turbulence_rans::sst_a1 = 0.31d0

◆ sst_beta1

double precision variables_turbulence_rans::sst_beta1 = 0.075d0

◆ sst_beta2

double precision variables_turbulence_rans::sst_beta2 = 0.0828d0

◆ sst_beta_star

double precision variables_turbulence_rans::sst_beta_star = 0.09d0

◆ sst_gamma1

double precision variables_turbulence_rans::sst_gamma1 = 0.553166667d0

◆ sst_gamma2

double precision variables_turbulence_rans::sst_gamma2 = 0.440354667d0

◆ sst_kappa

double precision variables_turbulence_rans::sst_kappa = 0.41d0

◆ sst_sigma_k1

double precision variables_turbulence_rans::sst_sigma_k1 = 0.85d0

◆ sst_sigma_k2

double precision variables_turbulence_rans::sst_sigma_k2 = 1d0

◆ sst_sigma_omega1

double precision variables_turbulence_rans::sst_sigma_omega1 = 0.5d0

◆ sst_sigma_omega2

double precision variables_turbulence_rans::sst_sigma_omega2 = 0.856d0

◆ turbulence_dissipation_bc_initializer

class(t_cell_bc_initializer), pointer variables_turbulence_rans::turbulence_dissipation_bc_initializer => null()

◆ turbulence_dissipation_boundary_condition

type(t_boundary_condition) variables_turbulence_rans::turbulence_dissipation_boundary_condition

◆ turbulence_dissipation_has_linear_term

logical variables_turbulence_rans::turbulence_dissipation_has_linear_term = .true.

◆ turbulence_dissipation_has_source_term

logical variables_turbulence_rans::turbulence_dissipation_has_source_term = .true.

◆ turbulence_dissipation_ibc_initializer

class(t_rans_ibc_initializer_item), dimension(:), allocatable variables_turbulence_rans::turbulence_dissipation_ibc_initializer

◆ turbulence_dissipation_initializer

class(t_scalar_initializer), pointer variables_turbulence_rans::turbulence_dissipation_initializer => null()

◆ turbulence_dissipation_linear_term_initializer

class(t_scalar_initializer), pointer variables_turbulence_rans::turbulence_dissipation_linear_term_initializer => null()

◆ turbulence_dissipation_source_term_initializer

class(t_scalar_initializer), pointer variables_turbulence_rans::turbulence_dissipation_source_term_initializer => null()

◆ turbulent_kinetic_energy_bc_initializer

class(t_cell_bc_initializer), pointer variables_turbulence_rans::turbulent_kinetic_energy_bc_initializer => null()

Boundary conditions initializer.

◆ turbulent_kinetic_energy_boundary_condition

type(t_boundary_condition) variables_turbulence_rans::turbulent_kinetic_energy_boundary_condition

Boundary conditions.

◆ turbulent_kinetic_energy_has_linear_term

logical variables_turbulence_rans::turbulent_kinetic_energy_has_linear_term = .false.

Has linear term?

◆ turbulent_kinetic_energy_has_source_term

logical variables_turbulence_rans::turbulent_kinetic_energy_has_source_term = .false.

Has source term?

◆ turbulent_kinetic_energy_ibc_initializer

class(t_rans_ibc_initializer_item), dimension(:), allocatable variables_turbulence_rans::turbulent_kinetic_energy_ibc_initializer

Immersed boundary conditions initializers.

◆ turbulent_kinetic_energy_initializer

class(t_scalar_initializer), pointer variables_turbulence_rans::turbulent_kinetic_energy_initializer => null()

Initial condition initializer.

◆ turbulent_kinetic_energy_linear_term_initializer

class(t_scalar_initializer), pointer variables_turbulence_rans::turbulent_kinetic_energy_linear_term_initializer => null()

Linear term initializer.

◆ turbulent_kinetic_energy_source_term_initializer

class(t_scalar_initializer), pointer variables_turbulence_rans::turbulent_kinetic_energy_source_term_initializer => null()

Source term initializer.

◆ v2_f_c_1

double precision variables_turbulence_rans::v2_f_c_1 = 1.4d0

◆ v2_f_c_2

double precision variables_turbulence_rans::v2_f_c_2 = 0.3d0

◆ v2_f_c_e_2

double precision variables_turbulence_rans::v2_f_c_e_2 = 1.9d0

◆ v2_f_c_eta

double precision variables_turbulence_rans::v2_f_c_eta = 85d0

◆ v2_f_c_l

double precision variables_turbulence_rans::v2_f_c_l = 0.25d0

◆ v2_f_c_mu

double precision variables_turbulence_rans::v2_f_c_mu = 0.22d0

◆ v2_f_has_advection_term

logical variables_turbulence_rans::v2_f_has_advection_term = .true.

◆ v2_f_has_diffusion_term

logical variables_turbulence_rans::v2_f_has_diffusion_term = .true.

◆ v2_f_has_div_u_advection_term

logical variables_turbulence_rans::v2_f_has_div_u_advection_term = .true.

◆ v2_f_has_temporal_term

logical variables_turbulence_rans::v2_f_has_temporal_term = .true.

◆ v2_f_sigma_e

double precision variables_turbulence_rans::v2_f_sigma_e = 1.3d0

◆ v2_f_sigma_k

double precision variables_turbulence_rans::v2_f_sigma_k = 1d0