.. ############################################################################
.. manual/packages/vertex-cfd/closure_model.rst
.. ############################################################################

.. _sec_closure_model:

***********************
Closure model  block
***********************
      
.. literalinclude:: ../xml-blocks/closure_model.xml
   :language: xml
   :lines: 1-7
   :caption: `Closure Model` block in XML input file.

.. note::

   The sublist name `model_id` must match the value specified under `Model ID` in the `Physics Blocks` sublist. For example, if `Model ID` is defined as `fluids` in the `Physics Blocks`, the corresponding sublist in `Closure Models` must also be named `fluids`.

   .. literalinclude:: ../../../../examples/inputs/incompressible/incompressible_2d_concentric_cylinder_convection.xml
      :language: xml
      :linenos:
      :lines: 20-31
      :emphasize-lines: 7

   .. literalinclude:: ../../../../examples/inputs/incompressible/incompressible_2d_concentric_cylinder_convection.xml
      :language: xml
      :linenos:
      :lines: 94-128
      :emphasize-lines: 2

.. dropdown:: Fluid Properties
   :icon: multi-select
   :color: primary
   :animate: fade-in-slide-down
      
   .. py:data:: Build Viscous Flux

      :type: bool
      :value: True or False
      :usage: Optional
      :default: False
      :description: Add viscous flux to momentum equation.

   .. py:data:: Build Temperature Equation

      :type: bool
      :value: True or False
      :usage: Optional
      :default: False
      :description: Build the temperature equation.

   .. py:data:: Build Buoyancy Source

      :type: bool
      :value: True or False
      :usage: Optional
      :default: False
      :description: Add Buoyancy force to momentum equation

   .. py:data:: Build Viscous Heat

      :type: bool
      :value: True or False
      :usage: Optional
      :default: False
      :description: Add viscous heating to temperature equation
      
   .. py:data:: Continuity Model

      :type: string
      :value: AC, EDAC, NCTempEDAC
      :usage: Optional
      :default: AC
      :description: Continuity model to chose between artificial compressibility (AC), entropically damped AC (EDAC), and non-conservative temperature with EDAC.
      
   .. py:data:: Density

      :type: double
      :value: :math:`[0;\infty]`
      :usage: Optional
      :default: 1.0
      :description: Fluid density (:math:`\rho`).

   .. py:data:: Kinematic viscosity

      :type: double
      :value: :math:`[0;\infty]`
      :usage: Required
      :description: Fluid kinematic viscosity (:math:`\nu`).

   .. py:data:: Artificial compressibility

      :type: double
      :value: :math:`[0;\infty]`
      :usage: Required.
      :description: Artificial compressibility coefficient (:math:`\beta`) in the continuity equation.

   .. py:data:: Thermal conductivity

      :type: double
      :value: :math:`[0;\infty]`
      :usage: Required if temperature equation is enabled.
      :description: Fluid thermal conductivity (:math:`\kappa`).

   .. py:data:: Specific heat capacity

      :type: double
      :value: :math:`(0;\infty]`
      :usage: Required if temperature equation is enabled.
      :description: Fluid specific heat capacity (:math:`c_p`).

   .. py:data:: Expansion coefficient

      :type: double
      :value: :math:`(0;\infty]`
      :usage: Required if temperature equation and Buoyancy effects are enabled.
      :description: Fluid thermal expension coefficient (:math:`\alpha`) to use with Buoyancy force :math:`\rho \alpha (T -T_{ref})`.

   .. py:data:: Reference temperature

      :type: double
      :value: :math:`(0;\infty]`
      :usage: Required if temperature equation and Buoyancy effects are enabled.
      :description: Fluid reference temperature (:math:`T_{ref}`) to use with Buoyancy force :math:`\rho \beta (T -T_{ref})`.

   .. literalinclude:: ../../../../examples/inputs/incompressible/incompressible_2d_concentric_cylinder_convection.xml
      :language: xml
      :linenos:
      :lines: 96-108

.. dropdown:: Turbulence Parameters
   :icon: multi-select
   :color: primary
   :animate: fade-in-slide-down

   .. py:data:: Turbulence Model Name

      :type: string
      :value: No Turbulence Model, Spalart-Allmaras, Chien K-Epsilon, Standard K-Epsilon, Realizable K-Epsilon, K-Omega, SST K-Omega, K-Tau, WALE
      :usage: Required
      :description: Name of the turbulence model to use.

   .. literalinclude:: ../../../../examples/inputs/incompressible/incompressible_2d_k_tau_channel.xml
      :language: xml
      :linenos:
      :lines: 149-150

   .. dropdown:: Spalart-Allamras turbulence model
      :icon: bookmark
      :color: light
      :animate: fade-in-slide-down

      The Spalart–Allmaras turbulence model has no user-exposed parameters in the input file.

   .. dropdown:: Standard K-Epsilon turbulence model
      :icon: bookmark
      :color: light
      :animate: fade-in-slide-down

      The Standard K-Epsilon turbulence model has no user-exposed parameters in the input file.

   .. dropdown:: Realizabe K-Epsilon turbulence model
      :icon: bookmark
      :color: light
      :animate: fade-in-slide-down

      The Realizable K-Epsilon turbulence model has no user-exposed parameters in the input file.

   .. dropdown:: K-Omega turbulence model
      :icon: bookmark
      :color: light
      :animate: fade-in-slide-down

      .. py:data:: sigma_k

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.6
         :usage: Optional
         :description: Coefficient that multiplies the turbulent eddy viscosity :math:`\nu_t` to compute the diffusivity coefficient of the turbulent kinetic energy equation: :math:`\nu + \sigma_k \nu_t`.

      .. py:data:: sigma_w

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.5
         :usage: Optional
         :description: Coefficient that multiplies the turbulent eddy viscosity :math:`\nu_t` to compute the diffusivity coefficient of the turbulent dissipation equation: :math:`\nu + \sigma_w \nu_t`.

      .. py:data:: beta_star

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.09
         :usage: Optional
         :description: Controls the turbulent kinetic energy destruction term.

      .. py:data:: gamma

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.52
         :usage: Optional
         :description: Multiplies the production term in the specific dissipation rate equation.

      .. py:data:: beta_0

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.0708
         :usage: Optional
         :description: Controls the destruction term in the specific dissipation rate equation.

      .. py:data:: sigma_d

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.125
         :usage: Optional
         :description: Multiplies the cross-diffusion term in the dissipation rate equation.

      .. py:data:: Limit Production Term

         :type: bool
         :value: true, false
         :default: true
         :usage: Optional
         :description: Limits the production term in the turbulent kinetic energy. The production term is limited to 20 times the destruction term.

      .. literalinclude:: ../../../../examples/inputs/incompressible/incompressible_2d_k_omega_turbulence_channel.xml
         :language: xml
         :linenos:
         :lines: 126-129

   .. dropdown:: K-Tau turbulence model
      :icon: bookmark
      :color: light
      :animate: fade-in-slide-down

      .. py:data:: sigma_k

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.6
         :usage: Optional
         :description: Coefficient that multiplies the turbulent eddy viscosity :math:`\nu_t` to compute the diffusivity coefficient of the turbulent kinetic energy equation: :math:`\nu + \sigma_k \nu_t` (inverse of the turbulent Prandtl number).

      .. py:data:: sigma_w

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.5
         :usage: Optional
         :description: Coefficient that multiplies the turbulent eddy viscosity :math:`\nu_t` to compute the diffusivity coefficient of the turbulent dissipation equation: :math:`\nu + \sigma_w \nu_t` (inverse of the turbulent Prandtl number).

      .. py:data:: beta_star

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.09
         :usage: Optional
         :description: Controls the turbulent kinetic energy destruction term.

      .. py:data:: gamma

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.52
         :usage: Optional
         :description: Multiplies the production term in the specific dissipation rate equation.

      .. py:data:: beta_0

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.0708
         :usage: Optional
         :description: Controls the destruction term in the specific dissipation rate equation.

      .. py:data:: sigma_d

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.125
         :usage: Optional
         :description: Multiplies the cross-diffusion term in the dissipation rate equation.

      .. py:data:: sigma_t

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.5
         :usage: Optional
         :description: Multiplies the destruction term in :math:`\tau` equation.

      .. py:data:: Limit Production Term

         :type: bool
         :value: true, false
         :default: true
         :usage: Optional
         :description: Limits the production term in the turbulent kinetic energy. The production term is limited to 10 times the destruction term.

      .. py:data:: Limit Destruction Term

         :type: bool
         :value: true, false
         :default: true
         :usage: Optional
         :description: Limits the destruction term in the :math:`\tau` equation.

      .. literalinclude:: ../../../../examples/inputs/incompressible/incompressible_2d_k_tau_channel.xml
         :language: xml
         :linenos:
         :lines: 149-156

   .. dropdown:: Chien K-Epsilon turbulence model
      :icon: bookmark
      :color: light
      :animate: fade-in-slide-down

      .. py:data:: Boundary Surface Area

         :type: double
         :value: :math:`(0;\infty]`
         :usage: Required
         :description: Surface area of the boundary that has the "Friction Velocity" Scalar response.

      .. note::

         The friction velocity is computed on a wall surface area using a scalar response. The scalar response is defined in the input file by the user. The wall surface area is to be set as the `Boundary Surface Area`.

      .. literalinclude:: ../../../../examples/inputs/incompressible/incompressible_2d_chien_k_epsilon_turbulence_channel.xml
         :language: xml
         :linenos:
         :lines: 147-150

   .. dropdown:: SST turbulence model
      :icon: bookmark
      :color: light
      :animate: fade-in-slide-down

      .. py:data:: sigma_k1

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.85
         :usage: Optional
         :description: Coefficient that multiplies the turbulent eddy viscosity :math:`\nu_t` to compute the diffusivity coefficient of the turbulent kinetic energy equation: :math:`\nu + (\sigma_{k1} f + \sigma_{w1} (1. -f ) \nu_t`.

      .. py:data:: sigma_w1

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.5
         :usage: Optional
         :description: Coefficient that multiplies the turbulent eddy viscosity :math:`\nu_t` to compute the diffusivity coefficient of the turbulent kinetic energy equation: :math:`\nu + (\sigma_{k1} f + \sigma_{w1} (1. -f )) \nu_t`.

      .. py:data:: sigma_k2

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.85
         :usage: Optional
         :description: Coefficient that multiplies the turbulent eddy viscosity :math:`\nu_t` to compute the diffusivity coefficient of the turbulent kinetic energy equation: :math:`\nu + (\sigma_{k2} f + \sigma_{w2} (1. -f )) \nu_t`.

      .. py:data:: sigma_w2

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.5
         :usage: Optional
         :description: Coefficient that multiplies the turbulent eddy viscosity :math:`\nu_t` to compute the diffusivity coefficient of the turbulent kinetic energy equation: :math:`\nu + (\sigma_{k2} f + \sigma_{w2} (1. -f )) \nu_t`.

      .. py:data:: beta_star

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.09
         :usage: Optional
         :description: Control the turbulence length scale denoted by :math:`A` in the log region. :math:`A` decreases as `beta_star` increases. 

      .. py:data:: a_1

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.31
         :usage: Optional
         :description: Tuning parameter used in the turbulent eddy viscosity :math:`\nu_t`.

      .. py:data:: beta_1

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.075
         :usage: Optional
         :description: Coefficient used to compute `gamma_1` that controls the blending of the production term in the dissipation rate equation.

      .. py:data:: beta_2

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.828
         :usage: Optional
         :description: Coefficient used to compute `gamma_2` that controls the blending of the production term in the dissipation rate equation.

      .. py:data:: sigma_w1

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.5
         :usage: Optional
         :description: Coefficient used to compute `gamma_1` that controls the blending of the production term in the dissipation rate equation.

      .. py:data:: sigma_w2

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.856
         :usage: Optional
         :description: Tuning parmater used in the positive part of the cross diffusion term. This parameter is also used to compute `gamma_2` that controls the blending of the production term in the dissipation rate equation.

      .. py:data:: kappa

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.075
         :usage: Optional
         :description: Coefficient used to compute `gamma_1` and `gamma_2` that control the blending of the production term in the dissipation rate equation.

      .. py:data:: Limit Production Term

         :type: bool
         :value: true, false
         :default: true
         :usage: Optional
         :description: Limits the production term in the turbulent kinetic energy. The production term is limited to 20 times the destruction term.

      .. literalinclude:: ../../../../examples/inputs/incompressible/incompressible_2d_sst_turbulence_channel.xml
         :language: xml
         :linenos:
         :lines: 127-130

   .. dropdown:: WALE turbulence model
      :icon: bookmark
      :color: light
      :animate: fade-in-slide-down

      .. py:data:: C_w

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.275
         :usage: Optional
         :description: Value of the wall coefficient used in the WALE turbulence model to adjust dissipation in the turbulent boundary layers.

      .. py:data:: LES Element Length

         :type: string
         :value: ElementLength, MeasureElementLength, MetricTensorElementLength, SingularValueElementLength
         :default: ElementLength
         :usage: Optional
         :description: Method to compute the local mesh size :math:`\Delta` when using WALE turbulence model.

      .. py:data:: Element Length Method

         :type: string
         :value: singular_value_min, singular_value_max
         :usage: Required when setting `LES Element Length` to `SingularValueElementLength`.
         :description: `SingularValueElementLength` computes the eigenvalues of the local cell Jacobian matrix. `singular_value_min` returns the minimum local eigenvalue while `singular_value_max` returns the maximum local eigenvalue.

      .. py:data:: C_k

         :type: double
         :value: :math:`(0;\infty]`
         :default: 0.094
         :usage: Optional
         :description: Value of the sub-grid kinetic energy coefficient used in the WALE turbulence model to adjust dissipation in the turbulent boundary layers :math:`\left(\frac{\nu_t}{C_k\Delta}\right)^2` where :math:`\Delta` is a measure of the local mesh size..

      .. literalinclude:: ../../../../examples/inputs/incompressible/incompressible_3d_wale_cavity.xml
         :language: xml
         :linenos:
         :lines: 171-175

   .. dropdown:: SUPG Parameters
      :icon: multi-select
      :color: secondary
      :animate: fade-in

      .. py:data:: Tau model

         :type: string
         :value: Steady, Transient, NoSUPG
         :usage: Required
         :description: Model for stabilization parameter used in SUPG numerical method.

      .. py:data:: Tau coefficient

         :type: double
         :value: :math:`[0;1]`
         :default: 0.5
         :conflict: None
         :usage: Optional
         :description: Coefficient that multiplies the stabilization parameter :math:`\tau` defined with *Tau model*.

      .. literalinclude:: ../../../../examples/inputs/incompressible/incompressible_2d_k_tau_channel.xml
         :language: xml
         :linenos:
         :lines: 152-156

.. dropdown:: Stability Parameters
   :icon: multi-select
   :color: primary
   :animate: fade-in-slide-down

   .. py:data:: GradDiv Stabilization Coefficient

      :type: double
      :value: :math:`[0;\infty]`
      :usage: Required
      :description: Stabilization coefficient denoted by :math:`\gamma` used in the Grad-Div stabilization method: :math:`\nabla ( \gamma \nabla \vec{u}  )`.