.. ############################################################################
.. manual/packages/vertex-cfd/initial_conditions.rst
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.. _sec_initial_conditions:

***********************
Initial conditions block
***********************
      
.. literalinclude:: ../xml-blocks/initial_conditions.xml
   :language: xml
   :lines: 1-5
   :caption: `Initial Conditions` block in XML input file.

Initial conditions are specified for each mesh block, and all variables defined as degrees of freedom within a block must be assigned initial values. Vertex-CFD provides several types of initial conditions, listed below. The syntax for defining initial conditions in a mesh block is as follows:

.. literalinclude:: ../../../../examples/inputs/incompressible/incompressible_2d_channel_periodic.xml
   :language: xml
   :lines: 76-92
   :caption: Initial conditions for mesh block `eblock-0_0`.

.. literalinclude:: ../../../../examples/inputs/cht/solid_to_solid_fluid_cht.xml
   :language: xml
   :lines: 170-201
   :caption: Initial conditions for mesh blocks `fluid_1`, `fluid_2`, `solid_1` and `solid_2`.

The initial conditions for mesh block `eblock-0_0` are defined in a sub-list whose value matches the mesh block name. Individual initial conditions are then specified within sub-lists selected from the options below. The name of each sub-list is provided by the user. Some initial-condition types apply to a single variable, such as `Constant`, while others define conditions for a set of variables on a mesh block — for example, `Laminar Flow`.

.. dropdown:: <Constant initial condition>
   :icon: multi-select
   :color: primary
   :animate: fade-in-slide-down

   .. py:data:: Type

      :type: string
      :value: Constant
      :usage: Required
      :description: Define an uniform initial conditions for the variable defined in Equation Set Name.
      
   .. py:data:: Equation Set Name

      :type: string
      :value: Variable name
      :usage: Required
      :description: Variable name to initialize (should be the same name as defined in the source code).
      
   .. py:data:: Value

      :type: double
      :value: :math:`[-\infty;\infty]`
      :usage: Required
      :description: Value to initialize the variable set in Equation Set Name with.
      
   .. literalinclude:: ../../../../examples/inputs/incompressible/incompressible_2d_channel_periodic.xml
      :language: xml
      :linenos:
      :lines: 77-81
      :caption: Set an initial condition of 0.0 for the variable `lagrange_pressure`.

.. dropdown:: <Laminar Flow>
   :icon: multi-select
   :color: primary
   :animate: fade-in-slide-down
      
   .. note::

      The laminar initial condition is only supported in the x-direction. When selecting this initial condition type, the pressure and velocity components are initialized. The temperature is set to an uniform value when enabled.

   .. py:data:: Type

      :type: string
      :value: IncompressibleLaminarFlow
      :usage: Required
      :description: Define a laminar profile in the x-direction.
      
   .. py:data:: Minimum height

      :type: double
      :value: :math:`[-\infty;\infty]`
      :usage: Required
      :description: Position of the bottom wall perpandicular to the flow direction.
      
   .. py:data:: Maximum height

      :type: double
      :value: :math:`[-\infty;\infty]`
      :usage: Required
      :description: Position of the top wall perpandicular to the flow direction.
      
   .. py:data:: Average velocity

      :type: double
      :value: :math:`[0;\infty]`
      :usage: Required
      :description: Average velocity in the flow direction.
      
   .. py:data:: Temperature

      :type: double
      :value: :math:`[0;\infty]`
      :usage: Optional
      :description: Uniform value for the temperature when solving temperature equation.
      
   .. literalinclude:: ../../../../examples/inputs/cht/solid_to_solid_fluid_cht.xml
      :language: xml
      :linenos:
      :lines: 171-177
      :caption: Set laminar flow initial conditions (parabolic velocity profile) and uniform temperature.

.. dropdown:: <Taylor Green Vortex>
   :icon: multi-select
   :color: primary
   :animate: fade-in-slide-down

   .. note::

      The Taylor-Green-Vortex problem initializes the pressure and velocity components with sinusoidal functions.

   .. py:data:: Type

      :type: string
      :value: IncompressibleTaylorGreenVortex
      :usage: Required
      :description: Initialize the Navier-Stokes equations with the Taylor-Green-Vortex.

   .. literalinclude:: ../../../../examples/inputs/incompressible/incompressible_2d_taylor_green_vortex.xml
      :language: xml
      :linenos:
      :lines: 69-71
      :caption: Initialize the velocity and the pressure for the Taylor-Green-Vortex problem.

.. dropdown:: <Turbulent Channel>
   :icon: multi-select
   :color: primary
   :animate: fade-in-slide-down

   .. note::

      The turbulent channel assumes a flow in the x-direction. The wall boundaries are perpandicular to the y-direction and periodic boundaries are assumed in the z-direction.

   .. py:data:: Type

      :type: string
      :value: IncompressibleTurbulentChannel
      :usage: Required
      :description: Initialize a turbulent flow in a 3-D channel.

   .. py:data:: Kinematic Viscosity

      :type: double
      :value: :math:`[0;\infty]`
      :usage: Required
      :description: Kinematic viscosity of the turbulent flow.

   .. py:data:: Half Width

      :type: double
      :value: :math:`[0;\infty]`
      :usage: Required
      :description: Half-width of the turbulent channel (y-direction).

   .. py:data:: Friction Reynolds Number

      :type: double
      :value: :math:`[0;\infty]`
      :usage: Required
      :description: Targeted friction Reynolds number.

   .. py:data:: Lx

      :type: double
      :value: :math:`[0;\infty]`
      :usage: Required
      :description: Geometry dimension in the x-direction/flow direction.

   .. py:data:: Ly

      :type: double
      :value: :math:`[0;\infty]`
      :usage: Required
      :description: Geometry dimension in the y-direction/spanwise direction.

   .. py:data:: LNumber of M

      :type: int
      :value: :math:`[0;\infty]`
      :usage: Optional
      :default: 3
      :description: Number of modes used to generate the turbulent initial conditions.

   .. py:data:: Add Random Perturbations

      :type: bool
      :value: true, false
      :usage: Optional
      :default: false
      :description: Add random perturbations to the initial turbulent flow.

   .. py:data:: Temperature

      :type: double
      :value: :math:`[0;\infty]`
      :usage: Optional
      :description: Initial value for the temperature. Required when solving for the temperature equation.

   .. literalinclude:: ../../../../examples/inputs/incompressible/incompressible_3d_wale_channel_re_tau_180.xml
      :language: xml
      :linenos:
      :lines: 133-141
      :caption: Initial conditions for a turbulent channel flow.

.. dropdown:: <Circle initial condition>
   :icon: multi-select
   :color: primary
   :animate: fade-in-slide-down

   .. py:data:: Type

      :type: string
      :value: Circle
      :usage: Required
      :description: Define a circle/sphere step condition for the variable defined in Equation Set Name.

   .. py:data:: Equation Set Name

      :type: string
      :value: Variable name
      :usage: Required
      :description: Variable name to initialize (should be the same name as defined in the source code).

   .. py:data:: Inside Value

      :type: double
      :value: :math:`[-\infty;\infty]`
      :usage: Required
      :description: Value inside the circle/sphere to initialize the variation set in Equation Set Name with.

   .. py:data:: Outside Value

      :type: double
      :value: :math:`[-\infty;\infty]`
      :usage: Required
      :description: Value outside the circle/sphere to initialize the variation set in Equation Set Name with.

   .. py:data:: Radius

      :type: double
      :value: :math:`[0;\infty]`
      :usage: Required
      :description: Radius of the circle/sphere.

   .. py:data:: Center

      :type: Array(double)
      :value: :math:`[-\infty;\infty]`
      :usage: Required
      :description: Coordiantes of the center of the circle/sphere.

.. dropdown:: <Sinusoidal initial condition>
   :icon: multi-select
   :color: primary
   :animate: fade-in-slide-down

   .. py:data:: Type

      :type: string
      :value: Sinusoidal
      :usage: Required
      :description: Define a sinusoidal initial condition for the variable defined in Equation Set Name of the type :math:`A \sin(|\vec{x}| + \phi)`.

   .. py:data:: Equation Set Name

      :type: string
      :value: Variable name
      :usage: Required
      :description: Variable name to initialize (should be the same name as defined in the source code).

   .. py:data:: Amplitude

      :type: double
      :value: :math:`[0;\infty]`
      :usage: Required
      :description: Value of the amplitude :math:`A` multiplying the sinusoidal function.

   .. py:data:: Phase Angle

      :type: double
      :value: :math:`[-\infty;\infty]`
      :usage: Required
      :description: Phase angle :math:`\phi`.

.. dropdown:: <Step initial condition>
   :icon: multi-select
   :color: primary
   :animate: fade-in-slide-down

   .. py:data:: Type

      :type: string
      :value: Step
      :usage: Required
      :description: Specific a step initial condition with left and right values separated by an axis/plane perpandicular to the x-axis.

   .. py:data:: Equation Set Name

      :type: string
      :value: Variable name
      :usage: Required
      :description: Variable name to initialize (should be the same name as defined in the source code).

   .. py:data:: Origin

      :type: double
      :value: :math:`[-\infty;\infty]`
      :usage: Required
      :description: x-coordinate of the axis/plane separating the left and right values.

   .. py:data:: Left Value

      :type: double
      :value: :math:`[-\infty;\infty]`
      :usage: Required
      :description: Left value to axis/plane specified by the `Origin` x-coordinate.

   .. py:data:: Right Value

      :type: double
      :value: :math:`[-\infty;\infty]`
      :usage: Required
      :description: Right value to axis/plane specified by the `Origin` x-coordinate.

.. dropdown:: <Gaussian initial condition>
   :icon: multi-select
   :color: primary
   :animate: fade-in-slide-down

   .. py:data:: Type

      :type: string
      :value: Gaussian
      :usage: Required
      :description: Gaussian profile with the following definition: :math:`d + \prod_{i=0}^{d} a_i \exp \left( (b_i - x_i ) (\frac{1}{2\sigma^2} - x_i) \right)`

   .. py:data:: Equation Set Name

      :type: string
      :value: Variable name
      :usage: Required
      :description: Variable name to initialize (should be the same name as defined in the source code).

   .. py:data:: Center

      :type: Array(double)
      :value: :math:`[-\infty;\infty]`
      :usage: Required
      :description: Speficy :math:`\vec{b}`.

   .. py:data:: Sigma

      :type: Array(double)
      :value: :math:`[-\infty;\infty]`
      :usage: Required
      :description: Speficy :math:`\vec{\sigma}`.

   .. py:data:: Base

      :type: Array(double)
      :value: :math:`[-\infty;\infty]`
      :usage: Required
      :description: Speficy :math:`d`.

   .. py:data:: Scaling

      :type: string
      :value: scaled, unscaled
      :usage: Optional
      :default: unscaled
      :description: Scaling factor multiplying the Gaussian function. If `unscaled` is specified, the scaling is defaulted to :math:`\sqrt(2\pi) \sigma`.

   .. py:data:: Scale

      :type: Array(double)
      :value: :math:`[-\infty;\infty]`
      :usage: Optional if `Scaling` is set to `unscaled`.
      :default: :math:`\sqrt(2\pi) \sigma`
      :description: Scaling to use when `Scaling` is set to `scaled`.

   .. literalinclude:: ../../../../examples/inputs/rad/rad_2d_reaction_advection_diffusion.xml
      :language: xml
      :lines: 67-75
      :caption: Gaussian initial conditions used in a Vertex-RAD input file.

.. dropdown:: <Inverse Gaussian initial condition>
   :icon: multi-select
   :color: primary
   :animate: fade-in-slide-down

   .. py:data:: Type

      :type: string
      :value: InverseGaussian
      :usage: Required
      :description: Gaussian profile with the following definition: :math:`\frac{1}{d + \prod_{i=0}^{d} a_i \exp \left( (b_i - x_i ) (\frac{1}{2\sigma^2} - x_i) \right)}`

   .. py:data:: Equation Set Name

      :type: string
      :value: Variable name
      :usage: Required
      :description: Variable name to initialize (should be the same name as defined in the source code).

   .. py:data:: Center

      :type: Array(double)
      :value: :math:`[-\infty;\infty]`
      :usage: Required
      :description: Speficy :math:`\vec{b}`.

   .. py:data:: Sigma

      :type: Array(double)
      :value: :math:`[-\infty;\infty]`
      :usage: Required
      :description: Speficy :math:`\vec{\sigma}`.

   .. py:data:: Base

      :type: Array(double)
      :value: :math:`[-\infty;\infty]`
      :usage: Required
      :description: Speficy :math:`d`.

   .. py:data:: Scaling

      :type: string
      :value: scaled, unscaled
      :usage: Optional
      :default: unscaled
      :description: Scaling factor multiplying the Gaussian function. If `unscaled` is specified, the scaling is defaulted to :math:`\sqrt(2\pi) \sigma`.

   .. py:data:: Scale

      :type: Array(double)
      :value: :math:`[-\infty;\infty]`
      :usage: Optional if `Scaling` is set to `unscaled`.
      :default: :math:`\sqrt(2\pi) \sigma`
      :description: Scaling to use when `Scaling` is set to `scaled`.