Scalar

The scalar object allows to add a scalar transport equation to the solution. The solution variable is called s by default, but can be controlled by the field_name entry in the case file. In the fld files, it is saved as temperature. Some properties of the object are inherited from fluid: the value of the density, and the output control.

Material properties

The scalar equation requires defining additional material properties: the specific heat capacity and thermal conductivity. These are provided as cp and lambda. Similarly to the fluid, one can provide the Peclet number, Pe, as an alternative. In this case, cp is set to 1 and lambda to the inverse of Pe.

Different from the setup in the fluid, turbulence modelling is enabled by setting the alphat json entry.

Turbulence modelling

The user could choose to either relate the eddy diffusivity field to the eddy viscosity field in the Fluid, or model the eddy diffusivity field by some particular SGS models, by setting up the nut_dependency entry. If the eddy diffusivity field is associated to the eddy viscosity field by a coefficient Pr_t, the eddy viscosity values will be divided by it to produce eddy diffusivity. And the corresponding setting could be done by the following:

{
  "alphat": {
    "nut_dependency": true,
    "nut_field": "nut",
    "Pr_t": 0.7
  }
}

Otherwise one could have some SGS models providing an eddy diffusivity field, and the user could set it up by the following manner to include an eddy diffusivity field called temperature_alphat:

{
  "alphat": {
    "nut_dependency": false,
    "alphat_field": "temperature_alphat"
  }
}

Boundary conditions

The boundary conditions for the scalar are specified through the boundary_conditions keyword, which follows the same format as the fluid, for specifying the type of the condition and where it is applied. The following types of conditions are available for the scalar:

• dirichlet. Sets the value of the scalar, controlled by the value keyword.

  {
    "type": "dirichlet",
    "value": 1,
    "zone_indices": [1, 2]
  }

• expression_dirichlet. Sets the value of the scalar from a mathematical expression, given as a string under the value keyword. See expressions for the syntax.

  {
    "type": "expression_dirichlet",
    "value": "T_wall + dT*tanh((x - x0)/L)",
    "zone_indices": [1, 2]
  }

• neumann. Sets the flux of the scalar, controlled by the flux keyword.

  {
    "type": "neumann",
    "flux": 1,
    "zone_indices": [1, 2]
  }

• user_dirichlet. User-updated Dirichlet boundary condition, see the user-file documentation.

  {
    "type": "user_dirichlet",
    "zone_indices": [1, 2]
  }

• user_neumann. User-updated Neumann boundary condition, see the user-file documentation.

  {
    "type": "user_neumann",
    "zone_indices": [1, 2]
  }

• user_neumann. User-defined scalar flux, configured through the user-file Neumann callback.

  {
    "type": "user_neumann",
    "zone_indices": [1, 2]
  }

• overset_interface. Retrieves scalar Dirichlet data from another concurrent Neko simulation on an overlapping domain. It accepts name, order, relaxation, interpolation.tolerance, interpolation.padding, and log with the same meanings and defaults as the fluid overset interface. The first IEXT update of each physical timestep is unrelaxed; relaxation is applied only if the boundary is updated again at the same timestep.

  {
    "type": "overset_interface",
    "zone_indices": [1, 2],
    "order": 3,
    "relaxation": 0.7,
    "interpolation": {
      "tolerance": 1.0e-8,
      "padding": 0.01
    },
    "log": false
  }

Initial conditions

The object initial_condition is used to provide initial conditions. It is mandatory. The means of prescribing the values are controlled via the type keyword:

1. user, the values are set inside the compiled user file as explained in the user defined initial condition section of the user file documentation.
2. uniform, the value is a constant scalar, looked up under the value keyword.
3. expression, the value keyword holds a single string, a mathematical expression prescribing the initial value. See expressions for the syntax. For example

   {
     "type": "expression",
     "value": "T_hot + dT*tanh((z - z0)/L)"
   }

4. point_zone, the values are set to a constant base value, supplied under the base_value keyword, and then assigned a zone value inside a point zone. The point zone is specified by the zone_name keyword, and should be defined in the case.point_zones object. See more about point zones.
5. field, where the initial condition is retrieved from a field file. Works in the same way as for the fluid. See the fluid section for detailed explanations.

Source terms

The configuration of source terms is the same as for the fluid. A demonstration of using source terms for the scalar can be found in the scalar_mms example.

Linear solver configuration

Should be provided as an object under the solver keyword. For available configuration options, see the corresponding documentation for the fliud. A standard choice would be "type": "cg" and "preconditioner": "jacobi".

Full parameter table

Name	Description	Admissible values	Default value
enabled	Whether to enable the scalar computation.	true or false	true
name	The name associated to the scalar solver.	String	scalar
field_name	The name of the solution in the field registry.	A string	s
Pe	The Peclet number.	Positive real	-
cp	Specific heat capacity.	Positive real	-
lambda	Thermal conductivity.	Positive real	-
alphat.nut_dependency	Whether the eddy diffusivity depends on the eddy kinematic viscosity.	true or false	-
alphat.alphat_field	Name of the turbulent diffusivity field.	String	Empty string
alphat.nut_field	Name of the turbulent kinematic viscosity field.	String	Empty string
alphat.Pr_t	Turbulent Prandtl number	Positive real	-
boundary_types	Boundary types/conditions labels.	Array of strings	-
initial_condition.type	Initial condition type.	user, uniform, expression, point_zone, field	-
initial_condition.value	Value of the scalar initial condition.	Real, or a string if "type" = "expression"	-
source_terms	Array of JSON objects, defining additional source terms.	See list of source terms above	-
gradient_jump_penalty	Array of JSON objects, defining additional gradient jump penalty.	See list of gradient jump penalty above	-
advection	Whether to compute the advetion term.	true or false	true
solver.type	Linear solver for scalar equation.	cg, pipecg, bicgstab, cacg, gmres	-
solver.preconditioner.type	Linear solver preconditioner for the momentum equation.	ident, hsmg, jacobi	-
solver.absolute_tolerance	Linear solver convergence criterion for the momentum equation.	Positive real	-
solver.max_iterations	Linear solver max iteration count for the scalar equation.	Positive integer	1000
solver.space_size	Krylov space size of gmres for the scalar equation.	Positive integer	30
solver.projection_space_size	Projection space size for the scalar equation.	Positive integer	0
solver.projection_hold_steps	Holding steps of the projection for the scalar equation.	Positive integer	5