boundary

This section describes the input file definition used to prescribe boundary conditions in TOSCA. TOSCA expects a file for each solved field, where boundary and initial conditions are specified. Pressure boundary conditions are not required, as they are always of the Neumann type except when periodicity is present. Therefore, boundary conditions are expected for U (velocity) and nut (turbulent viscosity) fields, as well as for T (potential temperature), when this is activated in the control.dat file. Specifically, TOSCA expects to find U, nut and T (if applicable) files, inside a directory named boundary. Within each file, boundary conditions have to be specified for each side of the domain. These are identified as kLeft, kRight, jLeft, jRight, iLeft and iRight. In addition, the keyword internalField has to be specified, which sets the type of initial condition for each of these fields. An example of a boundary/U file is given below:

# TOSCA Input file - U boundary conditions
# ----------------------------------------

internalField spreadInflow

iLeft   periodic
iRight  periodic
jLeft   noSlip
jRight  slip
kLeft   fixedValue (5.0 0.0 0.0)
kRight  zeroGradient

In addition to common boundary conditions, which are available at all boundaries, TOSCA also features some special boundary conditions, which are only available on specific boundaries. These are used for specific simulations, the user is suggested to consider such constraint when designing and setting up a TOSCA case.

Boundary Conditions

The boundary conditions available in TOSCA are summarized in the following table. The table also specifies the fields for which a given boundary condition is available, together with their entry type and description.

BC type	entry type	description
fixedValue	scalar or vector	Available for U, nut and T.
fixedGradient	scalar	Available for T. Entry is a scalar value that refers to the gradient normal to the patch.
zeroGradient	none	Available for U, nut and T.
slip	none	Available for U.
noSlip	none	Available for U.
periodic	none	Available for U, nut and T. Requires keywords -iPeriodicType, -jPeriodicType, -kPeriodicType at the top of the mesh file, depending on the patch to which it is applied. These should be placed in the header, before the number of points in each direction, and indicate the type of parallel connectivity between the periodic boundaries. For type 1, the domain is decomposed such that periodic cell-pairs lie within the same processor. Type 2 allows for a more general decomposition (suggested).
velocityWallFunction	dictionary	Available only for U. Applies wall models to velocity. Only available for iLeft, iRight, jLeft and jRight patches. Not really tested on i-patches. It is usually applied on the jLeft patch in combination with an inletFunction on the kLeft patch.
thetaWallFunction	dictionary	Available only for T. Applies wall models to temperature. Only available for iLeft, iRight, jLeft and jRight patches. Not really tested on i-patches. It is usually applied on the jLeft patch in combination with an inletFunction on the kLeft patch.
inletFunction	dictionary	Available for U, nut and T only at the kLeft patch.

The last three boundary conditions listed in the previous table are not available on all patches. On the one hand, the velocityWallFunction and thetaWallFunction, used to prescribe wall models, are not available on kLeft and kRight boundaries, plus at additional boundaries, depending on the wall model type, as detailed below. On the other hand, the inletFunction type, used to prescribe special inlet boundary conditions for inlet velocity, temperature and turbulent viscosity, is only available on the kLeft patch. The user should keep this constraint in mind when setting up a TOSCA case.

Wall Functions

The velocityWallFunction applies the Shumann wall model, used for ABL flows, or the Cabot wall model, used for wall surfaces, to the velocoty field. In the Shumann model, the modeled wall shear stress is directly enforced in the stress term of the momentum equations, while a constant normal gradient condition is applied to the velocity. In order to avoid double counting at the wall when using this condition (the wall shear stress should be entirely and only modeled), the turbulent viscosity at the wall should be set to zero in the boundary/nut file. Entries for velocity wall functions are summarized in the folllwing table:

WF type	name	description
-1	Cabot wall model	Available at jLeft, jRight, iLeft and iRight patches. Mostly tested for the first two. Usage: velocityWallFunction { type -1 kRough 0.003 // equivalent roughness length }
-3	Shumann wall model	Available at jLeft, jRight, iLeft and iRight patches. Mostly tested for the first two. Usage: velocityWallFunction { type -3 kRough 0.003 // equivalent roughness length gammaM 4.9 // Shumann model constant kappa 0.4 // von Karman constant thetaRef 300.0 // reference potential // temperature in Kelvin uStarEval averaged // for laterally homogeneous // flows (e.g. ABL), otherwise // set to 'localized' (e.g. // wind farm flows) }

The thetaWallFunction is used to select different formulations of the Shumann wall model for potential temperature. In particular, the modeled heat flux is directly enforced in the stress term of the potential temperature equations, while a zero normal gradient condition is applied to the temperature field. In order to avoid double counting at the wall when using this condition, the turbulent viscosity at the wall should be set to zero in the boundary/nut file. Entries for temperature wall functions are summarized in the folllwing table:

WF type	name	description
-3	Shumann wall model, standard.	Only available at jLeft and jRight patches. Usage: thetaWallFunction { type -3 kRough 0.003 // equivalent roughness length gammaM 4.9 // Shumann model constant gammaH 7.8 // Shumann model constant alphaH 1.0 // Shumann model constant kappa 0.4 // von Karman constant thetaRef 300.0 // reference potential // temperature in Kelvin uStarEval averaged // for laterally homogeneous // flows (e.g. ABL), otherwise // set to 'localized' (e.g. // wind farm flows) heatingRate -0.00014 // K/s }
-2	Shumann wall model, with specified heat flux.	Only available at jLeft patch. Usage: thetaWallFunction { type -2 qWall 0.003 // wall heat flux in J/m2 }
-4	Shumann wall model, with specified time history of surface temperature and Obhukhov length.	Only available at jLeft patch. Usage: thetaWallFunction { type -4 kRough 0.003 // equivalent roughness length gammaM 4.9 // Shumann model constant gammaH 7.8 // Shumann model constant alphaH 1.0 // Shumann model constant kappa 0.4 // von Karman constant // temperature in Kelvin uStarEval averaged // for laterally homogeneous // flows (e.g. ABL), otherwise // set to 'localized' (e.g. // wind farm flows) } Look up tables of time (s), surface temperature (K), and Obhukhov length (m), stored in inflowDatabase/mesoscaleData/time, inflowDatabase/mesoscaleData/surfTemp and inflowDatabase/mesoscaleData/L, respectively. All vectors should have same size.

Inlet Functions

The inletFunction boundary condition has several different types, each corresponding to a different inlet boundary condition. These are summarized in the following table:

IF type	name	description
1	power law profile	Power law velocity profile \(\mathbf{U}= \mathbf{U}_\text{ref}\left(z/H_\text{ref}\right) ^\alpha\), with \(\alpha=0.107027\). Usage: inletFunction { type 1 Uref vector Href scalar uPrimeRMS scalar }
2	logarithmic profile	Logarithmic velocity profile \(\mathbf{U}= u*/0.4\ln(z/z_0)\mathbf{e}_U\). \(\mathbf{U}\) is constant above the inversion height \(H\) and equal to \(\mathbf{U}(H)\). Usage: inletFunction { type 2 directionU vector hInversion scalar frictionU scalar kRough scalar }
3	unsteady mapped inflow	Maps 2D planes contained in inflowDatabase directory at the inlet. Planes can be tiled laterally or vertically. Data can also be extrapolated in the vertical direction. The extrapolated value can be unsteady or steady. The latter is calculated by averaging the top data contained in the 2D planes and slowly merging with the unsteady data within the last 10 cells of the 2D plane. Note: 2D planes and inlet mesh should be identical as data is only mapped. Usage: inletFunction { type 3 n1Inflow integer n2Inflow integer n1Periods integer n2Periods integer n1Merge bool }
4	unsteady interpolated inflow	Same as type 3, but data is interpolated, hence the 2D plane mesh and inlet mesh can be different. Spanwise shift of the inflow data is also available by setting a lateral shift velocity. Note that this velocity is not added to the flow velocity, but rather data are shifted with this constant lateral velocity. Usage: inletFunction { type 4 n1Inflow integer n2Inflow integer n1Periods integer n2Periods integer n1Merge bool n2Shift bool shiftSpeed scalar sourceType string cellWidth1 integer cellWidth2 integer }
5	Nieuwstadt (1983) model	Applies the Nieuwstadt (1983) model. This is more sophisticated than the logarithmic profile, as it also contains wind veer. The wind profile is rotated such that the prescribed direction is imposed at the prescribed reference height. Usage: inletFunction { type 5 directionU vector hInversion scalar hReference scalar frictionU scalar kRough scalar latitude scalar }
6	sinusoidally varying i-th component	Uniform inflow, where the spanwise component varies sinusoidally with given amplitude and frequency. Useful to test turbine yaw controllers. Usage: inletFunction { type 6 Uref vector amplitude scalar periods scalar }

The different entries required in the inletFunction dictionary for each function type are detailed below:

entry	entry type	description
type 1 - power law profile
Uref	vector	reference velocity in m/s
Href	scalar	height where \(\mathbf{U}= \mathbf{U}_\text{ref}\) in m
uPrimeRMS	scalar	isotropic fluctuation value in m/s
type 2 - logarithmic profile
directionU	vector	velocity direction (will be normalized)
hInversion	scalar	inversion height in m
frictionU	scalar	friction velocity in m/s
kRough	scalar	equivalent roughness length in m
type 3 - unsteady mapped inflow
n1Inflow	integer	number of points in direction 1 (j for kLeft patch)
n2Inflow	integer	number of points in direction 2 (i for kLeft patch)
n1Periods	integer	number of points in direction 1 for tiling (if target is larger data is extrapolated)
n2Periods	integer	number of points in direction 2 for tiling (if target is larger data is extrapolated)
n1Merge	bool	average top cell values from 2D planes and merge within 10 top cells. Useful to make the geostrophic region steady, removing e.g. inertial oscillations.
type 4 - unsteady interpolated inflow
n1Inflow	integer	number of points in direction 1 (j for kLeft patch)
n2Inflow	integer	number of points in direction 2 (i for kLeft patch)
n1Periods	integer	number of periods in direction 1 for tiling. If target is larger data is extrapolated.
n2Periods	integer	number of periods in direction 2 for tiling. If target is larger data is extrapolated.
n1Merge	bool	if set to 1 averages top-most cell from 2D planes and merges it with the unsteady data smoothly within the 10 top-most cells of the target mesh. It ensures that the extrapolated data is precisely steady.
n2Shift	bool	spanwise shift of inflow data
shiftSpeed	scalar	spanwise shift velocity in m/s
sourceType	string	uniform (requires next two entries) or grading (requires the mesh file used in the simulation that generated the 2D planes, renamed inflowMesh.xyz to be located inside the inflowDatabase directory)
cellWidth1	integer	inflow mesh cell width in direction 1 if sourceType uniform
cellWidth2	integer	inflow mesh cell width in direction 2 if sourceType uniform
type 5 - Nieuwstadt (1983) model
directionU	vector	velocity direction (will be normalized)
hInversion	scalar	inversion height in m
hReference	scalar	reference height in m at which the wind has the provided direction
frictionU	scalar	friction velocity in m/s
hRough	scalar	equivalent roughness length in m
latitude	scalar	latitude in degrees
type 6 - sinusoidally varying i-th component
Uref	vector	reference velocity in m/s
amplitude	scalar	amplitude of the spanwise velocity oscillation in m/s
periods	scalar	number of periods contained in the domain length along the i curvilinear direction

As an example, a logarithmic profile on the kLeft patch is prescribed as follows

kLeft inletFunction
      {
         type        2             // type 2 is logarithmic profile
         directionU  (1.0 0.0 0.0) // velocity is along the x direction
         hInversion  500           // ABL height is 500 m
         frictionU   0.5           // friction velocity is 0.5 m/s
         kRough      0.001         // equivalent roughness lenght is 0.001 m
      }

Initial Condition

The initial field is finally prescribed after the internalField keyword within each boundary condition file. Initial conditions available within TOSCA are summarized in the following table:

initial condition type	description
uniform	Available for U, nu, T. The value entry can be vector or scalar. If the perturbations entry is set to 1, sinusoidal perturbations are applied to trigger turbulence (only required for U field) Usage: uniform { value vector or scalar perturbations bool }
readField	Available for U, nu, T. Reads field data from the fields directory. Used for simulation restart.
ABLFlow	Sets initial log profile for U, while T is set according to the Rampanelli and Zardi (2003) model. Requires -abl set to 1 in the control.dat file, as it picks input parameters from the ABLProperties.dat file. Perturbations to trigger turbulence can be added using the perturbations entry in the ABLProperties.dat file.
spreadInflow	Copies the flow from the kLeft ghost cells at every k-plane. Useful for ensuring perfect consistency between the inlet boundary condition and the internal field when using inletFunction. In practice, sets the internal field to whatever the inletFunction is.
linear	Only available for T. Sets an initial temperature profile characterized by a linear lapse rate tLapse along j and a ground temperature tRef. Used to prescribe an initially-linear potential temperature stratification. Usage: linear { tRef scalar tLapse scalar }