### Table des matières

## Boundary conditions

The problem gets different type of boundary conditions :

- For the velocity :
- Common wall boundary conditions : No slip and impermeable boundary conditions
- Inflow boundary condition : uniform velocity profile imposed.
- Outflow boundary condition : mass flowrate conservation

- For the heat transfer :
- Wall boundary conditions : Temperature imposed
- Inflow boundary condition : Temperature imposed
- Outflow boundary condition : zero temperature gradient

### Wall boundary conditions

The walls are associated with two different immersed bodies:

- the domain ends which gets the top and bottom walls
- the step

The wall boundary conditions for the velocity are identical for every walls of the domain and they correspond to the wall boundary conditions stated by default in the code SUNFLUIH. As a consequence, they need not to be explicitly declared.

The wall temperature are however different according to the immersed bodies cited above ($T_c*=1$ for the bottom and the top walls, $T_h*=2$ for the step walls). We must define two sets of boundary conditions for the temperature.

*Set 1 (for the walls of domain ends)* : Only the data associated to the top (front) and bottom (back) walls are present, the other ones are useless as the corresponding walls are absent.

&Heat_Wall_Boundary_Condition_Setup Wall_BC_DataSetName ="Set1", Back_Heat_BC_Option = 0 , Front_Heat_BC_Option = 0 , !--- option value for temperature imposed Back_Heat_Function_Type = 0 , Front_Heat_Function_Type= 0 , !--- option value for defining a uniform value of T over the wall Back_Wall_BC_Value = 1.0 , Front_Wall_BC_Value = 1.0 / !--- temperature value (here Tc)

*Set 2 (for the walls of the step)*_ : Only the data associated to the top (noted back for immersed bodies) and right (noted west for immersed bodies) walls are present, the other ones are useless as the corresponding walls have no role in the current problem.

&Heat_Wall_Boundary_Condition_Setup Wall_BC_DataSetName ="Set2", Back_Heat_BC_Option = 0 , East_Heat_BC_Option = 0 , !--- option value for temperature imposed Back_Heat_Function_Type = 0 , East_Heat_Function_Type= 0 , !--- option value for defining a uniform value of T over the wall Back_Wall_BC_Value = 2.0 , East_Wall_BC_Value = 2.0 / !--- temperature value (here Tc)

We must now build the immersed bodies.

On the walls of the domain ends :

This is already made. Keep in mind that the computational domain is enclosed by default. Walls are automatically placed at the domain ends by the code except when other boundary conditions are specified by the user (which are going to replace the walls).

For building the step :

&Polyhedral_Immersed_Bodies Xi_1= 0.0 , Xj_1= 0.0 ,Xk_1= 0.0 , !--- Coordinates of the 1st corner Xi_2= 2.0 , Xj_2= 0.0 ,Xk_2= 0.0 , !--- Coordinates of the 2nd corner Xi_3= 2.0 , Xj_3= 1.0 ,Xk_3= 0.0 , !--- Coordinates of the 3rd corner Xi_4= 0.0 , Xj_4= 1.0 ,Xk_4= 0.0 , !--- Coordinates of the 4th corner Wall_BC_DataSetName ="Set2"/ !--- ID name associated to the suitable set of wall boundary conditions

- By default, the set of wall boundary conditions identified as “Wall_BC_DataSetName=Set1” is automatically associated to walls placed at the domain ends.
- For other immersed solid bodies, the variable “Wall_BC_DataSetName” links the body walls with the set of wall boundary conditions that have got the same name.
- For more information on the rules of construction Click here
- For more details on the data setup of the wall boundary conditions
- For more details on the data setup for building immersed solid bodies

Return to the page Tutorial : How to build the input data file ?

### Inlet boundary conditions

The inflow conditions are uniform profiles of velocity ($U_b=1$) and temperature ($T_c= 1$).

&Inlet_Boundary_Conditions Type_of_BC = "INLET", !--- Specify inflow conditions (mass flowrate and other physical quantities imposed) Direction_Normal_Plan = 1 , !--- Normal vector of the inlet plan oriented along the I-direction Plan_Location_Coordinate = 0.0 , !--- Position of the inlet along the normal direction Start_Coordinate_of_First_Span = 1.0 , !--- Start coordinate of the inlet along the direction related to the 1st span (here J-direction, just above the step) End_Coordinate_of_First_Span = 2.0 , !--- End coordinate of the inlet along the direction related to the 1st span (here J-direction, at the top wall) Start_Coordinate_of_Second_Span= 0.0 , !--- Start coordinate of the inlet along the direction related to the 2nd span (here K-direction) End_Coordinate_of_Second_Span = 0.0 , !--- End coordinate of the inlet along the direction related to the 1st span (here K-direction) Flow_Direction = 1 , !--- The flow is oriented along the increasing I-index Define_Velocity_profile = 0 , !--- Option value for a uniform velocity profile Normal_Velocity_Reference_Value= 1.0 , !--- Value of the normal velocity-component (here Ub= 1) , the other ones are null. Temperature_Reference_Value = 1.0 / !--- Value of the temperature (uniform distribution, here Tc= 1)

Return to the page Tutorial : How to build the input data file ?

### Outlet boundary conditions

We here select usual outflow boundary conditions based on the flowrate conservation for treating the normal velocity component. The outflow boundary conditions other physical quantities are zero gradient condition.

&Inlet_Boundary_Conditions Type_of_BC = "OUTLET", !--- Specify the outflow conditions cited above Direction_Normal_Plan = 1 , !--- Normal vector of the inlet plan oriented along the I-direction Plan_Location_Coordinate = 0.0 , !--- Position of the inlet along the normal direction Start_Coordinate_of_First_Span = 0.0 , !--- Start coordinate of the inlet along the direction related to the 1st span (here J-direction, at the floor wall) End_Coordinate_of_First_Span = 2.0 , !--- End coordinate of the inlet along the direction related to the 1st span (here J-direction, at the top wall) Start_Coordinate_of_Second_Span= 0.0 , !--- Start coordinate of the inlet along the direction related to the 2nd span (here K-direction) End_Coordinate_of_Second_Span = 0.0 , !--- End coordinate of the inlet along the direction related to the 1st span (here K-direction) Flow_Direction = 1 / !--- The outflow is mainly oriented along the increasing I-index

Return to the page Tutorial : How to build the input data file ?

### Border boundary condition

The boundary conditions related to our example are already specified (walls, inflow, outflow conditions). No more boundary conditions must be defined. The namelist “Border_Domain_Boundary_Conditions” is therefore not required :

&Border_Domain_Boundary_Conditions West_BC_Name = "None" , !--- Boundary conditions already defined for the left end of the domain (corresponding to the lower I-index) East_BC_Name = "None" , !--- Boundary conditions already defined for the right end of the domain (corresponding to the upper I-index) Back_BC_Name = "None" , !--- Boundary conditions already defined for the bottom end of the domain (corresponding to the lower J-index) Front_BC_Name= "None" / !--- Boundary conditions already defined for the top end of the domain (corresponding to the upper J-index)

- In this case, this namelist could be removed
- This dataset is used for specifying periodical or symmetrical boundary conditions at the domain ends. Click here for more details and here for other examples)

Return to the page Tutorial : How to build the input data file ?