# Documentation du code de simulation numérique SUNFLUIDH

## Web LIMSI

sunfluidh:gravity_namelist

## Namelist "Gravity"

This data set is related to the characteristics of the gravity force.
If no gravitational effect is considered, this namelist can be omitted.

## Full data set of the namelist

&Gravity  Gravity_Enabled= .true. ,
Gravity_Angle_IJ= 0.0   ,
Gravity_Angle_IK= 90.0  ,
Reference_Gravity_Constant= 9.81D+00/

## Definition of the data set

### Gravity_Enabled

• Type : boolean value
• The gravity effects are enabled or disabled
• Default value= .false.

### Gravity_Angle_IJ

• Type : real value
• Angle between the I-axis and of the projection of $-\vec{G}$ on the IJ-plan (in degrees). The I-axis is the origin axis.
• Default value = 0.0

### Gravity_Angle_IK

• Type : real value
• angle between the K-axis and $-\vec{G}$ (in degrees). The K-axis is the origin axis.
• Default value = 0.0

### Reference_Gravity_Constant

• Type : real value
• Reference value of the gravity constant
• Default value = 9.81

## IMPORTANT NOTE

The orientation of the gravity vector $\vec{g}$ in the cartesian referential $(\vec{I},\vec{J},\vec{K})$ is defined from the below formulation (spherical coordinates) : $$G_I= -G_0.cos(\text{Gravity_Angle_IJ}).sin(\text{Gravity_Angle_IK})$$ $$G_J= -G_0.sin(\text{Gravity_Angle_IJ}).sin(\text{Gravity_Angle_IK})$$ $$G_K= -G_0.cos(\text{Gravity_Angle_IK})$$

Where $G_0$ is norm of the force of gravity (or the buoyancy force).

Remarks

• The angle ranges are $-90 \le$ Gravity_Angle_IJ $\le +90$ and $0 \le$ Gravity_Angle_IK $\le +180$.
• From the definition of angles, note that the vector $\vec{g}$ is oriented along the $-\vec{K}$ axis while Gravity_Angle_IK= 0 and $\vec{g}$ is in the plan IJ while Gravity_Angle_IK= 90.

Following the type of simulation and the choice on the form of equations (dimensional, dimensionless, the scales used in order to define the non-dimensional form of equations, etc …), the term $G_0$ can be written following different ways. For instance, the buoyancy force can be read as : $$F_b= (\rho - \rho_0).g_0$$ in the momentum equations under Low Mach number hypothesis. In this case

• $G_O= g_0$ where $g_0$ is the constant of gravity.
• $\rho_0$ is the reference density defined in the namelist "Fluid_Properties".

The buoyancy force can also be read as : $$F_b= -\rho_0.\beta.g_0.(T - T_0)$$ in the momentum equations for incompressible flows under Boussinesq hypothesis. In this case

• $G_0= \beta.g_0$ where $\beta$ is the thermal expansion coefficient of the fluid considered.
• $T_0$ is the reference temperature defined in the namelist "Temperature_Initialization".

As a consequence the generalized form of $G_0$ in the code is : $$G_0= \beta.g_0$$ where $g_0$ is defined from the data “Reference_Gravity_Constant” and $\beta$ from the data “Thermal_Expansion_Coefficient” (in the namelist "Fluid_Properties" ).
The Default values of these variables are :

• Reference_Gravity_Constant= 9.81
• Thermal_Expansion_Coefficient = 1.0

These values are automatically taken into account by the code if these variables are not explicitly modified by the user in the data file.
Clearly, the variable “Thermal_Expansion_Coefficient” is only needed in the simulations of incompressible flows with thermal buoyancy effect .
In every other cases, it can be omitted because the buoyancy/gravity force can be defined from the variable “Reference_Gravity_Constant” only.

sunfluidh/gravity_namelist.txt · Dernière modification: 2019/08/01 09:27 de yann