===== 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/
              

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===== Definition of the data set =====
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==== 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

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===== IMPORTANT NOTE =====
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<WRAP important>
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 [[sunfluidh:fluid_properties_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 [[sunfluidh:temperature_initialization_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 [[sunfluidh:fluid_properties_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.
</WRAP>