VDF
===

The Finite Volume Difference (VDF) discretization (class ``VDF_discretisation`` and alias ``VDF``) is the simplest and most efficient discretization of the TRUST platform. This discretization is compatible with conform mesh with hexahedral type of elements. Attention: do not confuse between a hexahedral mesh and a cartesian mesh. The VDF mesh is not structured and does not follow the IJK indexing!

As stated by its name, the VDF is a conservative finite volume scheme of Marker-and-Cell (MAC) type, :cite:p:`HW65`. The discretization of each term of the equation is performed by integrating over a control volume. The diffusion gradient terms are approximated by a linear difference equation. All scalars are stored at the center of each control volume except the velocity field which is defined on a staggered mesh.

This discretization **supports** 2D axi-symmetrical configurations and **is compatible** with ``Pb_Multiphase``.


.. figure:: ./FIGURES/VDF-cut.png
   :name: fig:scheme-vdf
   :align: center
   :width: 600px
   :alt: Grille décalée VDF 2D avec description détaillée
   
   Scheme of a VDF grid: scalars are stored at the center of the elements and normal component of the vorticities at the faces of the element