Computation of integral
Definition: reminder
The computation of integral enables the user to interactively integrate a spatial quantity on a part or on the entire study domain.
Use
The integral calculation can be carried out in two ways:
- directly: by means of the command Integral of a spatial quantity in the Advanced menu
- indirectly: by using a sensor
Computation of integral (1)
To compute an integral, the user must define: a type of support, a type of integral, a spatial quantity or a formula to be integrated.
The types of integral as function of the support are presented in the table below. (See as well the complete table in the block below).
| Type of support | Type of integral | ||
|---|---|---|---|
| volume | face | line | |
| Entire domain | volume | ||
| Volume / Volume region / 3D grid | volume | contour | |
| Face / Face region / 2D grid | face | ||
| Line / Line region / etc. | line | ||
The formula is the formula with spatial quantities.
About supports
The types of support associated to the type of integral, are presented in detail in the table below.
| Type of integral | Type of support | Comment |
|---|---|---|
| Integral on the entire domain | ||
| Volume integral |
Volume regions Volumes |
|
| Face integral |
Faces associated with a region1 Faces of face regions 2 Face regions 2D grid |
1 = faces selected by the user after selecting a face region 2 = set of the faces of a face region |
|
Inner border of volume regions Outer border of volume regions Inner border of volumes Outer border of volumes |
||
| Line integral |
Lines associated with a region 3 Lines of line regions 4 Line region Path |
3 = lines selected by the user after selecting a line region 4 = set of the lines of a line region |
To compute an integral on a face or line support, it is necessary for Flux to identify to which physical region belongs a support of integration.
Indeed, physical properties (permeability…) and a formulation are associated with each region in Flux. If the support is in an interface between two regions, computation will be different due to the chosen side of this interface, so it is necessary to know the region of computation.
This is why, it is necessary:
- to choose a region to select lines or faces
- to specify if one is interested in an inner or outer border (quantities “viewed” from the interior of the border or from its exterior)
Computation of integral and IB
To compute on the entire domain:
if there is an infinite box, then the computation takes it into account, the quantities are computed “to the infinity”.
Computation of integral and symmetries / periodicities
In the presence of symmetries/periodicities:
- computations are performed for the part of the device represented in the computation domain
- when a part of the border is on a symmetry plane and the quantity is viewed from the exterior, integration on this part is ignored.
Storage
An integral calculation is stored under the shape of an entity in the tree of the general data in the entity type Result of calculation under the root of the Postprocessing directory.