# 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.

Note: A detailed list of the predefined spatial quantities available for each physical application is presented in the paragraph concerning the analysis of results of activated physical application.

## 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.

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.

Note: For a calculation of the integral carried out "indirectly", the sensor associated must be evaluated and then its result must be created so that the calculation be stored in Result. These two operations to be carried out are described in the section Management of sensors