Volumetric Integration

This option enables computation of overall integrated quantities for a specific volume. Several standard options are available and the user is permitted to define his/her own integrand to be evaluated in this section. However, the current implementation of these volumetric integrals is limited to generalized Newtonian fluids. Output is to a specified file.

Post Processing Volumetric Integration

Post Processing Volumetric Integration =

Description / Usage

This card indicates that the cards between this and an END OF VOLUME_INT card are to be read and processed. If this card (Post Processing Volumetric Integration) is not present, VOLUME_INT cards will be ignored.


There are no input parameters for this card, which always appears as follows:

Post Processing Volumetric Integration =

Technical Discussion

No Discussion.


No References.


VOLUME_INT = {volume_type} <blk_id> <species_no> <file_string> [float_list]

Description / Usage

The VOLUME_INT card activates computation of specified volumetric integrals during post processing. As many of these VOLUME_INT cards as desired can be input to Goma. Definitions of the input parameters are as follows:


Several choices of volumetric integral are allowed and are referenced through this parameter. The permissible values and corresponding volume integral follow:

  • VOLUME-Volume of the element block specified by <blk_id>.

  • DISSIPATION-Total viscous dissipation, \(\tau\): \(\Delta v\) , in the element block specified by <blk_id>.

  • JOULE-Total Joule or Ohmic heating, \(\frac{1}{\sigma}\) (\(\underline{J}\)\(\underline{J}\)) , in the element block specified by <blk_id>.

  • SPECIES_MASS-Integral of concentration of the component specified by <species_no> in the element block specified by < blk_id>.

  • MOMENTUMX, MOMENTUMY, or MOMENTUMZ-Integral of appropriate component of the momentum flux \(\rho\vec{v}\) over the element block <blk_id>.

  • STRESS_TRACE-Integral of the trace of the complete stress tensor (-\(p\zeta + \tau\)) over the element block blk_id.

  • HEAT_ENERGY-Integral of the sensible heat over <blk_id> ( not currently implemented).

  • POSITIVE_FILL, NEGATIVE_FILL-Volume integral of region occupied by positive (negative) values of the FILL variable in element block < blk_id>. Note, for either of these cards, [float_list] is required. NOTE for Level-Set users: There are numerous other quantities (too-lengthy and esoteric to list here) that can be integraded vis-a-vis level set fields. Please see code.

  • NEGATIVE_VX, NEGATIVE_VY, NEGATIVE_VZ-Velocity integral in one of the three directions over just the region occupied by negative values of the FILL variable in level set problems. Note, for any of these cards, the [float_list] is required.

  • POROUS_LIQ_INVENTORY-Volume integral of bulk liquid component density (gas and liquid phase) in a porous medium. Result is a total inventory of liquid in the porous phase.

  • SPEED_SQUARED-Volume integral of the square of the speed, viz. \(\underline{v}\)\(\underline{v}\) . Used to measure norm of fluid kinetic energy level. Should tend to zero for a fluid at rest.

  • USER-Volume integral is supplied by the user (not currently implemented).

  • SURFACE_SPECIES-Generate locus of points which correspond to a surface of constant species concentration according to \(Ac_1\) + \(Bc_2\) + \(Cc_3\) + D=0. Currently only implemented for 3D linear elements.

  • LUB_LOAD-“Volume integral” of lubrication pressure over entire mesh shell block, which is useful for computing the overall lubrication load. This is actually an area integral over the shell, thereby yielding a force.

  • ELOADX; ELOADY; ELOADZ-Volume integral of electric field or the gradient of the electric potential for electrostatic problems.

  • RATE_OF_DEF_II-Volume integral of the second invariant of the rate-of-deformation tensor.


The element block id for which the volume integral is requested.


The species number for SPECIES_MASS volume integral.


A character string that corresponds to the name of the text file that will receive the results of the integration at each time step.


A floating point value that specifies the length scale of the smooth Heaviside function. This parameter is only used for VOLUME_INT cards in which the {volume_type} is {POSITIVE|NEGATIVE} _FILL or NEGATIVE_V{X|Y|Z}. The float list is also used for the constants A, B, C, etc in the SURFACE_SPECIES type.


Here is an example of an input deck with 3 VOLUME_INT cards.

Post Processing Volumetric Integration =
VOLUME_INT = VOLUME 1 0 volume.out
VOLUME_INT = SPECIES_MASS 2 3 species3.out
VOLUME_INT = NEGATIVE_FILL 1 0 fill.out 0.1

Technical Discussion

The volume integrations are carried out as follows:


volume integral


\(\int\) dV


\(\int\) (-p \(\zeta + \tau\)) • \(\Delta\) vdV


\(\int\) \(\frac{1}{\sigma}\) J • JdV


\(\int\) \(c_jdV\)


\(\int\) \(\rho\) (i|j|k) • vdV


\(\int\) tr(-p \(\zeta + \tau\)) dV


\(\int\) H(\(\phi\)) dV


\(\int\) H(\(\phi\)) {i|j|k} • vdV


\(\int\) [\(\rho_{gas}\) \(\phi\) (1-S) + \(\rho_{liq}\) \(\phi\) S] dV


No References.



Description / Usage

This card is used to denote the end of a set of VOLUME_INT cards and is only used when the Post Processing Volumetric Integration card is present and one or more VOLUME_INT cards are specified.


The VOLUME_INT card shows an example of using this card in context. Because the card has no input parameters, it always appears as


Technical Discussion

No Discussion.


No References.