************** **VOLUME_INT** ************** :: VOLUME_INT = {volume_type} [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 .| | | * **DISSIPATION**-Total viscous dissipation, :math:`\tau`: | | | :math:`\Delta v` , in the element block specified | | | by . | | | * **JOULE**-Total Joule or Ohmic heating, | | | :math:`\frac{1}{\sigma}` (:math:`\underline{J}` • | | | :math:`\underline{J}`) , in the element block specified | | | by . | | | * **SPECIES_MASS**-Integral of concentration of the | | | component specified by in the element | | | block specified by < blk_id>. | | | * **MOMENTUMX, MOMENTUMY,** or **MOMENTUMZ**-Integral of | | | appropriate component of the momentum flux | | | :math:`\rho\vec{v}` over the element block . | | | * **STRESS_TRACE**-Integral of the trace of the complete | | | stress tensor (-:math:`p\zeta + \tau`) over the element block| | | *blk_id*. | | | * **HEAT_ENERGY**-Integral of the sensible heat over | | | ( 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. :math:`\underline{v}` • :math:`\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 :math:`Ac_1` + :math:`Bc_2` + | | | :math:`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. | +----------------+----------------------------------------------------------------+ |[float_list] |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. | +----------------+----------------------------------------------------------------+ ------------ **Examples** ------------ 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 END OF VOLUME_INT ------------------------- **Technical Discussion** ------------------------- The volume integrations are carried out as follows: +------------------------+---------------------------------------------------------------+ |**volume_type** |**volume integral** | +------------------------+---------------------------------------------------------------+ |VOLUME |:math:`\int` dV | +------------------------+---------------------------------------------------------------+ |DISSIPATION |:math:`\int` (-p :math:`\zeta + \tau`) • :math:`\Delta` vdV | +------------------------+---------------------------------------------------------------+ |JOULE |:math:`\int` :math:`\frac{1}{\sigma}` J • JdV | +------------------------+---------------------------------------------------------------+ |SPECIES_MASS |:math:`\int` :math:`c_jdV` | +------------------------+---------------------------------------------------------------+ |MOMENTUM_{X|Y|Z} |:math:`\int` :math:`\rho` (i|j|k) • vdV | +------------------------+---------------------------------------------------------------+ |STRESS_TRACE |:math:`\int` tr(-p :math:`\zeta + \tau`) dV | +------------------------+---------------------------------------------------------------+ |{POSITIVE|NEGATIVE}_FILL|:math:`\int` H(:math:`\phi`) dV | +------------------------+---------------------------------------------------------------+ |NEGATIVE_V{X|Y|Z} |:math:`\int` H(:math:`\phi`) {i|j|k} • vdV | +------------------------+---------------------------------------------------------------+ |POROUS_LIQ_INVENTORY |:math:`\int` [:math:`\rho_{gas}` :math:`\phi` (1-S) + | | |:math:`\rho_{liq}` :math:`\phi` S] dV | +------------------------+---------------------------------------------------------------+ -------------- **References** -------------- No References.