# SURFACE_INTEGRATED_CONDITION

Specifies a condition on the surface integral of a solution variable.

## Type

AcuSolve Command

## Syntax

SURFACE_INTEGRATED_CONDITION("name") {parameters...}

## Qualifier

User-given name.

## Parameters

- shape (enumerated) [no default]
- Shape of the surfaces in this set.
- three_node_triangle or tri3
- Three-node triangle.
- four_node_quad or quad4
- Four-node quadrilateral
- six_node_triangle or tri6
- Six-node triangle.

- element_set or elem_set (string) [no default]
- User-given name of the parent element set.
- surfaces (array) [no default]
- List of element surfaces.
- surface_sets (list) [={}]
- List of surface set names (strings) to use in this command. When using this option, the connectivity, shape, and parent element of the surfaces are provided by the surface set container and it is unnecessary to specify the shape, element_set and surfaces parameters directly to the SURFACE_INTEGRATED_CONDITION command. This option is used in place of directly specifying these parameters. In the event that both of the surface_sets and surfaces parameters are provided, the full collection of surface elements is read and a warning message is issued. The surface_sets option is the preferred method to specify the surface elements. This option provides support for mixed element topologies and simplifies pre-processing and post-processing.
- variable or var (enumerated) [no default]
- Boundary condition variable.
- mass_flux or mass
- Mass flux.
- temperature or temp
- Temperature.
- species_1 or spec1
- Species 1.
- species_2 or spec2
- Species 2.
- species_3 or spec3
- Species 3.
- species_4 or spec4
- Species 4.
- species_5 or spec5
- Species 5.
- species_6 or spec6
- Species 6.
- species_7 or spec7
- Species 7.
- species_8 or spec8
- Species 8.
- species_9 or spec9
- Species 9.
- field
- Field.
- kinetic_energy or tke
- Turbulence kinetic energy.
- eddy_frequency or tomega
- Turbulence eddy frequency.
- dissipation_rate or teps
- Dissipation rate.
- intermittency or tintc
- Intermittency.
- transition_re_theta or treth
- Transition Re-theta.

- type (enumerated) [=constant]
- Type of the boundary surface.
- constant or const
- Constant value. Requires constant_value.

- constant_value or value (real) [=0]
- Constant value of the boundary condition. Used with constant type.
- field (string) [no default]
- Value of the boundary condition for field. Used with variable field.
- multiplier_function (string) [=none]
- User-given name of the multiplier function for scaling the boundary condition values. If none, no scaling is performed.

## Description

This command specifies a condition on the surface integral of a solution variable. Bulk (mass-averaged) definitions are used for the temperature and species variables. The bulk temperature on a surface is defined by:

where T is the temperature, ρ is the density,
**u** is the velocity,
**n** is the outward-pointing normal
to the surface, and S is the surface defined by
surfaces. Similar definitions are used for the species
variables. The mass_flux variable is given by the denominator of
the above equation.

```
ELEMENT_SET( "flow elements" ) {
shape = four_node_tet
elements = { ...
4, 2, 5, 6, 8 ;
5, 2, 6, 3, 5 ;
... }
...
}
SURFACE_INTEGRATED_CONDITION( "total mass flux at inlet" ) {
shape = three_node_triangle
element_set = "flow elements"
surfaces = { 4, 41, 2, 5, 6 ;
5, 51, 5, 6, 3 ; }
variable = mass_flux
type = contant
constant_value = 12
}
```

defines a surface integrated condition, with a constant value of 12 for the integral of mass flux over two surfaces of the element set "flow elements".

**Element Shape****Surface Shape**- four_node_tet
- three_node_triangle
- five_node_pyramid
- three_node_triangle
- five_node_pyramid
- four_node_quad
- six_node_wedge
- three_node_triangle
- six_node_wedge
- four_node_quad
- eight_node_brick
- four_node_quad
- ten_node_tet
- six_node_triangle

The surfaces parameter contains the faces of the element set. This parameter is a multi-column array. The number of columns depends on the shape of the surface. For three_node_triangle, this parameter has five columns, corresponding to the element number (of the parent element set), a unique (within this set) surface number, and the three nodes of the element face. For four_node_quad, surfaces has six columns, corresponding to the element number, a surface number, and the four nodes of the element face. For six_node_triangle, surfaces has eight columns, corresponding to the element number, a surface number, and the six nodes of the element face. One row per surface must be given. The three, four, or six nodes of the surface may be in any arbitrary order, since they are reordered internally based on the parent element definition.

```
4 41 2 5 6
5 51 5 6 3
```

```
SURFACE_INTEGRATED_CONDITION( "inlet" ) {
shape = three_node_triangle
element_set = "flow elements"
surfaces = Read( "inlet.ebc" )
variable = mass_flux
type = constant
constant_value = 12.
}
```

```
SURFACE_SET( "tri faces" ) {
surfaces = { 1, 1, 1, 2, 4 ;
2, 2, 3, 4, 6 ;
3, 3, 5, 6, 8 ; }
shape = three_node_triangle
volume_set = "tetrahedra"
}
SURFACE_SET( "quad faces" ) {
surfaces = { 1, 1, 1, 2, 4, 9 ;
2, 2, 3, 4, 6, 12 ;
3, 3, 5, 6, 8, 15 ; }
shape = four_node_quad
volume_set = "prisms"
```

```
SURFACE_INTEGRATED_CONDITION ( "inlet" ) {
surface_sets = {"tri_faces", "quad_faces"}
...
}
```

```
tri faces
quad faces
```

```
SURFACE_INTEGRATED_CONDITION ( "inlet" ) {
surface_sets = Read("surface_sets.srfst")
...
}
```

The mixed topology version of the SURFACE_INTEGRATED_CONDITION command is preferred. This version provides support for multiple element topologies within a single instance of the command and simplifies pre-processing and post-processing. In the event that both the surface_sets and surfaces parameters are provided in the same instance of the command, the full collection of surface elements is read and a warning message is issued. Although the single and mixed topology formats of the commands can be combined, it is strongly recommended that they are not.

The variable to which the integrated condition applies is given by variable. If the problem does not solve for a field associated with this variable, the condition is simply ignored. A separate SURFACE_INTEGRATED_CONDITION command must be issued for each variable and type.

The quadrature rule for the surface integral is inherited from the parent element set.

A constant type of surface integrated condition specifies that the surface integral of the given variable is equal to constant_value, as in the above example.

```
SURFACE_INTEGRATED_CONDITION( "time-varying mass flux" ) {
...
variable = mass_flux
type = constant
constant_value = 2.5
multiplier_function = "time varying"
}
MULTIPLIER_FUNCTION( "time varying" ) {
type = piecewise_linear
curve_fit_values = { 0, 0.0 ;
10, 1.0 ;
20, 0.5 ;
40, 0.7 ;
80, 1.2 ; }
curve_fit_variable = time
}
```