Adjoint Cost Functions Reference

An adjoint cost function corresponds to the engineering objective that is examined during the adjoint flow analysis. One example of an engineering objective is to reduce the pressure drop in a piping system. Another example is the reduction of drag force around a car.

Cost functions are differentiated to form the right-hand side of the adjoint flow equations. The adjoint solver solves the system of differential equations with regard to the cost function specified.

Only the report types supporting adjoint differentiation can be associated to a cost function. All the available report types are listed below:

Force: Estimates the sensitivity of the force on a specified set of boundary surfaces in a specified direction.

Moment: Estimates the sensitivity of the moment on a specified set of boundary surfaces with a specified direction and origin.

Pressure Drop: Estimates the sensitivity of the mass-flow averaged total pressure between two boundary surfaces or between two interfaces representing the high-pressure and low-pressure boundaries of the system.

Uniformity Deviation Report: Estimates the sensitivity of the deviation of the local normal velocity from the mass-flow averaged value on a specified set of boundary surfaces or on interfaces.

Tumble/Swirl Report: Estimates the sensitivity of tumble or swirl, usually for ICE applications.

Expression Report: Estimates the sensitivity of an expression that is defined through an expression report.

Mass Flow: Estimate the sensitivity of mass flow rate through boundaries.

Mass Flow Averaged: Estimate the sensitivity of the mass flow averaged scalar quantity through a surface.

Heat Transfer: Estimates the sensitivity of heat transfer at boundaries.

Sum: Estimates the sensitivity of a summed-up scalar quantity over surfaces or volumes.

Surface Average: Estimates the sensitivity of the surface average of a scalar quantity over surfaces.

Surface Integral: Estimates the sensitivity of the surface integral of a scalar or vector quantity.

Surface Standard Deviation: Estimates the sensitivity of the standard deviation of a scalar quantity across a surface.

Surface Uniformity: Estimates the sensitivity of the uniformity of a scalar quantity on a surface.

Volume Average: Estimates the sensitivity of the volume average of a scalar quantity.

Volume Integral: Estimates the sensitivity of the volume integral of a scalar quantity.

Volume Standard Deviation: Estimates the sensitivity of the standard deviation of a scalar quantity in a volume.

Volume Uniformity: Estimates the sensitivity of the uniformity of a scalar quantity in a volume.

There are certain limitations for reports that require the input of a field function and parts such as the sum or the surface uniformity report:

When these reports are associated to cost functions, they must only reference model parts or geometry parts; derived parts are not supported.
The field functions supported for full differentiation are scalar or vector field functions which are either primitive, derived (vector magnitude, vector component), or user-defined, and are available on boundary faces or region cells. For user-defined field functions, only a subset of operations are differentiable—operations which do not involve neighbor stencil field data, tabular data, or coordinate transformations. Supported operations are: arithmetic, logical, and trigonometric operations. The complete list of user-defined field function operations that are supported is:
- Index operator
- Alternate Value operator
- Conditional operator
- Unary operators: acos, asin, atan, cos, cosh, exp, abs, log, log10, sin, sinh, sqrt, cbrt, tan, tanh, mag, mag2, unit
- Binary operators: '+', '-', '*', '/', pow, fmod, min, max, atan2, dot, cross
- The Field Function expert property Inverse Distance Weight is not supported.
- The Report expert property Smooth Values is not supported.
The following field functions are supported for adjoint:
- Volume
- Area
- Centroid
- Grid Flux
- Density
- Temperature
- Total Enthalpy
- Boundary Heat Flux
- Boundary Conduction Heat Flux
- Pressure
- Total Pressure
- Absolute Total Pressure
- Vorticity Vector
- Helicity
- Face Flux
- Boundary Advection Heat Flux
- Wall Shear Stress
- Velocity
- Relative Velocity
- Mass Flux
- Static Pressure
- Total Temperature
- Sound Speed
- Mach Number
- Passive Scalar
- Boundary Passive Scalar Flux
- Modified Diffusivity
The following field functions are differentiable when temporary storage is retained:
- Reconstructed gradients of
  - Density
  - Pressure
  - Velocity
  - Temperature
  - Total Enthalpy
- Gradient of Pressure