Complex Quantities

In Simcenter STAR-CCM+, you use complex profiles to specify quantities that are defined by complex numbers.

For example, when Maxwell's equations are expressed in the frequency domain, the electromagnetic fields and material properties, such as the electrical conductivity, become complex quantities. See Harmonic Time Dependence.

In general, you can write a complex number A in terms of its real and imaginary parts:

Figure 1. EQUATION_DISPLAY
A=Re⁡[A]+iIm[A]
(1)

where i is the imaginary unit, defined by i2=−1.

You can also write A in polar form:

Figure 2. EQUATION_DISPLAY
A=|A|⋅eiθ=|A|(cos⁡θ+i⁢sin⁡θ)
(2)

where |A| is the magnitude:

Figure 3. EQUATION_DISPLAY
|A|=(Re⁡[A])2+(Im[A])2
(3)
and θ is the phase.

Complex Profile Methods

Simcenter STAR-CCM+ allows you to define complex profiles using the following methods:
MethodAssociated Profile Child Nodes
Composite Rectangular
Allows you to specify the complex profile in terms of its real and imaginary parts (see Eqn. (1)).
Composite Rectangular > Real
Specifies the real part as a scalar or vector profile.
Composite Rectangular > Imaginary
Specifies the imaginary part as a scalar or vector profile.
Composite Polar
Allows you to specify the complex profile in polar form (see Eqn. (2)).
Composite Polar > Magnitude
Specifies the magnitude as a scalar or vector profile.
Composite Polar > Phase
Specifies the phase as a scalar or vector profile.

When you define a complex profile, Simcenter STAR-CCM+ creates four field functions to represent its real part, imaginary part, magnitude, and phase.