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Post-Processing
Simcenter STAR-CCM+ allows you to post-process the solution after each iteration or time-step, (while the simulation is running), as well as when the simulation completes. For this reason, you generally create post-processing objects before running the simulation. Post-processing objects are also known as analysis objects.
Signal Processing
Signal processing applies data set functions to sets of wave data.
Data Set Functions Formulation
Frequency-Space Auto-Spectrum and Cross-Spectrum

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Post-Processing
Simcenter STAR-CCM+ allows you to post-process the solution after each iteration or time-step, (while the simulation is running), as well as when the simulation completes. For this reason, you generally create post-processing objects before running the simulation. Post-processing objects are also known as analysis objects.
- Analysis Workflow
  The key steps in successfully analyzing simulation results are to: (1) be clear on what quantities you want to extract; (2) locate or define surfaces on which to obtain the data; and, (3) present the data in visual scenes or numeric output.
- Data Interpolation
  Most visualization objects such as plots, reports, and scalar displayers allow for smooth and non-smooth values. For example, the contour style for scalar displayers provides a Smooth Filled option (smooth) and a Filled option (non-smooth). The way these values are calculated depends on the discretization method.
- Field Function Interpolation and Interfaces (FV)
  For finite volume meshes, understanding how Simcenter STAR-CCM+ deals with field function data is important for avoiding non-physical results in post-processing at an interface, and to appreciate the difference that smoothing makes when it is applied.
- Accessing Solution Data through Derived Parts
  Although Simcenter STAR-CCM+ can display, analyze, and report simulation data on regions, boundaries, and parts, there are many cases when you want to access data in other entities of the solution space. Derived parts provide a mechanism for defining additional entities on which you can access solution data.
- Visualizing the Solution
  The visualization tools in Simcenter STAR-CCM+ are integrated with the analysis, allowing for the interactive extraction and viewing of solution data from either a running or converged simulation.
- Transient Solution Data
  For transient solutions, Simcenter STAR-CCM+ provides the simulation history file (.simh) to which you can save selected data while a simulation is running. After the simulation completes, you can load this file and query its states for post-processing.
- Sampling Data Values Using Reports and Monitors
  This workflow incorporates the roles of both reports and monitors.
- Accessing Field Data from Previous Time-Steps or Iterations
  A field history is a type of field monitor that stores a finite number of past values (or samples) of a field function, captured at moments defined by its update policy, for a given set of input regions or boundaries (or both).
- Reporting Results
  Reports provide summaries of solution data.
- Monitoring the Solution
  Monitors sample, save, and plot solution data.
- Plots
  The plotting features in Simcenter STAR-CCM+ allow you to create three kinds of two-dimensional plots.
- Exploring Solutions with Data Focus
  This interactive tool lets you extract knowledge of merit -- information that facilitates a correct engineering decision -- from a large volume of data.
- Parametric Positioning for Analysis Surfaces in Turbomachine Domains
  In studies of cases of revolving volumes, such as turbomachinery, a typical requirement for post-processing is to render and plot data on surfaces or profiles that are positioned parametrically in relation to the domain bounding surfaces. For example, you may wish to view the total pressure on a surface located exactly half-way between the hub and shroud, or you may wish to plot pressure across both blade surfaces on a given slice.
- Triggers and Update Events
  Several features of Simcenter STAR-CCM+ require that you define a trigger for when an action takes place. Simcenter STAR-CCM+ provides three built-in trigger types, and one custom trigger type (defined by an update event).
- Signal Processing
  Signal processing applies data set functions to sets of wave data.
  - Signal Processing Concepts
    Signals can be expressed as oscillating changes of signal strength over time or as a function of signal strength over a range of frequencies. Both methods have their uses. Information can be converted from one form to the other by Fourier transforms.
  - Creating Data Set Functions
    To add a data set function, right-click the Data Set Functions node and select a type from the New submenu of the pop-up menu.
  - Point Time Histories
    Point Time Histories are time histories at a point in the input signal which are then processed using a Fourier transform.
  - Point Time Fourier Transforms
    Point Time Fourier Transforms are Fourier transforms for one time point in the input signal.
  - Point-to-Point Time Fourier Transforms
    You use Point-to-Point Time Fourier transforms to determine the correlation between two input signals. This data set function applies a Fourier transform to each of the input signals, then performs a convolution on both resulting transforms.
  - Point-to-Point Time Correlations
    You use Point-To-Point Time correlations to determine the phase differences between the dominant modes of two input signals.
  - Point Inverse Time Fourier Transforms
    This inverse transform allows data to be transformed from the frequency to the time domain.
  - Line Time Histories
    A Line Time History is a collection of Point Time Histories that are drawn from the points that make up a line probe.
  - Line Time Fourier Transforms
    Line Time Fourier Transforms let you calculate Fourier transforms at various point along a line probe.
  - Line Spatial Fourier Transforms
    Line Spatial Fourier Transforms allows the creation of a matrix of energy densities dependent on wavenumber and frequency along a line probe.
  - Surface Time Histories
    A Surface Time History is a collection of Point Time Histories that are drawn from the points that make up a presentation grid.
  - Surface Time Fourier Transforms
    Surface Time Fourier Transforms let you calculate Fourier transforms at various point within a presentation grid.
  - Line Time Domain Filter
    You can use Line Time Domain filters to create frequency-band filtered line time histories, which is similar to carrying out inverse line FFT. Using filtered line time histories enables you to visualize flow quantitites in a specified frequency range, which can be useful for identifying and analyzing periodic flow structures or time harmonic phenomena such as acoustic waves. Line Time Domain filtering can only be carried out on scalar quantities saved in .trn files.
  - Surface Time Domain Filter
    You can use Surface Time Domain filters to create frequency-band filtered surface time histories, which is similar to carrying out inverse surface FFT. Using filtered surface time histories enables you to visualize flow quantitites in a specified frequency range, which can be useful for identifying and analyzing periodic flow structures or time harmonic phenomena such as acoustic waves. Surface Time Domain filtering can only be carried out on scalar quantities saved in .trn files.
  - Exporting Filtered Time History Fields
    You can export filtered time history field data as a Matlab .mat file.
  - Derived Data
    Derived data objects allow a data set function to access data from various other objects in the simulation, as well as from external files.
  - Post-Processing Data Set Functions
    Simcenter STAR-CCM+ allows you to visualize Fourier transforms and surface spectra.
  - Pop-Up Menu of the Data Set Functions Manager
  - Data Set Functions Formulation
    - Basic Relations
    - Positive and Negative Frequency Ranges
      The real and imaginary parts of a frequency composing an FFT input can be considered as either positive or negative frequencies, based on their relative phase.
    - Time-Space Fourier Transforms
    - Frequency-Space Auto-Spectrum and Cross-Spectrum
    - Time Cross-Correlations
    - Frequency-Space Parseval’s Relation
    - Frequency-Wavenumber Auto-Spectrum
    - Spatial Cross-Correlations
    - Frequency-Wavenumber Parseval’s Relation
    - Wave Group Velocity
      The group velocity $v_{g}$ of a wave is the velocity of propagation of the envelope (or modulation) of the wave in space.
    - Spectra Averaging
    - Spectra Filtering
      It is possible to filter time histories using an ideal filter in the frequency domain.
    - Power Spectra Density
      The Power Spectra Density describes the total signal power over the frequency domain.
    - Sound Pressure Level
      The sound pressure is the local change in pressure from the reference ambient pressure that a sound wave causes.
    - Window Functions
      The window function is zero-valued outside a chosen interval and symmetric around the middle of the interval. When a signal is "multiplied" by a window function, the product is also zero-valued outside the interval: all that is left is the part where they overlap, the "view through the window." The window function makes the signal periodic: it is guaranteed to be zero at both start and end. The FT assumes the signal is periodic signal, and the window function enforces this assumption.

Frequency-Space Auto-Spectrum and Cross-Spectrum

The frequency-space (fs) auto-spectrum is defined as

Figure 1. EQUATION_DISPLAY

G (x; ω) = g^{*} (x; ω) g (x; ω)

(499)

where $g^{*}$ is the complex conjugate of $g$ .

The frequency-space (fs) cross-spectrum is

Figure 2. EQUATION_DISPLAY

G (x_{1}, x_{2}; ω) = g^{*} (x_{1}; ω) g (x_{2}; ω) \forall x_{1} \in S, \forall x_{2} \in S

(500)

Defining the “finite Fourier transform” for the $k^{t h}$ sample time block of length $T$ :

Figure 3. EQUATION_DISPLAY

g (x; f, T) = \int_{0}^{1} h (x, t) e^{- i ω t} ⅆ t

(501)

The one-sided cross-spectral density between random processes at any two points in space $x_{1,} x_{2}$ is defined as

Figure 4. EQUATION_DISPLAY

G (x_{1}, x_{2}; f) = \lim_{T \to \infty} \frac{2}{T} E 〈 g_{k}^{*} (x_{1}; f, T) g_{k} (x_{2}; f, T) 〉

(502)

The corresponding one-sided auto-spectral density of the random signal at a single point is:

Figure 5. EQUATION_DISPLAY

G (x, x; f) = \lim_{T \to \infty} \frac{2}{T} E 〈 g_{k}^{*} (x; f, T) g_{k} (x; f, T) 〉 = \lim_{T \to \infty} \frac{2}{T} E 〈 {| g_{k} (x; f, T) |}^{2} 〉

(503)

where $E 〈 〉$ represents the expectation operator averaging over all indices $k$ . The expectation is important to obtain the coherence between the two random processes, which are defined below.

Since the cross spectral density is in general complex, it is convenient to convert to magnitude and phase. Magnitude is defined as:

Figure 6. EQUATION_DISPLAY

| G (x_{1}, x_{2}; f) | = \sqrt{{[R e G (x_{1}, x_{2}; f)]}^{2} + {[I m G (x_{1}, x_{2}; f)]}^{2}}

(504)

and phase is defined as:

Figure 7. EQUATION_DISPLAY

θ (x_{1}, x_{2}; f) = a t a n (\frac{I m G (x_{1}, x_{2}; f)]}{R e G (x_{1}, x_{2}; f)]})

(505)

The coherence is the measure of how much of the random signal at position $x^{'}$ exhibits that time-averaged phase correlation with the random signal at position $x$ . Coherence is defined as

Figure 8. EQUATION_DISPLAY

γ^{2} (x_{1}, x_{2}; f) = \frac{{| G (x_{1}, x_{2}; f) |}^{2}}{G (x_{1}, x_{1}; f) G (x_{2}, x_{2}; f)}

(506)