Filters

3.5 Filters

Filters are a method for calculating a variety of useful quantities from the field variables as the solution evolves in time, such as time-averaged fields and extracting the field variables at certain points inside the domain. Each filter is defined in a FILTER tag inside a FILTERS block which lies in the main NEKTAR tag. In this section we give an overview of the modules currently available and how to set up these filters in the session file.

Here is an example FILTER:

1<FILTER TYPE="FilterName"> 
2    <PARAM NAME="Param1"> Value1 </PARAM> 
3    <PARAM NAME="Param2"> Value2 </PARAM> 
4</FILTER>

A filter has a name – in this case, FilterName – together with parameters which are set to user-defined values. Each filter expects different parameter inputs, although where functionality is similar, the same parameter names are shared between filter types for consistency. Numerical filter parameters may be expressions and so may include session parameters defined in the PARAMETERS section.

Some filters may perform a large number of operations, potentially taking up a significant percentage of the total simulation time. For this purpose, the parameter IO_FiltersInfoSteps is used to set the number of steps between successive total filter CPU time stats are printed. By default it is set to 10 times IO_InfoSteps. If the solver is run with the verbose -v flag, further information is printed, detailing the CPU time of each individual filter and percentage of time integration.

In the following we document the filters implemented. Note that some filters are solver-specific and will therefore only work for a given subset of the available solvers.

3.5.1 Phase sampling

Note: This feature is currently only supported for filters derived from the FieldConvert filter: AverageFields, MovingAverage, ReynoldsStresses.

When analysing certain time-dependent problems, it might be of interest to activate a filter in a specific physical phase and with a certain period (for instance, to carry out phase averaging). The simulation time can be written as t = mT + n_TT , where m is an integer representing the number of periods T elapsed, and 0 ≤ n_T ≤ 1 is the phase. This feature is not a filter in itself and it is activated by adding the parameters below to the filter of interest:

Option name	Required	Default	Description
`PhaseAverage`	✓		Feature activation
`PhaseAveragePeriod`	✓		Period T
`PhaseAveragePhase`	✓		Phase n_T.

For instance, to activate phase averaging with a period of T = 10 at phase n_T = 0.5:

1<FILTER TYPE="FilterName"> 
2    <PARAM NAME="Param1"> Value1 </PARAM> 
3    <PARAM NAME="Param2"> Value2 </PARAM> 
4    <PARAM NAME="PhaseAverage"> True </PARAM> 
5    <PARAM NAME="PhaseAveragePeriod"> 10 </PARAM> 
6    <PARAM NAME="PhaseAveragePhase"> 0.5 </PARAM> 
7</FILTER>

Since this feature monitors n_T every SampleFrequency, for best results it is recommended to set SampleFrequency= 1.
The maximum error in sampling phase is n_{T ,tol} = Δt-
2T ⋅ SampleFrequency, which is displayed at the beginning of the simulation if the solver is run with the verbose -v option.
The number of periods elapsed is calculated based on simulation time. Caution is therefore recommended when modifying time information in the restart field, because if the new time does not correspond to the same phase, the feature will produce erroneous results.

3.5.2 Aerodynamic forces

Note: This filter is only supported for the incompressible Navier-Stokes solver.

This filter evaluates the aerodynamic forces along a specific surface. The forces are projected along the Cartesian axes and the pressure and viscous contributions are computed in each direction.

The following parameters are supported:

Option name	Required	Default	Description
`OutputFile`	✗	`session`	Prefix of the output filename to which the forces are written.
`Frequency`	✗	1	Number of timesteps after which output is written.
`Boundary`	✓	-	Boundary surfaces on which the forces are to be evaluated.
`PivotPoint`	✗	(0. 0. 0.)	Pivot Point around which the Moments are calculated. If Doesn’t explicitly defined by user, the moments will be calculated around the point X = (0. 0. 0.)

An example is given below:

1  <FILTER TYPE="AeroForces"> 
2      <PARAM NAME="OutputFile">DragLift</PARAM> 
3      <PARAM NAME="OutputFrequency">10</PARAM> 
4      <PARAM NAME="Boundary"> B[1,2] </PARAM>            
5      <PARAM NAME="PivotPoint"> 1. 0.1 0. </PARAM>               
6  </FILTER>

During the execution a file named DragLift.fce will be created and the value of the aerodynamic forces on boundaries 1 and 2, defined in the GEOMETRY section, will be output every 10 time steps.

3.5.2.1 Extension for the SPM formulation

Note: This filter is only supported for the incompressible Navier-Stokes solver with the Smoothed Profile Method.

The lack of physical boundaries in the Smoothed Profile Method requires an alternative formulation to calculate the aerodynamic forces. Since the method imposes the boundary geometry by adding an impulse to the flow proportional to the difference between the flow velocity and the expected velocity of the immersed bodies, the forces in this filter are computed by integrating this difference where Φ≠0 [27]:

Fn 1 ∫ n+1 * n -ρ-= Δt- Φ (u - u p) dΩ Ω

Option name	Required	Default	Description
`OutputFile`	✗	`session`	Prefix of the output filename to which the forces are written.
`Frequency`	✗	1	Number of timesteps after which the output is written.
`StartTime`	✗	0	Forces before this instant are not written to the output.

For instance, a block like the following

1  <FILTER TYPE="AeroForcesSPM"> 
2      <PARAM NAME="OutputFile"> Forces </PARAM> 
3      <PARAM NAME="OutputFrequency"> 10 </PARAM> 
4      <PARAM NAME="StartTime"> 50.0 </PARAM> 
5  </FILTER>

will generate a file called Forces.fce with the values of the forces in the (X,Y,Z) directions, that must be scaled with the density of the fluid to get the real values. It is important to remark that the computed values are the sum of all the boundaries defined by Φ.

3.5.3 Benchmark

Note: This filter is only supported for the Cardiac Electrophysiology Solver.

Filter Benchmark records spatially distributed event times for activation and repolarisation (recovert) during a simulation, for undertaking benchmark test problems.

1<FILTER TYPE="Benchmark"> 
2  <PARAM NAME="ThresholdValue"> -40.0 </PARAM> 
3  <PARAM NAME="InitialValue">     0.0 </PARAM> 
4  <PARAM NAME="OutputFile"> benchmark </PARAM> 
5  <PARAM NAME="StartTime">        0.0 </PARAM> 
6</FILTER>

ThresholdValue specifies the value above which tissue is considered to be depolarised and below which is considered repolarised.
InitialValue specifies the initial value of the activation or repolarisation time map.
OutputFile specifies the base filename of activation and repolarisation maps output from the filter. This name is appended with the index of the event and the suffix ‘.fld‘.
StartTime (optional) specifies the simulation time at which to start detecting events.

3.5.4 Cell history points

Note: This filter is only supported for the Cardiac Electrophysiology Solver.

Filter CellHistoryPoints writes all cell model states over time at fixed points. Can be used along with the HistoryPoints filter to record all variables at specific points during a simulation.

1<FILTER TYPE="CellHistoryPoints"> 
2    <PARAM NAME="OutputFile">crn.his</PARAM> 
3    <PARAM NAME="OutputFrequency">1</PARAM> 
4    <PARAM NAME="Points"> 
5        0.00 0.0 0.0 
6    </PARAM> 
7</FILTER>

OutputFile specifies the filename to write history data to.
OutputFrequency specifies the number of steps between successive outputs.
Points lists coordinates at which history data is to be recorded.

3.5.5 Checkpoint cell model

Note: This filter is only supported for the Cardiac Electrophysiology Solver.

Filter CheckpointCellModel checkpoints the cell model. Can be used along with the Checkpoint filter to record complete simulation state and regular intervals.

1<FILTER TYPE="CheckpointCellModel"> 
2  <PARAM NAME="OutputFile"> session </PARAM> 
3  <PARAM NAME="OutputFrequency"> 1 </PARAM> 
4</FILTER>

OutputFile (optional) specifies the base filename to use. If not specified, the session name is used. Checkpoint files are suffixed with the process ID and the extension ‘.chk‘.
OutputFrequency specifies the number of timesteps between checkpoints.

3.5.6 Checkpoint fields

The checkpoint filter writes a checkpoint file, containing the instantaneous state of the solution fields at at given timestep. This can subsequently be used for restarting the simulation or examining time-dependent behaviour. This produces a sequence of files, by default named session_*.chk, where * is replaced by a counter. The initial condition is written to session_0.chk. Existing files are not overwritten, but renamed to e.g. session_0.bak0.chk. In case this file already exists, too, the chk-file is renamed to session_0.bak*.chk and so on.

Note: This functionality is equivalent to setting the IO_CheckSteps parameter in the session file.

The following parameters are supported:

Option name	Required	Default	Description
`OutputFile`	✗	`session`	Prefix of the output filename to which the checkpoints are written.
`OutputFrequency`	✓	-	Number of timesteps after which output is written.
`OutputStartTime`	✗	0	Specifies the simulation time at which to start writing checkpoint files.

For example, to output the fields every 100 timesteps we can specify:

1<FILTER TYPE="Checkpoint"> 
2    <PARAM NAME="OutputFile">IntermediateFields</PARAM> 
3    <PARAM NAME="OutputFrequency">100</PARAM> 
4    <PARAM NAME="OutputStartTime"> 50.0 </PARAM> 
5</FILTER>

It is also possible to specify the OutputStartTime option based on the simulation time step. For example, if checkpoint files should only be written after 500 time steps, one can write

1    <PARAM NAME="OutputStartTime"> TimeStep * 500 </PARAM>

3.5.7 Electrogram

Note: This filter is only supported for the Cardiac Electrophysiology Solver.

Filter Electrogram computes virtual unipolar electrograms at a prescribed set of points.

1<FILTER TYPE="Electrogram"> 
2  <PARAM NAME="OutputFile"> session </PARAM> 
3  <PARAM NAME="OutputFrequency"> 1 </PARAM> 
4  <PARAM NAME="Points"> 
5      0.0  0.5  0.7 
6      1.0  0.5  0.7 
7      2.0  0.5  0.7 
8  </PARAM> 
9</FILTER>

OutputFile (optional) specifies the base filename to use. If not specified, the session name is used. The extension ‘.ecg‘ is appended if not already specified.
OutputFrequency specifies the number of resolution of the electrogram data.
Points specifies a list of coordinates at which electrograms are desired. They must not lie within the domain.

3.5.8 Offset Phase

Note: This filter is only supported for the Cardiac Electrophysiology Solver.

Filter OffsetPhase computes the instantaneous phase of the action potential using a time delay-embedding technique [20]:

θ(t) = atan2[v(t - τ)- ¯v,v(t)- ¯v].

Option name	Required	Default	Description
`OutputFile`	✗	`session`	Prefix of the output filename to which the phase are written.
`OutputFrequency`	✓	-	Number of timesteps after which output is written.
`MeanV`	✗	-57.2986	Specifies the time-averaged AP value (v) in mV.

3.5.9 Hilbert Transform Phase based on FFTW

Note: This filter is only supported for the Cardiac Electrophysiology Solver. To use this filter, user must build Nektar++ with FFTW library.

Filter HilbertFFTPhase computes the instantaneous phase of the action potential by generating an analytic signal, v(t) + iH{v}(t).

∫ ∞ H{v}(t) = 1-p.v. v(τ)-dτ, π -∞ t- τ

and

θ(t) = atan2[H{v - ¯v}(t),v(t)- ¯v].

Option name	Required	Default	Description
`OutputFile`	✗	`session`	Prefix of the output filename to which the phase are written.
`OutputFrequency`	✓	-	Number of timesteps after which an output is written. It is equal to the sampling frequency for Fourier Transform.
`WindowSize`	✓	-	Number of output steps taken in each FFT. Note: output steps ≠ timesteps.
`OverlapSize`	✓	-	Number of output steps overlapped between each segment.
`MeanV`	✗	Time-average	Specifies the time-averaged AP value in mV.
`LinearTransitionOverlap`	✗	`true`	`true`: Use linear transition in overlapping region(s). `false`: Use simple average in overlapping region(s). Input must be either `true` or `false`.

3.5.10 Error

This filter produces a file containing the time-evolution of the L₂ and L_inf errors. By default this file is called session.err where session is the session name.

The following parameters are supported:

Option name	Required	Default	Description
`OutputFile`	✗	`session`	Prefix of the output filename to which the errors are written.
`OutputFrequency`	✗	1	Number of timesteps after which output is written.
`ConsoleOutput`	✗	0	Also output error in the console when writing to file.

An example syntax is given below:

1<FILTER TYPE="Error"> 
2    <PARAM NAME="OutputFile">ErrorFile</PARAM> 
3    <PARAM NAME="OutputFrequency">10</PARAM> 
4    <PARAM NAME="ConsoleOutput">1</PARAM> 
5</FILTER>

3.5.11 Integral

This filter produces a file containing the time-evolution of the integral of the solver variables on user defined composites. By default this file is called session.int where session is the session name.

The following parameters are supported:

Option name	Required	Default	Description
`OutputFile`	✗	`session`	Prefix of the output filename to which the integrals are written.
`OutputFrequency`	✗	1	Number of timesteps after which output is written.
`OutputPrecision`	✗	7	Decimal precision with which the output is written.
`Composites`	✓	-	Composites on which to calculate the integral.

Multiple composites can be defined together by using ranges with each composite grouping producing a summed output for each variable in the OutputFile. For example C[1,3,5-7] would produce a single integral output for each variable whilst C[1-3], C[4] would produce two.

An example syntax is given below:

1<FILTER TYPE="Integral"> 
2    <PARAM NAME="OutputFile">IntegralFile</PARAM> 
3    <PARAM NAME="OutputFrequency">10</PARAM> 
4    <PARAM NAME="OutputPrecision"> 12 </PARAM> 
5    <PARAM NAME="Composites"> C[1], C[2-4,6]</PARAM> 
6</FILTER>

3.5.12 Integral

The following parameters are supported:

Option name	Required	Default	Description
`OutputFile`	✗	`session`	Prefix of the output filename to which the integrals are written.
`OutputFrequency`	✗	1	Number of timesteps after which output is written.
`OutputPrecision`	✗	7	Decimal precision with which the output is written.
`Composites`	✓	-	Composites on which to calculate the integral.

An example syntax is given below:

1<FILTER TYPE="Integral"> 
2    <PARAM NAME="OutputFile">IntegralFile</PARAM> 
3    <PARAM NAME="OutputFrequency">10</PARAM> 
4    <PARAM NAME="OutputPrecision"> 12 </PARAM> 
5    <PARAM NAME="Composites"> C[1], C[2-4,6]</PARAM> 
6</FILTER>

3.5.13 FieldConvert checkpoints

This filter applies a sequence of FieldConvert modules to the solution, writing an output file. An output is produced at the end of the simulation into session_fc.fld, or alternatively every M timesteps as defined by the user, into a sequence of files session_*_fc.fld, where * is replaced by a counter.

Module options are specified as a colon-separated list, following the same syntax as the FieldConvert command-line utility (see Section 5).

The following parameters are supported:

Option name	Required	Default	Description
`OutputFile`	✗	`session.fld`	Output filename. If no extension is provided, it is assumed as .fld
`OutputFrequency`	✗	`NumSteps`	Number of timesteps after which output is written, M.
`Modules`	✗		FieldConvert modules to run, separated by a white space.
`OutputStartTime`	✗	0	Specifies the simulation time at which to start writing checkpoint files.

As an example, consider:

1<FILTER TYPE="FieldConvert"> 
2    <PARAM NAME="OutputFile">MyFile.vtu</PARAM> 
3    <PARAM NAME="OutputFrequency">100</PARAM> 
4    <PARAM NAME="OutputStartTime"> 50.0 </PARAM> 
5    <PARAM NAME="Modules"> vorticity isocontour:fieldid=0:fieldvalue=0.1 </PARAM> 
6</FILTER>

See the Checkpoint fields filter for more details about the OutputStartTime parameter.

This will create a sequence of files named MyFile_*_fc.vtu containing isocontours. The result will be output every 100 time steps.

3.5.14 History points

The history points filter can be used to evaluate the value of the fields in specific points of the domain as the solution evolves in time. By default this produces a file called session.his. For each timestep, and then each history point, a line is output containing the current solution time, followed by the value of each of the field variables. Commented lines are created at the top of the file containing the location of the history points and the order of the variables.

The following parameters are supported:

Option name	Required	Default	Description
`OutputFile`	✗	`session`	Prefix of the output filename to which the checkpoints are written.
`OutputFrequency`	✗	1	Number of timesteps after which output is written.
`OutputOneFile`	✗	`true`	If `OutputOneFile` is `true` or `yes`, only one file is generated for all points and the whole history. Otherwise, a separate file is created for each time snapshot.
`OutputPlane`	✗	-1	If the simulation is homogeneous, the plane on which to evaluate the history point. If set, all points will be reset to lie on this plane.
`WaveSpace`	✗	false	If the simulation is homogeneous and `WaveSpace` is `true` or `yes`, the Fourier coefficient on the nearest plane will be output.
`Points`	✗	-	A list of the history points.
`line`	✗	-	`npts,x0,y0,x1,y1` in 2D or `npts,x0,y0,z0,x1,y1,z1` in 3D. Set the history points as npts equispaced points between (x0,y0,z0) and (x1,y1,z1).
`plane`	✗	-	`npts1,npts2,x0,y0,z0,x1,y1,z1,x2,y2,z2,x3,y3,z3`. Set the history points as `npts1 * npts2` equispaced points on a plane. `npts1,npts2` is the number of equispaced points in each direction and (x₀,y₀,z₀), (x₁,y₁,z₁), (x₂,y₂,z₂) and (x₃,y₃,z₃) define the plane of points specified in a clockwise or anticlockwise direction. Be careful about the size of history points file when using this option.
`box`	✗	-	`npts1,npts2,npts3,xmin,xmax,ymin,ymax,zmin,zmax`. Set the history points as `npts1 * npts2 * npts3` equispaced points in a box. `npts1,npts2,npts3` is the number of equispaced points in each direction and (x_min,y_min,z_min) and (x_max,y_max,z_max) define the limits of the box of points. Be careful about the size of history points file when using this option.

One of Points , line , plane or box must be specified.

For example, to output the value of the solution fields at three points (1,0.5,0), (2,0.5,0) and (3,0.5,0) into a file TimeValues.his every 10 timesteps, we use the syntax:

1<FILTER TYPE="HistoryPoints"> 
2    <PARAM NAME="OutputFile">TimeValues</PARAM> 
3    <PARAM NAME="OutputFrequency">10</PARAM> 
4    <PARAM NAME="Points"> 
5        1 0.5 0 
6        2 0.5 0 
7        3 0.5 0 
8    </PARAM> 
9</FILTER>

1<FILTER TYPE="HistoryPoints"> 
2    <PARAM NAME="OutputFile">TimeValues</PARAM> 
3    <PARAM NAME="OutputFrequency">10</PARAM> 
4    <PARAM NAME="line">3,1,0.5,0,3,0.5,0</PARAM> 
5</FILTER>

3.5.15 Kinetic energy and enstrophy

Note: This filter is only supported for the incompressible and compressible Navier-Stokes solvers in three dimensions.

The purpose of this filter is to calculate the kinetic energy and enstrophy

∫ ∫ Ek = --1--- ∥u∥2dx, E = --1--- ∥ω∥2dx 2μ(Ω ) Ω 2μ(Ω ) Ω

where μ(Ω) is the volume of the domain Ω. This produces a file containing the time-evolution of the kinetic energy and enstrophy fields. By default this file is called session.eny where session is the session name.

The following parameters are supported:

Option name	Required	Default	Description
`OutputFile`	✗	`session.eny`	Output file name to which the energy and enstrophy are written.
`OutputFrequency`	✓	-	Number of timesteps at which output is written.

To enable the filter, add the following to the FILTERS tag:

1<FILTER TYPE="Energy"> 
2    <PARAM NAME="OutputFrequency"> 1 </PARAM> 
3</FILTER>

3.5.16 Mean values

This filter calculates time-evolution of the averaged velocity components over the flow domain and can be used to track flow rates.

The following parameters are supported:

Option name	Required	Default	Description
`OutputFile`	✗	`session`	Prefix of the output filename to which averaged values are written.
`OutputFrequency`	✗	1	Number of timesteps after which output is written.

An example syntax is given below:

1<FILTER TYPE="Mean"> 
2    <PARAM NAME="OutputFile">mean</PARAM> 
3    <PARAM NAME="OutputFrequency">10</PARAM> 
4</FILTER>

3.5.17 Modal energy

Note: This filter is only supported for the incompressible Navier-Stokes solver.

This filter calculates the time-evolution of the kinetic energy. In the case of a two- or three-dimensional simulation this is defined as

∫ Ek (t) = 1- ∥u ∥2dx 2 Ω

However if the simulation is written as a one-dimensional homogeneous expansion so that

∑N u(x,t) = ^uk(t)e2πikx k=0

then we instead calculate the energy spectrum

∫ Ek (t) = 1- ∥^uk∥2dx. 2 Ω

Note that in this case, each component of û_k is a complex number and therefore N = HomModesZ∕2 lines are output for each timestep. This is a particularly useful tool in examining turbulent and transitional flows which use the homogeneous extension. In either case, the resulting output is written into a file called session.mdl by default.

The following parameters are supported:

Option name	Required	Default	Description
`OutputFile`	✗	`session`	Prefix of the output filename to which the energy spectrum is written.
`OutputFrequency`	✗	1	Number of timesteps after which output is written.

An example syntax is given below:

1<FILTER TYPE="ModalEnergy"> 
2    <PARAM NAME="OutputFile">EnergyFile</PARAM> 
3    <PARAM NAME="OutputFrequency">10</PARAM> 
4</FILTER>

3.5.18 Moving body

Note: This filter is only supported for the Quasi-3D incompressible Navier-Stokes solver, in conjunction with the MovingBody forcing.

This filter MovingBody is encapsulated in the forcing module to evaluate the aerodynamic forces along the moving body surface. It is described in detail in section 11.3.8.1

3.5.19 Moving average of fields

This filter computes the exponential moving average (in time) of fields for each variable defined in the session file. The moving average is defined as:

¯u = αu + (1- α )¯u n n n-1

with 0 < α < 1 and u₁ = u₁.

The same parameters of the time-average filter are supported, with the output file in the form session_*_movAvg.fld. In addition, either α or the time-constant τ must be defined. They are related by:

α = --ts-- τ + ts

where t_s is the time interval between consecutive samples.

As an example, consider:

1<FILTER TYPE="MovingAverage"> 
2    <PARAM NAME="OutputFile">MyMovingAverage</PARAM> 
3    <PARAM NAME="OutputFrequency">100</PARAM> 
4    <PARAM NAME="SampleFrequency"> 10 </PARAM> 
5    <PARAM NAME="tau"> 0.1 </PARAM> 
6</FILTER>

This will create a file named MyMovingAverage_movAvg.fld with a moving average sampled every 10 time steps. The averaged field is however only output every 100 time steps.

3.5.20 One-dimensional energy

This filter is designed to output the energy spectrum of one-dimensional elements. It transforms the solution field at each timestep into a orthogonal basis defined by the functions

ψ (ξ) = L (ξ) p p

where L_p is the p-th Legendre polynomial. This can be used to show the presence of, for example, oscillations in the underlying field due to numerical instability. The resulting output is written into a file called session.eny by default. The following parameters are supported:

Option name	Required	Default	Description
`OutputFile`	✗	`session`	Prefix of the output filename to which the energy spectrum is written.
`OutputFrequency`	✗	1	Number of timesteps after which output is written.

An example syntax is given below:

1<FILTER TYPE="Energy1D"> 
2    <PARAM NAME="OutputFile">EnergyFile</PARAM> 
3    <PARAM NAME="OutputFrequency">10</PARAM> 
4</FILTER>

3.5.21 Reynolds stresses

Note: This filter is only supported for the incompressible Navier-Stokes solver.

This filter is an extended version of the time-average fields filter (see Section 3.5.22). It outputs not only the time-average of the fields, but also the Reynolds stresses. The same parameters supported in the time-average case can be used, for example:

1<FILTER TYPE="ReynoldsStresses"> 
2    <PARAM NAME="OutputFile">MyAverageField</PARAM> 
3    <PARAM NAME="RestartFile">MyAverageRst.fld</PARAM> 
4    <PARAM NAME="OutputFrequency">100</PARAM> 
5    <PARAM NAME="SampleFrequency"> 10 </PARAM> 
6</FILTER>

By default, this filter uses a simple average. Optionally, an exponential moving average can be used, in which case the output contains the moving averages and the Reynolds stresses calculated based on them. For example:

1<FILTER TYPE="ReynoldsStresses"> 
2    <PARAM NAME="OutputFile">MyAverageField</PARAM> 
3    <PARAM NAME="MovingAverage">true</PARAM> 
4    <PARAM NAME="OutputFrequency">100</PARAM> 
5    <PARAM NAME="SampleFrequency"> 10 </PARAM> 
6    <PARAM NAME="alpha"> 0.01 </PARAM> 
7</FILTER>

3.5.22 Time-averaged fields

This filter computes time-averaged fields for each variable defined in the session file. Time averages are computed by either taking a snapshot of the field every timestep, or alternatively at a user-defined number of timesteps N. An output is produced at the end of the simulation into session_avg.fld, or alternatively every M timesteps as defined by the user, into a sequence of files session_*_avg.fld, where * is replaced by a counter. This latter option can be useful to observe statistical convergence rates of the averaged variables.

This filter is derived from FieldConvert filter, and therefore support all parameters available in that case. The following additional parameter is supported:

Option name	Required	Default	Description
`SampleFrequency`	✗	1	Number of timesteps at which the average is calculated, N.
`RestartFile`	✗		Restart file used as initial average. If no extension is provided, it is assumed as .fld

As an example, consider:

1<FILTER TYPE="AverageFields"> 
2    <PARAM NAME="OutputFile">MyAverageField</PARAM> 
3    <PARAM NAME="RestartFile">MyRestartAvg.fld</PARAM> 
4    <PARAM NAME="OutputFrequency">100</PARAM> 
5    <PARAM NAME="SampleFrequency"> 10 </PARAM>           
6</FILTER>

This will create a file named MyAverageField.fld averaging the instantaneous fields every 10 time steps. The averaged field is however only output every 100 time steps.

3.5.23 ThresholdMax

The threshold value filter writes a field output containing a variable m, defined by the time at which the selected variable first exceeds a specified threshold value. The default name of the output file is the name of the session with the suffix _max.fld. Thresholding is applied based on the first variable listed in the session by default.

The following parameters are supported:

Option name	Required	Default	Description
`OutputFile`	✗	session_max.fld	Output filename to which the threshold times are written.
`ThresholdVar`	✗	first variable name	Specifies the variable on which the threshold will be applied.
`ThresholdValue`	✓	-	Specifies the threshold value.
`InitialValue`	✓	-	Specifies the initial time.
`StartTime`	✗	0.0	Specifies the time at which to start recording.

An example is given below:

1  <FILTER TYPE="ThresholdMax"> 
2      <PARAM NAME="OutputFile"> threshold_max.fld </PARAM> 
3      <PARAM NAME="ThresholdVar"> u </PARAM> 
4      <PARAM NAME="ThresholdValue"> 0.1 </PARAM> 
5      <PARAM NAME="InitialValue">  0.4 </PARAM> 
6  </FILTER>

which produces a field file threshold_max.fld.

3.5.24 ThresholdMin value

Performs the same function as the ThresholdMax filter (see Section 3.5.23) but records the time at which the threshold variable drops below a prescribed value.

3.5.25 Maximun/minimun fields

This filter computes the local (pointwise) maximum or minimum field for each variable, including the addition variables for compressible flow solver, over the simulation.

The following parameters are supported:

Option name	Required	Default	Description
`MaxOrMin`	✓	max	Type of fields to compute. It can be either `max` or `min`.
`RestartFile`	✗	∓9999	Restart file used for initial comparison. If it is not provided, -9999 will be used for the `max` filter while 9999 will be used for the `min` filter. Output filename to which the threshold times are written.
`OutputFile`	✗	session_max.fld	Output filename to which the threshold times are written.
`OutputFrequency`	✗	1	Number of timesteps after which output is written.
`SampleFrequency`	✗	1	Number of timesteps after which the fields are used to compute max/min.

An example is given below:

1  <FILTERS> 
2    <FILTER TYPE="MaxMinFields"> 
3      <PARAM NAME="MaxOrMin">max</PARAM> 
4      <PARAM NAME="RestartFile">Baseflow.fld</PARAM> 
5      <PARAM NAME="OutputFile">DisturbedFields</PARAM> 
6      <PARAM NAME="OutputFrequency">100</PARAM> 
7      <PARAM NAME="SampleFrequency">1</PARAM> 
8    </FILTER> 
9  </FILTERS>

3.5.26 Python script

Note: This feature is only supported if Python support is enabled with the NEKTAR_BUILD_PYTHON flag enabled at configuration time.

The aim of this filter is to permit the execution of a Python script to implement more complex programmatic filters, but with the ease-of-use of the Python environment. Python filters mimic the action of C++ filters, and thus have three separate phases that should be implemented:

an initialisation phase, which is called when the filter is constructed;
an update phase, which is called typically at the end of a timestep;
a finalise phase, which is called at the end of the simulation.

Given a Python file as input, the filter can operate in one of two ways:

If only the Python file is supplied, then Nektar++ will try to call three Python functions: filter_initialise, filter_update and filter_finalise. Each function is passed a list of the ExpList fields, and the value of the solver time t.
If, in addition to the Python file, a filter name is supplied, then Nektar++ assumes that your Python file creates a subclass of the Filter class which has been registered with the Filter factory.

The following parameters are supported:

Option name	Required	Default	Description
`PythonFile`	✓	-	Name of the Python file to load.
`FilterName`	✗	-	Optional name of filter if Python subclass is implemented.

An example is given below:

1  <FILTERS> 
2    <!-- Python filter with function approach --> 
3    <FILTER TYPE="Python"> 
4      <PARAM NAME="PythonFile"> FilterPython_Function.py </PARAM> 
5    </FILTER> 
6    <!-- Python filter with class approach --> 
7    <FILTER TYPE="Python"> 
8      <PARAM NAME="PythonFile"> FilterPython_Class.py </PARAM> 
9      <PARAM NAME="FilterName"> TestFilter </PARAM> 
10    </FILTER> 
11  </FILTERS>

For the first example, a sample Python script may look something like:

1def filter_initialise(fields, time): 
2   pass 
3 
4def filter_update(fields, time): 
5   pass 
6 
7def filter_finalise(fields, time): 
8   pass

For the second example, we might expect something like:

1from NekPy.SolverUtils import Filter 
2 
3class TestFilter(Filter): 
4   def __init__(self, session, eqsys, params): 
5      # Call super’s constructor. 
6      super().__init__(session, eqsys) 
7      # Counter which is incremented at each timestep. 
8      self.num = 0 
9 
10   def Initialise(self, fields, time): 
11      pass 
12 
13   def Update(self, fields, time): 
14      self.num += 1 
15 
16   def Finalise(self, fields, time): 
17      # Print for testing purposes 
18      print(self.num) 
19 
20   def IsTimeDependent(self): 
21      return True 
22 
23# Register filter with factory. 
24Filter.Register("TestFilter", TestFilter)

3.5.27 Body-fitted velocity fields

The BodyFittedVelocity filter projects the velocity fields in the Cartesian coordinate system into a body-fitted coordinate system. Meanwhile the user can chose to record the local (pointwise) maximum or minimum for the body-fitted velocity components, or simply output their original values. This filter is designed for both compressible flow solver and incompressible flow solver.

The following parameters are supported:

Option name	Required	Default	Description
`BodyFittedCoordinateFile`	✓	N/A	Body-fitted coordinate system generated by FieldConvert module. See 5.6.40 for reference.
`RestartFile`	✓	N/A	Restart file for the initial field for body-fitted velocity components u_bfc and v_bfc (and w_bfc for 3D cases). This restart file is necessary in the currtnt filter. The restart file can use the same output of the FieldConvert modul as well. See 5.6.40 for reference
`OriginalOrMaxOrMin`	✗	original	Type of fields to compute. It can be `original` or `max` or `min`.
`OutputFile`	✗	session_max.fld	Output filename to which the threshold times are written.
`OutputFrequency`	✗	1	Number of timesteps after which output is written.
`SampleFrequency`	✗	1	Number of timesteps after which the fields are used to compute original/max/min.

An example is given below:

1  <FILTERS> 
2    <FILTER TYPE="BodyFittedVelocity"> 
3      <PARAM NAME="RestartFile">bfcFile.fld</PARAM> 
4      <PARAM NAME="BodyFittedCoordinateFile">bfcFile.fld</PARAM> 
5      <PARAM NAME="OriginalOrMaxOrMin">max</PARAM> 
6      <PARAM NAME="OutputFile">vel_bfc</PARAM> 
7      <PARAM NAME="OutputFrequency">100</PARAM> 
8      <PARAM NAME="SampleFrequency">1</PARAM> 
9    </FILTER> 
10  </FILTERS>

3.5.28 Lagrangian points Tracking

The FilterLagrangianPoints filter tracks Lagrangian points in parallel. The following parameters are supported:

Option name	Required	Default	Description
`OutputFile`	✗	Session name	OutputFile_R%05d_T%010.6lf.plt is output file name for the Lagrangian points. R is followed by the thread number and T is followed by the instantaneous time.
`OutputFrequency`	✗	1	Output frequency of the Lagrangian points.
`Box_n`	✓	N/A	Box_n = Nx,Ny,Nz, xmin,xmax, ymin,ymax, zmin,zmax. Points defined by a box that initially owned by the thread n. At least one box needs to be assigned
`RootOutputL2Norm`	✗	0	Root thread outputs the L2 norm of the physics values over the points if RootOutputL2Norm is 1.
`FrameVelocity`	✗	0	The frame velocity which will be subtracted from the points’ velocity.
`IntOrder`	✗	1	Time integration order for points tracking. The points will be set as stationary if IntOrder is 0.

An example is given below:

1  <FILTERS> 
2    <FILTER TYPE="LagrangianPoints"> 
3      <PARAM NAME="OutputFile">Points</PARAM> 
4      <PARAM NAME="OutputFrequency">10</PARAM> 
5      <PARAM NAME="Box_0">0, 1,32,0.3,0.6,0.0,0.49</PARAM> 
6      <PARAM NAME="Box_1">32, 1,32,0.3,0.6,0.51,1.0</PARAM> 
7      <PARAM NAME="RootOutputL2Norm">1</PARAM> 
8    </FILTER> 
9  </FILTERS>

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