3.4 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:

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.

3.4.1 Phase sampling

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_T T , 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:

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

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} = ⋅ 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.

3.4.2 Aerodynamic forces

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:

An example is given below:

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.

3.4.3 Benchmark

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

• 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.

3.4.4 Cell history points

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.

• 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.

3.4.5 Checkpoint cell model

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

• 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.

3.4.6 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.

The following parameters are supported:

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

3.4.7 Electrogram

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

• 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.

3.4.8 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:

As an example, consider:

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

3.4.9 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:

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:

3.4.10 Kinetic energy and enstrophy

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

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:

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

3.4.11 Modal energy

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

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

then we instead calculate the energy spectrum

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:

An example syntax is given below:

3.4.12 Moving body

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 11.3.4.1

3.4.13 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:

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:

where t_s is the time interval between consecutive samples.

As an example, consider:

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.

3.4.14 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

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:

An example syntax is given below:

3.4.15 Reynolds stresses

This filter is an extended version of the time-average fields filter (see Section 3.4.16). 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:

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:

3.4.16 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:

As an example, consider:

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.

3.4.17 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:

An example is given below:

which produces a field file threshold_max.fld.

3.4.18 ThresholdMin value

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