# Conservative Interpolation

The conservative interpolation computest the Right Hand Side force $f$ (computation of the source $f$ is described in [^1]) of an partial differential equation

$$\int_\Omega f \varphi {\mathrm {d}} \Omega \, ,$$

using first order nodal FEM to solve the system of equations [^2]. If you would like to use the conservative filters for higher oder FEM, please contact Stefan Schoder

## Theory - Publication

This publication covers the theory of the implemented conservative interpolation filters. When using the conservative filters please provide a citation in you publication:

Schoder, Stefan, et al. "Application limits of conservative source interpolation methods using a low Mach number hybrid aeroacoustic workflow." Journal of Theoretical and Computational Acoustics (2020).

and provide an acknowledge the usage at the end of the publication

The computational results presented have been achieved [in part] using the software openCFS [Cell Centroid Conservative Interpolation/Cut Volume Cell Conservative Interpolation].

If you have questions related to the interpolators please contact the corresponding author of the publication. For further development and future publications on the topic, we are happy to colaborate wit your research unit (company or university).

## Simulation setup

During the simulation setup, we will discuss how the variables inside the publication relate to the xml-scheme of the simulation setup. Having this knowledge, it should be able for you to start your own simulation using conservative interpolators. CGNS or ENSIGHT input data is supported.

<?xml version="1.0" encoding="UTF-8"?>
<cfsdat ...>
<pipeline>

<stepValueDefinition>
...
</stepValueDefinition>

<meshInput id="inputFilter" gridType="fullGrid">
...
</meshInput>
...
<interpolation type="TYPE" id="interp" inputFilterIds="inputFilter">
<targetMesh>
<hdf5 fileName="../mesh.h5"/>
</targetMesh>
<singleResult>
<inputQuantity resultName="..."/>
<outputQuantity resultName="..."/>
</singleResult>
<regions>
<sourceRegions>
<region name="..."/>
</sourceRegions>
<targetRegions>
<region name="..."/>
</targetRegions>
</regions>
</interpolation>
...
<meshOutput id="acousticSources" inputFilterIds="interp">
...
</meshOutput>

</pipeline>
</cfsdat>


### Cell Centroid Conservative Interpolation

The cell centroid interpolator is defined by the type variable FieldInterpolation_Conservative_CellCentroid.

type="FieldInterpolation_Conservative_CellCentroid"


Based on the following grafics, the interpolation is carried out:

### Cut Volume Cell Conservative Interpolation

The cut volume cell centroid interpolator is defined by the type variable FieldInterpolation_Conservative_CutCell.

type="FieldInterpolation_Conservative_CutCell"


Based on the following grafics, the interpolation is carried out:

# References

[^1]: Stefan Schoder, Klaus Roppert, Michael Weitz, Clemens Junger, and Manfred Kaltenbacher. Aeroacoustic source term computation based on radial basis functions. International Journal for Numerical Methods in Engineering, 121$9$:2051–2067, 2020.

[^2]: Stefan Schoder, Andreas Wurzinger, Clemens Junger, Michael Weitz, Clemens Freidhager, Klaus Roppert, and Manfred Kaltenbacher. Application limits of conservative source interpolation methods using a low mach number hybrid aeroacoustic workflow. Journal of Theoretical and Computational Acoustics, 2020.