# Lighthill Source Term¶

The Lighthill source term filter computes aeroacoustic source terms based on Lighthills analogy for incompressible flows. Therefore, first the Lighthill source term vector is computed

\begin{equation} \nabla \cdot [T] = \nabla(\frac{1}{2} u \cdot u ) + L \, , \end{equation}

with $u$ as velocity, and $L$ as Lamb vector, and $[T]$ as the Lighthill stress tensor. Finally, as actual source term the divergence of the source term vector is computed and establised as outputQuantity.

\begin{equation} \nabla \cdot \nabla \cdot [T] = \nabla \cdot (\nabla(\frac{1}{2} u \cdot u ) + L) \end{equation}

It is possible to compute the Lighthill source term only based on the velocity, or on the velocity and the vorticity. If only the velocity is defined the vorticity is computed internally.

• The epsilonScaling Parameter scales the radial basis functions used for computing spatial derivatives. It controlls the "smoothness" of the basis function. The smoother the gauss-like surface is, the better the results will be BUT only until a certain number, when the matrix becomes to ill-contioned, which will result in very bada results. Typical values: 1e-1 - 1e-4.
• The kScaling parameter is an optional parameter and defines a constant term that is added to the radial basic function.
• The betaScaling parameter defines the slope of a linear term that is added to the radial basis function.
• The logEps Parameter enables a detailes console output (minimal distance, maximal distance, optimized parameters). Therefore, it should only be used if the spatial derivatives are investigated, because it totally spams the console
• The density parameter is only meaningful to be a scalar, because the implementation only considers the incompressible case, where a spatially and temporally constant density is assumed.

<aeroacoustic type="AeroacousticSource_LighthillSourceTerm" inputFilterIds="..." id="...">
<RBF_Settings  epsilonScaling="1e-4"  kScaling="" betaScaling="" logEps=false/>
<sourceSum>true</sourceSum>
<targetMesh>
<hdf5 fileName="..."/>
</targetMesh>
<ResultList>
<velocity resultName="..."/>
<vorticity/>
<density/>
<outputQuantity resultName="..."/>
</ResultList>
<regions>
<sourceRegions>
<region name="..."/>
</sourceRegions>
<targetRegions>
<region name="..."/>
</targetRegions>
</regions>
</aeroacoustic>



## Acknowledgement¶

Please provide an acknowledgement at the end of your publication using this software part for simulations

The computational results presented have been achieved [in part] using the software openCFS [FE-based Interpolation].