# Viscous vortex particle wake

{% hint style="warning" %}
The viscous vortex particle wake is currently in development. It may be available in a future release of the APM Solver, if it passes all tests successfully. 
{% endhint %}

Currently, the APM Solver uses doublet panels to model the wake. The doublet panel wake does not model the effect of viscous diffusion. However, the effect of viscous diffusion can be modelled by a vortex particle wake.

Two rows of wake panels are used to couple the vortex particle wake to the unsteady panel method. The first row of panels satisfies the Kutta condition at the trailing edge, and the second row of panels is transformed to vortex particles. The second row is referred to as "buffer". The buffer row enables the coupling of the unsteady panel method and the vortex particle wake. After the buffer panels, the wake vorticity field is modelled by the vortex particles. The particles are obtained by equating each buffer panel to a vortex particle using the Hess equivalence principle. The image below shows a schematic of the buffer panels and their conversion to vortex particles.

![Conversion of wake panels to vortex particles](/files/-MhUhQM0n5k8B0De11o6)

The image below shows a simulation of the NACA4412 wing using a vortex particle wake.

![Simulation of a NACA4412 wing using vortex particle wake](/files/-MhTYIraj2wSUkEmbJFE)

{% embed url="<https://youtu.be/58pXSrcmdiQ>" %}
Vortex particle wake development for a NACA 4412 wing
{% endembed %}

{% embed url="<https://youtu.be/Xy3a95MqEIo>" %}
Vortex particle wake for the NREL Phase IV wind turbine
{% endembed %}


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