# Random walk source model in fluid dynamics

We find fluid dynamics around us without noticing it: In weather phenomena, wave movement in the ocean, in the drag of our car, in the flow through pipes or even the blood flow through our vanes, in the lift of airplanes, the power generated from wind turbines, or the field of climate change science.

The fluid dynamics is a field of interest that has developed very much in the last two centuries. Typical is a close relation between experiment and theory. The Navier- Stokes equations have been formulated relatively early, but useful solutions for broader tasks were available with the use of numerical computer solutions in the 1980 ‘s.

Today we try to use computer models which simulate each particle which is involved in fluid movement following the equation of continuity, feel inertia, pressure and viscosity to understand more about fluid dynamics.

In connection with the equation of continuity a model for unsteady potential flow in ideal fluids, called the “random walk source model” was published by one of the members of the group (Meyer 1997). In this model, it is possible to observe the shape of a front of particles coming out of a line source, creeping towards and around a wing section. It was shown that the lift coefficient could be explained by the difference of creeping distance of the fronts, which was segregated by the wing section and extended with a separation line to maintain the Kutta condition. In the next approach the deflection of the path of the common center of gravity of the particle cloud was observed while the particles where moving past the profile .

The path of the common center of gravity shows a deflection as the result of the geometry which acts as an obstacle to the particle front. The deflection in the path can be seen as the result of the addition of a vertical velocity on the particles while passing the profile, explaining a part of the drag of objects.

The model delivers an unusual view on fluid phenomena using a new on the Western Norway University of applied Sciences developed random walk algorithm.

The task of the research group is to find answers on:

- How can we use the model to understand more of fluid dynamics?
- How can we extend the model for future use?

## Head of Research Group

## Runald Walter Meyer

Associate Professor