von Karman Institute Lecture Series and Events

Presented by Prof. Miguel Hermanns from the Universidad Politécnica de Madrid

When solving large and complex fluid dynamic problems, the use of high-order finite difference methods leads to reduced computational costs and memory requirements. However, high-order finite difference methods tend to become unstable in the presence of boundaries and the imposition of boundary conditions. Different theoretical approaches exist to overcome these limitations, like the GKS theory or the summation-by-parts rule. Although all these approaches have shown to indeed lead to finite difference methods of orders q = 4 to 8, the extension to even higher orders seems to be too cumbersome or unclear.

In the present work a different approach is followed, namely the idea that the Runge phenomenon is behind the observed stability problems. 

By following the philosophy behind the Chebyshev interpolation theory, a non-uniform grid point distribution for piecewise polynomial interpolations of degree q N is developed, being N+1 the number of grid points. The application of the developed methods to standard evolution problems like wave equation or convection-dffusion equation shows that the methods are stable for orders well beyond q = 10, recovering even the spectral accuracy in the limit q = N. Applications to stability analyses of fluid dynamic problems will also be presented, showing that the developed finite difference methods outperform in terms of accuracy and speed all the other existing finite difference methods and even the Chebyshev collocation method.

Biography:

Prof. Miguel Hermanns holds a PhD (2006) in Aerospace Engineering from the Universidad Politécnica de Madrid (Spain) and a Masters Degree (2001) in Experimental and Numerical Fluid Dynamics from the von Karman Institute for Fluid Dynamics (Belgium). He teaches nowadays Fluid Mechanics and Heat Transfer at the School of Aerospace Engineering at the Universidad Politécnica de Madrid. His research has been mainly focused on the modeling of physical processes that involve fluids and energy exchanges and in the development and application of high order numerical methods to all kinds of problems. In recent years, he has completely changed his research area, being now mainly focused on energy efficiency issues in buildings and more recently on geothermal energy.

Location : Conference room, Chaussée de Waterloo 72, 1640 Rhode-St-Genèse

Free entrance, on registration