WK Differential Equations - Student Member:
Nikolaus Viertl

Address:
Institute of Fluid Dynamics and Heat Transfer
Vienna University of Technology
Resselgasse 3
A-1040 Wien
Austria

Telephone: +43 1 58801 32221
Fax: +43 1 58801 32299
Email: nviertl@fluid.tuwien.ac.at

Advisor: Alfred Kluwick
Co-advisor: Christian Schmeiser

Research: Small amplitude waves in two-layer shallow water flows are -- under certain circumstances -- described by a hyperbolic pde with a non-convex flux-function. Admissible shocks in that case, in contrast to the case of a convex flux, depend on the regularization; Non-classical shocks (violating the Oleinik criteria) are possible.
We study the regularization of these weak shocks, leading to a distinguished limit, described by a triple-deck problem, with a nonlinear interaction equation in the form of a forced modified kdv equation.
On the one hand a limiting solution of this triple-deck problem was found, which describes a non-classical shock of the hyperbolic problem. On the other hand we look for a numerical method for the full triple-deck problem.

Diploma thesis: On the outflow of a funnel; advisor: H. Steinr|ck