Invited Talk (Mathematics)

Numerical modelling of complex compressible flow

prof. Mária Lukáčová-Medviďová Institute of Mathematics,
Johannes Gutenberg University, Mainz, Germany

Abstract

Complex compressible flows appear in many areas of applications. Let us mention, e.g., airflow around an airplane, motion of oceans or rivers, atmospheric flows or blood flow. All of these examples can be governed by three fundamental physical laws: the conservation of mass, momentum and energy. Mathematically we will obtain a nonlinear system of partial differential equations of parabolic-hyperbolic type. In the talk we will discuss well-posedness (existence and uniqueness of solution) for these equations as well as suitable numerical methods for their discretization. The reliability of numerical schemes will be illustrated on a series of numerical experiments.

The present research has been done in cooperation with K.W. Morton (Oxford), G. Warnecke (Magdeburg) and S. Noelle (Aachen).