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Invitation to the Mathematical Colloquium

Wednesday, January 29, 2025, conference room (R107), 5 p.m. s.t.

Dr. Andrea Thomann, MACARON research team Inria center University of Lorraine and antenne University Strasbourg

will speak on the topic: "Numerical challenges of hyperbolic multi-scale equations illustrated at the case of ideal magnetohydrodynamics"

Abstract: We are concerned with the resolution of systems of hyperbolic conservation laws which contain several stiff terms in the flux function which describes the dynamics of the evolved variables.
These stiff terms can be associated to small paramters which have physical significance, e.g. the Mach number which describes the flow regime of a fluid with respect to the sound speed in the given system. Another important parameter is the so-called Alfvén number, which describes the influence of magnetic fields on the fluid. This arises for instance in the simulation of plasma flows in Tokamaks whose hydrodynamic aspect is modelled by the magneto-hydro-dynamic equations, short MHD equations. Such flows can cover a wide range of Mach and Alfvén numbers. Thus it is very important to have a numerical scheme which yields relieable results in all regimes and is able to satisfy physical constraints dictated by the problem. One constraint is the so-called solenoidal property of the magnetic field, which is mathematically speaking the preservation of the divergence free property of the magnetic field.Furthermore, it was shown that as the Mach number tends to zero, a transition from compressible to incompressible flow can be observed, which is the so-called asymptotic preserving property.
In this talk we will discuss the numerical challenges when constructing an efficient numerical scheme for such a multi-scale problem and present a novel structure-preserving scheme. The numerical method is illustrated on a series of test cases for the ideal MHD equations in several Mach and Alfvén number regimes highlighting the properties of the numerical method.

Starting at 16:30, there will be an opportunity for all interested parties to talk over coffee and tea in the meeting room (R206).

Olaf Ippisch

Organizer: Institute of Mathematics, Erzstraße 1, 38678 Clausthal-Zellerfeld

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