Research Projects

Computational Magnetohydrodynamics with Discrete Differential Forms

Principal investigators

  • Prof. Dr. Ralf Hiptmair, Seminar for Applied Mathematics, ETH Zurich
  • Prof. Dr. Siddharta Mishra, Seminar for Applied Mathematics, ETH Zurich

Researcher

  • Cecilia Pagliantini, Seminar for Applied Mathematics, ETH Zurich

Start date: 01.04.2013 / End date: 31.03.2016

Description

The study of the interaction of conducting fluids with electromagnetic fields is of core importance for many natural phenomena and industrial processes. Conducting fluids like plasmas are widely studied in many fields ranging from astrophysics and solar physics, to aerospace and electrical engineering.
A widely used macroscopic model of plasmas is provided by the equations of magneto-hydrodynamics (MHD), a mixed hyperbolic-parabolic system which couples balance equations for mass, momentum and energy together with material laws to the magneto-quasistatic Maxwell‚s equations for the electromagnetic fields. In particular, resistive MHD model, which will be the focus of this project, also takes into account change in the magnetic topology during the flow (magnetic reconnection). Due to the strongly non-linear hyperbolic character of the MHD system, the solutions display very high speeds of propagation and the emergence of shock waves. In addition, the zero divergence constraint for the magnetic induction is pre- served. These features together with the resistive term pose major challenges for a stable and accurate numerical discretization of the model.
In the present project, we aim at developing a new approach for the numerical treatment of resistive MHD where a Galerkin discretization of the electromagnetic part based on finite element exterior calculus (FEEC) will be coupled to advanced finite volume methods for the approximation of the balance laws for the fluid. The time discretization will rely on combined implicit-explicit Runge-Kutta timestepping using fast iterative solvers for the magnetic diffusion. See also SNF project page

Collaborations

  • Dr. Holger Heumann, Laboratoire J.A.Dieudonné, UMR CNRS-UNS N°7351, Université de Nice Sophia-Antipolis

References

  • H. Heumann and R. Hiptmair. Stabilized Galerkin methods for magnetic advection, M2AN Math. Mod. and Num. Anal. (2013), SAM Report 2012-26 , doi

Funding

  • SNF Project 146355

Contact

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