In the project P 35485-N (starting 2022) we study the numerical time integration of the equations of magneto-hydrodynamics for solar physics. Efficient and reliable numerical methods are essential for computationally feasible realistic simulations. Our approach also applies to problems in biology or mathematical finance. Splitting methods treat operators with different mathematical properties and physical significance separately. To increase efficiency and reliability, we use adaptive time-stepping to extend the scope of current theoretical studies of our sun by allowing higher resolution and guaranteed accuracy. The methods will allow refined numerical simulations of convective stellar surfaces. The evolution of the dynamical variables will be probed by observational data, which will benefit from the interaction between modellers and observers enabling refinement of the simulations while the computational results will suggest new observing campaigns. For further activities of our group, see also https://acore.univie.ac.at/.

Involved researchers:

Othmar Koch (PI, Wolfgang Pauli Institute Vienna)
Friedrich Kupka (National research partner, University of Applied Sciences Technikum Wien)
Norbert Mauser (National research partner, University of Vienna, research platform MMM)
Inmaculada Higueras (International cooperation partner, Universidad Publica de Navarra)
Roger Käppeli (International cooperation partner, ETH Zurich)
Siddharta Mishra (International cooperation partner, ETH Zurich)




So far, the project yielded the following articles and preprints and oral presentations and organized the following events. A collection of splitting methods constructed in the course of the project or taken from the literature and assessed as to their merits for computational purposes can be found at http://www.othmar-koch.org/splitting/.

Refereed Papers


• O. Koch, K. Acar, W. Auzinger, F. Kupka, and B. Moser, Adaptive exponential multi-operator splitting for MHD, submitted.
  
  You can download a preprint of this paper from https://arxiv.org/abs/2302.01092.
  
  
  

Oral Presentations

• W. Auzinger, Adaptive Exponential Splitting, joint with O. Koch. FAATNA 22 - Functional Analysis, Approximation Theory and Numerical Analysis, Matera, Italy, July 2022.
  
  
• O. Koch, joint with K. Acar, W. Auzinger, D. Hoffmann, F. Kupka, and B. Moser, Adaptive exponential multi-operator splitting for MHD, Austrian Numerical Analysis Day 2023, Vienna, April 2023.
  
  You can view the abstract of this talk here.
  
  
• Y. Zhang, joint with O. Koch, F. Kupka, and Norbert Mauser, Numerical Methods for Hydrodynamic Simulations and Linear Stability Analysis, Working group on 'Numerical methods for solar simulations', Vienna, January 2024.
  
  You can view the abstract of this talk here.
  
  
• I. Higueras, joint with O. Koch and F. Kupka, IMplicti-EXplicit time stepping methods for some problems in astrophysics, Working group on 'Numerical methods for solar simulations', Vienna, January 2024.
  
  You can view the abstract of this talk here.
  
  
• I. Higueras, joint with O. Koch, F. Kupka, and T. Roldan, IMplicit-EXplicit time stepping methods for stiff problems in astrophysics, Innovations in the Numerical Treatment of Stiff Differential Equations, Rome, February 2024.
  
  You can view the abstract of this talk here.
  
  
  

Events

• Working group on Numerical methods for solar simulations, organised by O. Koch, F. Kupka, and N.J. Mauser
  
  within the thematic program 'Models in Plasmas, Earth and Space Science' of the Wolfgang Pauli Institute Vienna.
  
  Details are given here.
  
  
  

This project is funded by FWF - The Science Fund

page written by Othmar Koch. last modification: Tue Feb 13 14:00 MET 2024