Research Projects

Well-balanced schemes for astrophysical applications

Principal investigators

  • Dr. Roger Käppeli, Seminar for Applied Mathematics, ETH Zurich
  • Prof. Dr. Siddhartha Mishra, Seminar for Applied Mathematics, ETH Zurich

Start date: / Last update: 18.02.2016

Description

In this project we develop well-balanced schemes especially tailored to the needs of computational astrophysics. Many interesting phenomena in astrophysics happen as a small perturbation of a certain stationary state. For instance convection inside stars, important for heat transport and the mixing of chemical elements, occurs on top of hydrostatic equilibrium. In this regime, pressure forces are almost balanced by gravitational forces. However, the adequate numerical resolution of these near stationary states is challenging for many standard schemes. This is due to their difficulty in respecting the subtle balance between the flux divergence and the gravitational source term at the discrete level. Numerical schemes that are able to preserve exactly a discrete equivalent of the balance between flux divergence and source term are termed as well-balanced. These types of schemes have been realized to be crucial in the accurate numerical simulation in many applications. Ongoing research focuses on the development of schemes sufficiently general for the coupling with complex multiscale and multiphysics algorithms commonly encountered in astrophysics.

References

  • R. Käppeli and S. Mishra. A well-balanced finite volume scheme for the Euler equations with gravitation, Astronomy and Astrophysics, 587/A94 (2016), SAM Report 2015-40 , doi
  • A. Perego, R. Cabezón and R. Käppeli. An advanced leakage scheme for neutrino treatment in astrophysical simulations, The Astrophysical Journal Supplement Series, 223/22 (2016), SAM Report 2015-41 , doi
  • R. Käppeli and S. Mishra. Well-balanced schemes for gravitationally stratified media, Astronomical Society of the Pacific Conference Series, 498 (2015), pp. 210-210, SAM Report 2014-37 , doi
  • R. Käppeli and S. Mishra. Well-balanced schemes for the Euler equations with gravitation, Journal of Computational Physics, 259 (2014), pp. 199-219, SAM Report 2013-05 , doi
  • R. Käppeli and S. Mishra. Structure preserving schemes, Proc. ASTRONUM 2013, 488 (2014), pp. 231, SAM Report 2014-02 , doi

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