Computation plays an increasingly important role in several fields of astrophysics, where theoretical work is now often driven by numerical results coming from hydrodynamic and magneto-hydrodynamic (MHD) codes. There remain several technical problems, a prime example of which is the need to include multi-dimensional flow effects when treating electric fields in divergence-free MHD codes. This project will build on recent advances in order to arrive at a genuinely three-dimensional Riemann solver for hydrodynamics and MHD and their relativistic variants. The work will also devise very low dissipation and large time-step versions of the multidimensional Riemann solvers. Integrating the resulting solvers with very efficient higher order algorithms for adaptive calculations will produce astrophysical adaptive mesh refinement codes with extremely high scalability to hundreds or thousands of processors. The result will be a new class of higher order schemes for simulating hyperbolic systems.

Although astrophysical codes are widely used, they are often not very well understood: to help bridge this gap, Dr. Balsara is writing a pedagogical textbook, and some of the codes embodying techniques developed in the present project will be freely distributed to complement the textbook. Of course, these techniques are applicable to several exciting areas of astrophysics. Students and postdoctoral researchers involved in this study will receive well-organized interdisciplinary training through a coordinated educational plan.

Project Report

Intellectual Merit: The ability to simulate high temperature plasmas that are threaded by magnetic fields falls unser a discipline called numerical magnetohydrodynamics. This is a very important field of research because it impacts computational astrophysics. But it also has an impact of fusion-based energy generation, which bears the promise of supplying mankind with an almost limitless supply of green energy. There were several numerical challenges in developing numerical methods for MHD. It was well-recognized in the scientific community that the principal challenge was the development of a multidimensional Riemann solver. This was the task that we were charged to resolve via the peer review process. Outcomes: Over the last four years we have developed multidimensional Riemann solver methods for carrying out astrophysical MHD simulations. The core algorithms have been documented in Balsara (2010, 2012, 2014), Balsara, Dumbser & Abgrall (2014), Balsara & Dumbser (2014) and Kim & Balsara (2014). We have also developed two-fluid models for application to molecular cloud physics and star formation with the help of two graduate students. This line of research has been published in Meyer et al. (2014)and Burkhart et al. (2014). Broader Impact: Another very important activity was the development of an educational website. Please see: www.nd.edu/~dbalsara/Numerical-PDE-Course Via that website, we are making codes as well as polished instructional material on how to use those codes freely available to the community. The website includes lectures on multidimensional Riemann solvers, which is the topic of this NSF grant. It also provides instructional lectures on parallel computing, which is the topic of other NSF grants.

Agency
National Science Foundation (NSF)
Institute
Division of Astronomical Sciences (AST)
Type
Standard Grant (Standard)
Application #
1009091
Program Officer
Nigel Sharp
Project Start
Project End
Budget Start
2010-09-15
Budget End
2014-08-31
Support Year
Fiscal Year
2010
Total Cost
$362,747
Indirect Cost
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