Multidimensional Riemann Solvers and Higher Order Schemes with AMR for Computational Astrophysics

University Of Notre Dame, Notre Dame IN

Investigators

Abstract

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.