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

计算在天体物理学的几个领域中扮演着越来越重要的角色，在这些领域中，理论工作现在经常由来自流体力学和磁流体力学（MHD）代码的数值结果驱动。仍然存在一些技术问题，其中一个主要的例子是在无散度MHD代码中处理电场时需要包括多维流动效应。该项目将建立在最近的进展，以达到一个真正的三维黎曼解算流体力学和MHD及其相对论变体。该工作还将设计非常低耗散和大时间步长的多维黎曼解算器版本。将结果求解器与非常高效的高阶自适应计算算法集成，将产生具有极高可扩展性的天体物理自适应网格细化代码，可扩展到数百或数千个处理器。结果将是一类新的用于模拟双曲系统的高阶格式。尽管天体物理代码被广泛使用，但它们往往不被很好地理解：为了弥补这一差距，巴尔萨拉博士正在编写一本教学教科书，一些体现了本项目开发的技术的代码将免费分发，以补充教科书。当然，这些技术也适用于天体物理学的几个令人兴奋的领域。参与本研究的学生和博士后研究人员将通过协调的教育计划接受组织良好的跨学科培训。

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.