Collaborative Research: High Order Accurate Weighted Essentially Non-Oscillatory Algorithms with Applications to Cosmological Hydrodynamic Simulations

AST-0506734 Shu本项目将试图把联合收割机算法的发展与流体动力学模拟中的宇宙学应用结合起来，以便为求解高速、高马赫数、含有强激波和其它复杂流动结构的无粘流而开发高精度、加权的基本无振荡格式。 目标是发展有效和强大的数值方法，宇宙学的应用，并考虑再电离时代的流体动力学，周围的暗物质奇点重子气体的流体动力学行为，星系际介质和暗物质之间的统计差异在非线性制度的集群，引力冲击的熵产生，和其他复杂的结构问题。 解决宇宙学的独特困难，如极强奇点的存在以及双曲流体动力学方程与自引力椭圆方程的有效耦合，需要计算数学和科学计算的进步。更广泛的影响包括加强两所大学的合作，推进天体物理学的数学复杂性，并使算法和通用代码可用于更广泛的天体物理学，物理学和工程社区。

AST-0506734ShuThis project will attempt to combine algorithm development for high order accurate, weighted essentially non-oscillatory schemes for solving high speed, high Mach number inviscid flows containing strong shocks and other complex flow structures, with cosmological applications in hydrodynamic simulations. The objective is to develop efficient and robust numerical methods for cosmological applications, and to consider the hydrodynamics of the epoch of reionization, the hydrodynamical behavior of baryon gas around dark matter singularities, the statistical discrepancy between the intergalactic medium and dark matter in the non-linear regime of clustering, the entropy production of gravitational shocks, and other complex structural problems. Addressing cosmology's unique difficulties, such as the existence of extremely strong singularities and the effective coupling of hyperbolic hydrodynamic equations with elliptic equations for self-gravity, requires advances in computational mathematics and scientific computing.Broader impacts include enhancing a collaboration across two universities, advancing the mathematical sophistication of astrophysics, and making algorithms and codes of general utility available to the wider astrophysics, physics, and engineering communities.