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

AST-0507340Fang本项目将尝试将高精度、加权基本无振荡格式的算法开发与宇宙学在流体动力学模拟中的应用结合起来，用于求解包含强激波的高速、高马赫数无粘流和其他复杂的流动结构。其目的是为宇宙学应用发展高效和稳健的数值方法，并考虑再电离时代的流体力学，暗物质奇点周围重子气体的流体动力学行为，星系际介质和暗物质在非线性星系团区域中的统计差异，引力激波的熵产生，以及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，以及双曲型流体动力学方程与自重椭圆方程的有效耦合，需要计算数学和科学计算的进步。广泛的影响包括加强两所大学的合作，提高天体物理学的数学复杂性，以及使算法和通用代码可供更广泛的天体物理、物理和工程界使用。

AST-0507340FangThis 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.