Relativistic Hydrodynamics with Wavelets
Relativistic Hydrodynamics with Wavelets
复制标题
小波相对论流体动力学
DOI：
10.3847/1538-4357/aae5f9
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
S. Paolucci
中科院分区：
文献类型：
--
作者：
J. DeBuhr;Bo Zhang;Matthew Anderson;D. Neilsen;E. Hirschmann;T. Grenga;S. Paolucci
在大量的天体物理模拟中，求解相对论流体动力学方程的方法是非常重要的，这些天体物理模拟可能是非常动态的，并且涉及多尺度特征。这需要高度自适应的计算方法，能够自动解决在计算领域和许多时间尺度上出现的许多局部特征和不稳定性。虽然这在历史上是通过基于自适应网格细化的方法完成的，但使用小波基和小波变换的替代方法最近在高级工程应用的自适应表示中取得了重大成功。本文提出了一种新的方法，扩展了小波自适应多分辨率表示方法，利用迭代插值小波对相对论流体动力学方程进行积分，并引入了一种高度自适应的多维模拟实现。小波系数提供了解决方案的局部近似误差的直接度量，并放置了自然适应流体流动的配点，同时提供了良好的流体量守恒。最终实现的oahu应用于一系列高要求的1D和2D问题，这些问题探索了高洛伦兹因子流出和几种不稳定性的形成，包括Kelvin-Helmholtz不稳定性和Rayleigh-Taylor不稳定性。
Methods to solve the relativistic hydrodynamic equations are important in a large number of astrophysical simulations, which may be very dynamic and involve multiscale features. This requires computational methods that are highly adaptive and capable of automatically resolving numerous localized features and instabilities that emerge across the computational domain and over many temporal scales. While this has been historically accomplished with adaptive-mesh-refinement-based methods, alternatives using wavelet bases and the wavelet transformation have recently achieved significant success in adaptive representation for advanced engineering applications. The current work presents a new method, extending the wavelet adaptive multiresolution representation method, for the integration of the relativistic hydrodynamic equations using iterated interpolating wavelets and introduces a highly adaptive implementation for multidimensional simulation. The wavelet coefficients provide a direct measure of the local approximation error for the solution and place collocation points that naturally adapt to the fluid flow while providing good conservation of fluid quantities. The resulting implementation, oahu, is applied to a series of demanding 1D and 2D problems that explore high Lorentz factor outflows and the formation of several instabilities, including the Kelvin–Helmholtz instability and the Rayleigh–Taylor instability.
DOI：
10.1088/0067-0049/193/1/6
发表时间：
2011-01
期刊：
The Astrophysical Journal Supplement Series
影响因子：
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作者：
K. Beckwith;J. Stone
通讯作者：
K. Beckwith;J. Stone