Dusty gas with SPH - I. Algorithm and test suite
Dusty gas with SPH - I. Algorithm and test suite
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含尘气体与 SPH - I. 算法和测试套件
DOI：
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发表时间：
2011
期刊：
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通讯作者：
Daniel J. Price
中科院分区：
文献类型：
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作者：
G. Laibe;Daniel J. Price
我们提出了一种新的算法来模拟光滑粒子流体动力学（SPH）中的两流体气体和粉尘混合物，系统地解决了许多关键问题，包括多流体系统中SPH密度的广义估计，可变平滑长度项的一致处理，有限粒径，时间步长稳定性，热耦合项以及在阻力算子中使用的核和平滑长度的选择。我们发现，与使用标准SPH钟形核相比，使用双驼峰形核可将阻力插值的精度提高数百倍，而无需额外的计算费用。为了对我们的算法进行基准测试，我们为气体和粉尘混合物开发了一套全面的标准化，简单的测试问题：粉尘盒，粉尘波，粉尘冲击，粉尘多夫和粉尘盘，其中前三个有已知的解析解。我们针对所有这些测试验证了我们的算法。在这样做的过程中，我们表明空间分辨率准则\Delta < cs ts是所有气体+尘埃代码的必要条件，在高阻力（即小停止时间ts）下，为了正确预测动力学，它变得至关重要。隐式时间步进和现实天体物理阻力机制的实现在一篇配套论文中得到了解决。
We present a new algorithm for simulating two-fluid gas and dust mixtures in Smoothed Particle Hydrodynamics (SPH), systematically addressing a number of key issues including the generalised SPH density estimate in multi-fluid systems, the consistent treatment of variable smoothing length terms, finite particle size, time step stability, thermal coupling terms and the choice of kernel and smoothing length used in the drag operator. We find that using double-hump shaped kernels improves the accuracy of the drag interpolation by a factor of several hundred compared to the use of standard SPH bell-shaped kernels, at no additional computational expense. In order to benchmark our algorithm, we have developed a comprehensive suite of standardised, simple test problems for gas and dust mixtures: dustybox, dustywave, dustyshock, dustysedov and dustydisc, the first three of which have known analytic solutions. We present the validation of our algorithm against all of these tests. In doing so, we show that the spatial resolution criterion \Delta < cs ts is a necessary condition in all gas+dust codes that becomes critical at high drag (i.e. small stopping time ts) in order to correctly predict the dynamics. Implicit timestepping and the implementation of realistic astrophysical drag regimes are addressed in a companion paper.