气流中颗粒尺寸分布的演变
Evolving grain-size distributions embedded in gas flows
摘要：
我们提出了一种数值方法，准确地演变的尘埃粒度分布经历数量守恒（如溅射）和/或质量守恒（如粉碎）的过程。由于通常观察到的星际尘埃分布遵循幂律，我们的方法采用幂律离散化，并使用每个仓中的颗粒质量和数量密度来确定幂律参数。这种幂律方法是对文献中的分段常数和线性方法的补充。我们发现，幂律方法优于其他两种方法，特别是对于小箱数。在溅射试验中，总晶粒质量的相对误差保持在0.01%以下，与仓数N无关，而其他方法仅在N > 50或更高时才能实现这一点。同样，破碎试验表明，该方法也产生小的相对误差的总粒数，而保持质量。幂律方法不仅保留了全局分布特性，而且还保留了区间特性，从而在很大程度上恢复了分布的形状。对于常数和线性方法，这并不总是发生，特别是对于小的箱数。因此，在流体动力学代码中实施幂律方法可以最大限度地减少数值成本，同时保持高精度。该方法不仅限于尘埃颗粒的分布，但也可以应用到任何分布函数的演变，如宇宙射线分布受同步辐射或逆康普顿散射。
英文摘要：
We present a numerical approach for accurately evolving a dust grain-size distribution undergoing number-conserving (such as sputtering) and/or mass-conserving (such as shattering) processes. As typically observed interstellar dust distributions follow a power-law, our method adopts a power-law discretisation and uses both the grain mass and number densities in each bin to determine the power-law parameters. This power-law method is complementary to piecewise-constant and linear methods in the literature. We find that the power-law method surpasses the other two approaches, especially for small bin numbers. In the sputtering tests the relative error in the total grain mass remains below 0.01% independent of the number of bins N, while the other methods only achieve this for N > 50 or higher. Likewise, the shattering test shows that the method also produces small relative errors in the total grain numbers while conserving mass. Not only does the power-law method conserve the global distribution properties, it also preserves the inter-bin characteristics so that the shape of the distribution is recovered to a high degree. This does not always happen for the constant and linear methods, especially not for small bin numbers. Implementing the power-law method in a hydrodynamical code thus minimises the numerical cost whilst maintaining high accuracy. The method is not limited to dust grain distributions, but can also be applied to the evolution of any distribution function, such as a cosmic-ray distribution affected by synchrotron radiation or inverse-Compton scattering.
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