In the context of intra-cluster medium turbulence, it is essential to be able to split the turbulent velocity field in a compressive and a solenoidal component. We describe and implement a new method for this aim, i.e., performing a Helmholtz–Hodge decomposition, in multi-grid, multi-resolution descriptions, focusing on (but not being restricted to) the outputs of AMR cosmological simulations. The method is based on solving elliptic equations for a scalar and a vector potential, from which the compressive and the solenoidal velocity fields, respectively, are derived through differentiation. These equations are addressed using a combination of Fourier (for the base grid) and iterative (for the refinement grids) methods. We present several idealised tests for our implementation, reporting typical median errors in the order of 1‰-1%, and with 95-percentile errors below a few percents. Additionally, we also apply the code to the outcomes of a cosmological simulation, achieving similar accuracy at all resolutions, even in the case of highly non-linear velocity fields. We finally take a closer look to the decomposition of the velocity field around a massive galaxy cluster.

在集群内部介质湍流的情况下，必须能够将湍流速度场分成压缩分量和螺线管分量。我们为此目的描述并实现了一种新方法，即在多网格，多分辨率描述中执行Helmholtz-Hodge分解，重点是（但不限于）AMR宇宙学模拟的输出。该方法基于求解标量和导数的椭圆方程。向量势，可通过微分分别得出压缩和螺线管速度场。这些方程式是通过使用傅里叶（对于基本网格）和迭代（对于细化网格）方法的组合来解决的。我们为实现提供了一些理想化的测试，报告的典型中值误差为1‰-1％左右，而95％的误差低于几个百分点。此外，我们还将代码应用于宇宙学模拟的结果，即使在高度非线性速度场的情况下，在所有分辨率下都可以达到相似的精度。最后，我们进一步仔细研究大型星系团周围的速度场的分解。