Adaptive mesh refinement
To widen the dynamical range of the numerical schemes, mesh refinement strategies have been applied in several grid codes (e.g., ART, RAMSES, ENZO, and FLASH). In most of the cases, a simple density (e.g., mass per cell) criterion is used. If the mass within one cell exceeds a certain threshold, $m \equiv \rho \, \Delta x^3 > m_{min}$, the cell is divided in multiple (e.g., eight) sub-cells and the internal properties are interpolated from the original cell onto the new sub-cells. This ensures that the gravitational mass (e.g., the source of gravity) is homogeneously distributed within the computational domain. In this way, the underlying grid evolves in a quasi-Lagrangian fashion following the mass flow, as illustrated in the left panel of Fig. 4, which shows the typical structure of the refinement grid in a cosmological simulation.
Other refinement strategies based on velocity criteria are often used [75] ,[76] to study shocks and turbulence in galaxy clusters. By extending the aforementioned criteria to additionally refining on velocity jumps, the formation of turbulence and shocks can be followed with unprecedented high spatial resolution throughout the cosmic structures, as shown in the right part of Fig. 4. In order to follow the turbulent cascade with high precision and accuracy, sub-scale turbulence models can additionally be used to initialize the velocities on the refined cells: this prevents the turbulent cascade from being suppressed [77] .
评论