Star Formation with Adaptive Mesh Refinement Radiation Hydrodynamics

Abstract

Abstract. I provide a pedagogic review of adaptive mesh refinement (AMR) radiation hydrodynamics (RHD) methods and codes used in simulations of star formation, at a level suitable for researchers who are not computational experts. I begin with a brief overview of the types of RHD processes that are most important to star formation, and then I formally introduce the equations of RHD and the approximations one uses to render them computationally tractable. I discuss strategies for solving these approximate equations on adaptive grids, with particular emphasis on identifying the main advantages and disadvantages of various approximations and numerical approaches. Finally, I conclude by discussing areas ripe for improvement.

Hybrid Adaptive Ray-Moment Method (HARM2): A highly parallel method for radiation hydrodynamics on adaptive grids

“…where n src,i = (x − x i )/|x − x i | for any position x in the computational domain, x i and I src,i are the position and intensity of the ith point source, and we assume that the sources are isotropic emitters, so I src,i is independent of n. 1 With this formulation I dir is non-zero only at special values of n, such as along radial directions between the point sources and position x, and zero for all others; while I diff will be non-zero everywhere. However, because the four-force vector (G 0 , G) depends on integrals over n, the δ-function contributions from I dir may dominate at some positions, while the contribution from I diff dominates elsewhere.…”

“…Our initial setup of our test problem is the same as the strong scaling test discussed in section 5.2.1 in which a radiating source is at the center of a (1 pc) 3 box. We terminate the rays after they have travelled 0.5 pc and perform tests for N ν = (1,2,8,16,20,32,48, 64) frequency bins. Our base grid is 256 3 and we ran our scaling tests on 128 processors for 50 time steps per test.…”

“…One common approach to solving the RHD equations is to reduce the dimensionality of the problem. This class of approximations are known as moment methods because they take the moments of the radiative transfer equation in direct analogy to the Chapman-Enskog procedure used to derive the hydrodynamic equations from the kinetic theory of gases [1,2]. This method averages over the angular dependence, and thus is a good approximation for smooth, diffuse radiation fields such as those present in optically thick media when the radiation is tightly coupled to the matter.…”

“…Common approximations include flux-limited diffusion (FLD; closure at first moment) [3][4][5], the M1 method (closure at the 2nd moment using a minimum entropy closure) [6,7], and Variable Eddington Tensor (VET; closure at the 2nd moment using an approximate solution to the full transfer equation) [8][9][10]. Regardless of the order and closure relation, the computational cost of these methods usually scales as N or N log N , where N is the number of cells, and the technique is highly parallelizable [1].…”