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Register a new userHybrid Adaptive Ray-Moment Method (HARM$^2$): A Highly Parallel Method for Radiation Hydrodynamics on Adaptive Grids
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We present a highly-parallel multi-frequency hybrid radiation hydrodynamics algorithm that combines a spatially-adaptive long characteristics method for the radiation field from point sources with a moment method that handles the diffuse radiation field produced by a volume-filling fluid. Our Hybrid Adaptive Ray-Moment Method (HARM$^2$) operates on patch-based adaptive grids, is compatible with asynchronous time stepping, and works with any moment method. In comparison to previous long characteristics methods, we have greatly improved the parallel performance of the adaptive long-characteristics method by developing a new completely asynchronous and non-blocking communication algorithm. As a result of this improvement, our implementation achieves near-perfect scaling up to $mathcal{O}(10^3)$ processors on distributed memory machines. We present a series of tests to demonstrate the accuracy and performance of the method.
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We present a new radiative transfer method (SPH-M1RT) that is coupled dynamically with smoothed particle hydrodynamics (SPH). We implement it in the (task-based parallel) SWIFT galaxy simulation code but it can be straightforwardly implemented in other SPH codes. Our moment-based method simultaneously solves the radiation energy and flux equations in SPH, making it adaptive in space and time. We modify the M1 closure relation to stabilize radiation fronts in the optically thin limit. We also introduce anisotropic artificial viscosity and high-order artificial diffusion schemes, which allow the code to handle radiation transport accurately in both the optically thin and optically thick regimes. Non-equilibrium thermo-chemistry is solved using a semi-implicit sub-cycling technique. The computational cost of our method is independent of the number of sources and can be lowered further by using the reduced speed of light approximation. We demonstrate the robustness of our method by applying it to a set of standard tests from the cosmological radiative transfer comparison project of Iliev et al. The SPH-M1RT scheme is well-suited for modelling situations in which numerous sources emit ionising radiation, such as cosmological simulations of galaxy formation or simulations of the interstellar medium.
We present an implementation of an adaptive ray tracing (ART) module in the Athena hydrodynamics code that accurately and efficiently handles the radiative transfer involving multiple point sources on a three-dimensional Cartesian grid. We adopt a recently proposed parallel algorithm that uses non-blocking, asynchronous MPI communications to accelerate transport of rays across the computational domain. We validate our implementation through several standard test problems including the propagation of radiation in vacuum and the expansions of various types of HII regions. Additionally, scaling tests show that the cost of a full ray trace per source remains comparable to that of the hydrodynamics update on up to $sim 10^3$ processors. To demonstrate application of our ART implementation, we perform a simulation of star cluster formation in a marginally bound, turbulent cloud, finding that its star formation efficiency is $12%$ when both radiation pressure forces and photoionization by UV radiation are treated. We directly compare the radiation forces computed from the ART scheme with that from the M1 closure relation. Although the ART and M1 schemes yield similar results on large scales, the latter is unable to resolve the radiation field accurately near individual point sources.
Aims. The importance of radiation to the physical structure of protoplanetary disks cannot be understated. However, protoplanetary disks evolve with time, and so to understand disk evolution and by association, disk structure, one should solve the combined and time-dependent equations of radiation hydrodynamics. Methods. We implement a new implicit radiation solver in the AZEuS adaptive mesh refinement magnetohydrodynamics fluid code. Based on a hybrid approach that combines frequency-dependent ray-tracing for stellar irradiation with non-equilibrium flux limited diffusion, we solve the equations of radiation hydrodynamics while preserving the directionality of the stellar irradiation. The implementation permits simulations in Cartesian, cylindrical, and spherical coordinates, on both uniform and adaptive grids. Results. We present several hydrostatic and hydrodynamic radiation tests which validate our implementation on uniform and adaptive grids as appropriate, including benchmarks specifically designed for protoplanetary disks. Our results demonstrate that the combination of a hybrid radiation algorithm with AZEuS is an effective tool for radiation hydrodynamics studies, and produces results which are competitive with other astrophysical radiation hydrodynamics codes.
Flows in which the primary features of interest do not rely on high-frequency acoustic effects, but in which long-wavelength acoustics play a nontrivial role, present a computational challenge. Integrating the entire domain with low-Mach-number methods would remove all acoustic wave propagation, while integrating the entire domain with the fully compressible equations can in some cases be prohibitively expensive due to the CFL time step constraint. For example, simulation of thermoacoustic instabilities might require fine resolution of the fluid/chemistry interaction but not require fine resolution of acoustic effects, yet one does not want to neglect the long-wavelength wave propagation and its interaction with the larger domain. The present paper introduces a new multi-level hybrid algorithm to address these types of phenomena. In this new approach, the fully compressible Euler equations are solved on the entire domain, potentially with local refinement, while their low-Mach-number counterparts are solved on subregions of the domain with higher spatial resolution. The finest of the compressible levels communicates inhomogeneous divergence constraints to the coarsest of the low-Mach-number levels, allowing the low-Mach-number levels to retain the long-wavelength acoustics. The performance of the hybrid method is shown for a series of test cases, including results from a simulation of the aeroacoustic propagation generated from a Kelvin-Helmholtz instability in low-Mach-number mixing layers. It is demonstrated that compared to a purely compressible approach, the hybrid method allows time-steps two orders of magnitude larger at the finest level, leading to an overall reduction of the computational time by a factor of 8.
A generalized method of moments (GMM) estimator is unreliable for a large number of moment conditions, that is, it is comparable, or larger than the sample size. While classical GMM literature proposes several provisions to this problem, its Bayesian counterpart (i.e., Bayesian inference using a GMM criterion as a quasi-likelihood) almost totally ignores it. This study bridges this gap by proposing an adaptive Markov Chain Monte Carlo (MCMC) approach to a GMM inference with many moment conditions. Particularly, this study focuses on the adaptive tuning of a weighting matrix on the fly. Our proposal consists of two elements. The first is the use of the nonparametric eigenvalue-regularized precision matrix estimator, which contributes to numerical stability. The second is the random update of a weighting matrix, which substantially reduces computational cost, while maintaining the accuracy of the estimation. We then present a simulation study and real data application to compare the performance of the proposed approach with existing approaches.
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