James Bordner

ENZO: AN ADAPTIVE MESH REFINEMENT CODE FOR ASTROPHYSICS

This paper describes the open-source code Enzo, which uses block-structured adaptive mesh refinement to provide high spatial and temporal resolution for modeling astrophysical fluid flows. The code is Cartesian, can be run in one, two, and three dimensions, and supports a wide variety of physics including hydrodynamics, ideal and non-ideal magnetohydrodynamics, N-body dynamics (and, more broadly, self-gravity of fluids and particles), primordial gas chemistry, optically thin radiative cooling of primordial and metal-enriched plasmas (as well as some optically-thick cooling models), radiation transport, cosmological expansion, and models for star formation and feedback in a cosmological context. In addition to explaining the algorithms implemented, we present solutions for a wide range of test problems, demonstrate the codes parallel performance, and discuss the Enzo collaborations code development methodology.

Simulating Radiating and Magnetized Flows in Multiple Dimensions with ZEUS-MP

This paper describes ZEUS-MP, a multi-physics, massively parallel, message-passing implementation of the ZEUS code. ZEUS-MP differs significantly from the thoroughly documented ZEUS-2D code, the completely undocumented (in peer-reviewed literature) ZEUS-3D code, and a marginally documented “version 1” of ZEUS-MP first distributed publicly in 1999. ZEUS-MP offers an MHD algorithm which is better suited for multidimensional flows than the ZEUS-2D module by virtue of modifications to the Method of Characteristics scheme first suggested by Hawley & Stone (1995). This MHD module is shown to compare quite favorably to the TVD scheme described by Ryu et al. (1998). ZEUS-MP is the first publicly-available ZEUS code to allow the advection of multiple chemical (or nuclear) species. Radiation hydrodynamic simulations are enabled via an implicit flux-limited radiation diffusion (FLD) module. The hydrodynamic, MHD, and FLD modules may be used, singly or in concert, in one, two, or three space dimensions. Additionally, so-called “1.5-D” and “2.5-D” grids, in which the “half-D” denotes a symmetry axis along which a constant but non-zero value of velocity or magnetic field is evolved, are supported. Self gravity may be included either through the assumption of a GM/r potential or a solution of Poisson’s equation using one of three linear solver packages (conjugategradient, multigrid, and FFT) provided for that purpose. Point-mass potentials are also supported. Because ZEUS-MP is designed for large simulations on parallel computing platforms, considerable attention is paid to the parallel performance characteristics of each module in the code. Strong-scaling tests involving pure hydrodynamics (with and without self-gravity), MHD, and RHD are performed in which large problems (256 3 zones) are distributed among as many as 1024 processors of an IBM SP3. Parallel efficiency is a strong function of the amount of communication required between processors in a given algorithm, but all modules are shown to scale well on up to 1024 processors for the chosen fixed problem size. Subject headings: hydrodynamics – methods:numerical – methods:parallel – MHD – radiative transfer

Introducing Enzo, an AMR Cosmology Application

In this paper we introduce Enzo, a 3D MPI-parallel Eulerian block-structured adaptive mesh refinement cosmology code. Enzo is designed to simulate cosmological structure formation, but can also be used to simulate a wide range of astrophysical situations. Enzo solves dark matter N-body dynamics using the particle-mesh technique. The Poisson equation is solved using a combination of fast fourier transform (on a periodic root grid) and multigrid techniques (on non-periodic subgrids). Euler’s equations of hydrodynamics are solved using a modified version of the piecewise parabolic method. Several additional physics packages are implemented in the code, including several varieties of radiative cooling, a metagalactic ultraviolet background, and prescriptions for star formation and feedback. We also show results illustrating properties of the adaptive mesh portion of the code. Information on profiling and optimizing the performance of the code can be found in the contribution by James Bordner in this volume.

Simulating the Cosmic Dawn With Enzo

We review two decades of progress using the Enzo hydrodynamic cosmology code to simulate the Cosmic Dawn, a period of roughly 1 billion years beginning with the formation of the first stars in the universe, and ending with cosmic reionization. Using simulations of increasing size and complexity, working up in length and mass scale and to lower redshifts, a connected narrative is built up covering the entire epoch. In the first part of the paper, we draw on results we and our collaborators have achieved using the Enzo cosmological adaptive mesh refinement code. Topics include the formation of Population III stars, the transition to Population II star formation, chemical enrichment, the assembly of the first galaxies, their high redshift galaxy statistics, and their role in reionization. In the second part of the paper we highlight physical difficulties that will require new, more physically complex simulations to address, drawing from a broader literature survey. We discuss the healthy interplay between self-consistent numerical simulations and analytic and semi-analytic approaches. Finally, we discuss technical advances in hardware and software that will enable a new class of more realistic simulations to be carried out on exascale supercomputers in the future.