Adaptive Mesh Refinement Simulations Research Articles

Magnetic field and kinetic helicity evolution in simulations of interacting disk galaxies

There are indications that the magnetic field evolution in galaxies is influenced by tidal interactions and mergers between galaxies. We carried out a parameter study of interacting disk galaxies with impact parameters ranging from central collisions to weakly interacting scenarios. The orientations of the disks were also varied. In particular, we investigated how magnetic field amplification depends on these parameters. We used magnetohydrodynamics for gas disks in combination with live dark-matter halos in adaptive mesh refinement simulations. The disks were initialized using a setup for isolated disks in hydrostatic equilibrium. Since we focused on the impact of tidal forces on magnetic field evolution, adiabatic physics was applied. Small-scale filtering of the velocity and magnetic field allowed us to estimate the turbulent electromotive force (EMF) and kinetic helicity. Time series of the average magnetic field in central and outer disk regions show pronounced peaks during close encounters and mergers. This agrees with observed magnetic fields at different interaction stages. The central field strength exceeds $10\; (corresponding to an amplification factor of 2 to 3) for small impact parameters. As the disks are increasingly disrupted and turbulence is produced by tidal forces, the small-scale EMF reaches a significant fraction of the total EMF. The small-scale kinetic helicity is initially antisymmetric across the disk plane. Though its evolution is sensitive to both the impact parameter and inclinations of the rotation axes with respect to the relative motion of the disks, antisymmetry is generally broken through interactions and the merger remnant loses most of the initial helicity. The EMF and the magnetic field also decay rapidly after coalescence. The strong amplification during close encounters of the interacting galaxies is mostly driven by helical flows and a mean-field dynamo. The small-scale dynamo contributes significantly in post-interaction phases. However, the amplification of the magnetic field cannot be sustained.

Radiation from global topological strings using adaptive mesh refinement: Massive modes

We implement adaptive mesh refinement (AMR) simulations of global topological strings using the public code, GRChombo. We perform a quantitative investigation of massive radiation from single sinusoidally displaced string configurations, studying a range of string widths defined by the coupling parameter $\lambda$ over two orders of magnitude, effectively varying the mass of radiated particles $m_H \sim \sqrt{\lambda}$. We perform an in-depth investigation into the effects of AMR on massive radiation emission, including radiation trapping and the refinement required to resolve high frequency modes. We use quantitative diagnostic tools to determine the eigenmode decomposition, showing a complex superposition of high frequency propagating modes with different phase and group velocities. We conclude that massive radiation is generally strongly suppressed relative to the preferred massless channel, with suppression increasing at lower amplitudes and higher $\lambda$. Only in extreme nonlinear regimes (e.g.\ with relative amplitude $\varepsilon \sim 1.5$ and $\lambda < 1$) do we observe massive and massless radiation to be emitted at comparable magnitude. We find that massive radiation is emitted in distinct high harmonics of the fundamental frequency of the string, and we demonstrate that, for the sinusoidal configurations studied, massive radiation is exponentially suppressed with $\sqrt{\lambda}$ (i.e. the particle mass). Finally, we place these results in the context of axions and gravitational waves produced by cosmological cosmic string networks, and note that AMR provides a significant opportunity to explore higher $\lambda$ (thin string) regimes whilst using fewer computational resources.

Spatial filtering in a 6D hybrid-Vlasov scheme to alleviate adaptive mesh refinement artifacts: a case study with Vlasiator (versions 5.0, 5.1, and 5.2.1)

Abstract. Numerical simulation models that are used to investigate the near-Earth space plasma environment require sophisticated methods and algorithms as well as high computational power. Vlasiator 5.0 is a hybrid-Vlasov plasma simulation code that is able to perform 6D (3D in ordinary space and 3D in velocity space) simulations using adaptive mesh refinement (AMR). In this work, we describe a side effect of using AMR in Vlasiator 5.0: the heterologous grid approach creates discontinuities due to the different grid resolution levels. These discontinuities cause spurious oscillations in the electromagnetic fields that alter the global results. We present and test a spatial filtering operator for alleviating this artifact without significantly increasing the computational overhead. We demonstrate the operator's use case in large 6D AMR simulations and evaluate its performance with different implementations.

Three-dimensional simulations of reshocked inclined Richtmyer-Meshkov instability: Effects of initial perturbations

A Mach 1.55 shock and subsequent reshock interacting with predominantly single-mode and multi-mode interfaces between nitrogen and carbon dioxide is studied through three-dimensional adaptive mesh refinement simulations using the FLASH code. The simulations are directly compared with the PLIF/PIV experimental measurements to validate the computational code. Development of instability after first shock and chaotic turbulent mixing after reshock are discussed for the entire shock tube domain.

Efficient algorithm for proper orthogonal decomposition of block-structured adaptively refined numerical simulations

Adaptive mesh refinement (AMR) is increasingly being used to simulate fluid flows that have vastly different resolution requirements throughout the computational domain. Proper orthogonal decomposition (POD) is a common tool to extract coherent structures from flow data and build reduced order models, but current POD algorithms do not take advantage of potential efficiency gains enabled by multi-resolution data from AMR simulations. Here, we explore a new method for performing POD on AMR data that eliminates repeated operations arising from nearest-neighbor interpolation of multi-resolution data onto uniform grids. We first outline our approach to reduce the number of computations with examples and provide the complete algorithms in the appendix. We examine the computational acceleration of the new algorithms compared to the standard POD method using synthetically generated AMR data and operation counting. We then use CPU times and operation counting to analyze data from an AMR simulation of an axisymmetric buoyant plume, finding that we are able to reduce the computational time by a factor of approximately 2−5 when using three levels of grid refinement. The new POD algorithm is the first to eliminate redundant operations for matrix multiplications with repeated values in each matrix, making it ideal for POD of data from AMR simulations.

Parallel-GPU AMR implementation for phase-field lattice Boltzmann simulation of a settling dendrite

The motion of the equiaxed grains plays an important role in macrosegregation. To simulate the motion of three-dimensional (3D) equiaxed dendrites growing in an undercooled melt, a large computational domain with small grids is required. In this study, we investigated the morphology and velocity of the settling dendrite and the growth velocity of its primary arms by implementing parallel computing with multiple graphics processing units (GPUs) for the adaptive mesh refinement (AMR) method (parallel-GPU AMR). A multiple-grid (MG) method that assigns different grid sizes to each field was also applied to the parallel-GPU AMR. A large-scale phase-field lattice Boltzmann (PF-LB) parallel-GPU AMR simulation of the settling dendrite was performed. The parallel GPU AMR method developed for the 3D PF-LB solidification model can evaluate the growth and motion of 3D equiaxed dendrite settling in an undercooled melt. The results are achieved with a significant acceleration of the 3D PF-LB simulations of settling dendrite and using a significantly reduced number of GPUs required for the simulation.

Parallel GPU-accelerated adaptive mesh refinement on two-dimensional phase-field lattice Boltzmann simulation of dendrite growth

Simulations of dendritic solidification involving melt convection and solid motion usually require a considerably higher computational domain than the dendrite size, whose computational efficiency with a uniform mesh is extremely low. In this study, to accelerate those two-dimensional simulations using the phase-field and lattice Boltzmann (PF-LB) methods, we developed a parallel computing method with multiple graphics processing units (GPUs) for the adaptive mesh refinement (AMR) method with dynamic load balancing (parallel-GPU AMR). It was confirmed that parallel-GPU AMR simulations were faster than those with the uniform mesh when the number of grid points in the adaptive mesh was around 40% or less than those in the uniform mesh. We also demonstrate that the developed parallel-GPU AMR can greatly accelerate the PF-LB simulations of dendrite growth with melt convection and solid motion.

A new wake detection methodology to capture wind turbine wakes using adaptive mesh refinement and Large Eddy Simulation

The development of turbulent vortical wakes released downstream of wind turbines is crucial as it presents many technological implications for wind farm design and exploitation. The numerical prediction of these wakes constitutes a challenging problem as they involve the shedding of fine vortical structures, their instabilities, and interactions with a turbulent ambient flow. A Large Eddy Simulation (LES) approach allows capturing such flow phenomena, which implies a suitable mesh. Adaptive Mesh Refinement (AMR) is used to refine the mesh in the wind turbine wake to limit the computational cost. A methodology is developed to define and capture the wake envelope adequately. Three main parts of this methodology can be identified: The wind turbine wake detection, the target cell size required and adaptation frequency. The target cell size needed to properly capture the wind turbine wake is investigated in previous work [1], while this paper focuses on wind turbine wake detection. A strategy based on a progress variable with a source term in the rotor region is used to capture the wake. This variable is transported by the flow and thus defines the wake envelope. AMR is used to refine the mesh within this region. To validate the method, a comparison between an adaptive mesh case and a reference mesh case has been performed on a single rotor and a two aligned rotor configuration. For both, the wind turbine wake tracking method is effective. The progress variable is transported correctly and leads to a well-defined wake area. The mesh is refined adequately within it. The physical comparison between cases showed similar results, while the performance comparison showed a computational cost reduction of 30% in the single turbine configuration and 50% in the two turbines configuration. Therefore, our methodology coupled with adaptive mesh refinement can adequately capture wind turbine wake, define an accurate wake envelope and decrease the computational cost for the same physical precision.

Radiation from global topological strings using adaptive mesh refinement: Methodology and massless modes

We implement adaptive mesh refinement (AMR) simulations of global topological strings using the public numerical relativity code, GRChombo. We perform a quantitative investigation of the dynamics of single sinusoidally displaced string configurations, studying a wide range of string energy densities $\mu \propto \ln{\lambda}$, defined by the string width parameter $\lambda$ over two orders of magnitude. We investigate the resulting massless (Goldstone boson or axion) radiation signals, using quantitative diagnostic tools to determine the eigenmode decomposition. Given analytic radiation predictions, we compare the oscillating string trajectory with a backreaction model accounting for radiation energy losses, finding excellent agreement. We establish that backreaction decay is accurately characterised by the inverse square of the amplitude being proportional to the inverse tension $\mu$ for $3\lesssim \lambda \lesssim 100$. We conclude that analytic radiation modelling in the thin-string (Nambu-Goto) limit provides the appropriate cosmological limit for global strings. We contextualise these results with respect to axions and gravitational waves produced by cosmic string networks.

An application of Gaussian process modeling for high-order accurate adaptive mesh refinement prolongation

We present a new polynomial-free prolongation scheme for Adaptive Mesh Refinement (AMR) simulations of compressible and incompressible computational fluid dynamics. The new method is constructed using a multi-dimensional kernel-based Gaussian Process (GP) prolongation model. The formulation for this scheme was inspired by the GP methods introduced by A. Reyes et al. (A New Class of High-Order Methods for Fluid Dynamics Simulation using Gaussian Process Modeling, Journal of Scientific Computing, 76 (2017), 443-480; A variable high-order shock-capturing finite difference method with GP-WENO, Journal of Computational Physics, 381 (2019), 189-217). In this paper, we extend the previous GP interpolations and reconstructions to a new GP-based AMR prolongation method that delivers a high-order accurate prolongation of data from coarse to fine grids on AMR grid hierarchies. In compressible flow simulations special care is necessary to handle shocks and discontinuities in a stable manner. To meet this, we utilize the shock handling strategy using the GP-based smoothness indicators developed in the previous GP work by A. Reyes et al. We demonstrate the efficacy of the GP-AMR method in a series of testsuite problems using the AMReX library, in which the GP-AMR method has been implemented.

Dark matter from axion strings with adaptive mesh refinement

Axions are hypothetical particles that may explain the observed dark matter density and the non-observation of a neutron electric dipole moment. An increasing number of axion laboratory searches are underway worldwide, but these efforts are made difficult by the fact that the axion mass is largely unconstrained. If the axion is generated after inflation there is a unique mass that gives rise to the observed dark matter abundance; due to nonlinearities and topological defects known as strings, computing this mass accurately has been a challenge for four decades. Recent works, making use of large static lattice simulations, have led to largely disparate predictions for the axion mass, spanning the range from 25 microelectronvolts to over 500 microelectronvolts. In this work we show that adaptive mesh refinement simulations are better suited for axion cosmology than the previously-used static lattice simulations because only the string cores require high spatial resolution. Using dedicated adaptive mesh refinement simulations we obtain an over three order of magnitude leap in dynamic range and provide evidence that axion strings radiate their energy with a scale-invariant spectrum, to within ~5% precision, leading to a mass prediction in the range (40,180) microelectronvolts.

Black hole fuelling in galaxy mergers: a high-resolution analysis

ABSTRACT Using parsec scale resolution hydrodynamical adaptive mesh refinement simulations, we have studied the mass transport process throughout a Galactic merger. The aim of such study is to connect both the peaks of mass accretion rate on to the BHs and star formation bursts with both gravitational and hydrodynamic torques acting on the galactic gaseous component. Our merger initial conditions were chosen to mimic a realistic system. The simulations include gas cooling, star formation, supernovae feedback, and AGN feedback. Gravitational and hydrodynamic torques near pericentre passes trigger gas funneling to the nuclei that is associated with bursts of star formation and black hole growth. Such episodes are intimately related with both kinds of torques acting on the galactic gas. Pericentres trigger both star formation and mass accretion rates of ∼few $(1\!-\!10)\, \mathrm{ M}_\odot$ yr−1. Such episodes last $\sim \, (50\!-\!75)$ Myr. Close passes also can produce black hole accretion that approaches and reaches the Eddington rate, lasting ∼few Myrs. Our simulation shows that both gravitational and hydrodynamic torques are enhanced at pericentre passes with gravitational torques tending to have higher values than the hydrodynamic torques throughout the merger. We also find that in the closest encounters, hydrodynamic and gravitational torques can be comparable in their effect on the gas, the two helping in the redistribution of both angular momentum and mass in the galactic disc. Such phenomena allow inward mass transport on to the BH influence radius, fuelling the compact object and lighting up the galactic nuclei.

Dynamic mode decomposition in adaptive mesh refinement and coarsening simulations

Dynamic mode decomposition (DMD) is a powerful data-driven method used to extract spatio-temporal coherent structures that dictate a given dynamical system. The method consists of stacking collected temporal snapshots into a matrix and mapping the nonlinear dynamics using a linear operator. The classical procedure considers that snapshots possess the same dimensionality for all the observable data. However, this often does not occur in numerical simulations with adaptive mesh refinement/coarsening schemes (AMR/C). This paper proposes a strategy to enable DMD to extract features from observations with different mesh topologies and dimensions, such as those found in AMR/C simulations. For this purpose, the adaptive snapshots are projected onto the same reference function space, enabling the use of snapshot-based methods such as DMD. The present strategy is applied to challenging AMR/C simulations: a continuous diffusion–reaction epidemiological model for COVID-19, a density-driven gravity current simulation, and a bubble rising problem. We also evaluate the DMD efficiency to reconstruct the dynamics and some relevant quantities of interest. In particular, for the SEIRD model and the bubble rising problem, we evaluate DMD’s ability to extrapolate in time (short-time future estimates).

Cosmological magnetogenesis: the Biermann battery during the Epoch of reionization

ABSTRACT We investigate the effect of the Biermann battery during the Epoch of reionization (EoR) using cosmological Adaptive Mesh Refinement simulations within the framework of the sphinx project. We develop a novel numerical technique to solve for the Biermann battery term in the Constrained Transport method, preserving both the zero divergence of the magnetic field and the absence of Biermann battery for isothermal flows. The structure-preserving nature of our numerical method turns out to be very important to minimize numerical errors during validation tests of the propagation of a Str’omgren sphere and of a Sedov blast wave. We then use this new method to model the evolution of a 2.5 and 5 co-moving Mpc cosmological box with a state-of-the-art galaxy formation model within the Ramses code. Contrary to previous findings, we show that three different Biermann battery channels emerge: the first one is associated with linear perturbations before the EoR, the second one is the classical Biermann battery associated with reionization fronts during the EoR, and the third one is associated with strong, supernova-driven outflows. While the two former channels generate spontaneously volume-filling magnetic fields with a strength on the order or below 10−20 G, the latter, owing to the higher plasma temperature and a marginally resolved turbulent dynamo, reaches a field strength as high as 10−18 G in the intergalactic medium around massive haloes.

Electrons in the supernova-driven interstellar medium

Context.Interstellar gas is in a highly turbulent dynamic state driven by successive supernova explosions and stellar winds, while its electron distribution is determined by microscopic processes such as ionization and recombination. In order to understand the properties of the electrons in the interstellar medium (ISM) it is necessary to follow numerically the nonlinear spatial and temporal evolution of the gas, its ionization structure, and its emission properties.Aims.We study the time evolution of the electrons in the ISM and how line of sight observations compare to volume analysis of the simulated medium populated with atoms and ions of the ten most abundant species. In particular, we make quantitative predictions about the occupation fractions and averaged densities of electrons, the dispersion measures, and their vantage point dependence.Methods.We carried out state-of-the-art adaptive mesh refinement simulations of the supernova-driven interstellar gas tracing the evolution of 112 ions and atoms of H, He, C, N, O, Ne, Mg, Si, S, and Fe and their emissivities in a time-dependent fashion. The gas is followed with the magnetohydrodynamical adaptive mesh refinement parallel code coupled with the Collisional + Photo Ionization Plasma Emission Software to trace the ionic structure and radiative emission of the plasma.Results.We show that more than 60% of the electrons are in thermally unstable regimes: about 50% at 200 &lt;T≤ 103.9K and 14% at 104.2&lt;T≤ 105.5K. The probability density functions for the electron distribution in different temperature regimes is rather broad, also a result of turbulence in the ISM. Comparing the calculated dispersion measures along different lines of sight to observation, we find a very good agreement. They increase linearly for distances greater than 300 pc from the observer at an average rate of 27 cm−3pc per kpc. The dispersion regarding the average dispersion measures does not decrease with distance along the line of sight, pointing to a high clumpiness of the electrons and of the turbulent ISM. The mean electron density in the Galactic midplane derived from the volume analysis varies between 0.029 and 0.031 cm−3, while that derived from the dispersion measures, varies between 0.0264 and 0.03 cm−3depending on the vantage point and on the time averaged period. These variations can be as high as 8.3% between vantage points.

EDGE: a new approach to suppressing numerical diffusion in adaptive mesh simulations of galaxy formation

ABSTRACT We introduce a new method to mitigate numerical diffusion in adaptive mesh refinement (AMR) simulations of cosmological galaxy formation, and study its impact on a simulated dwarf galaxy as part of the ‘EDGE’ project. The target galaxy has a maximum circular velocity of $21\, \mathrm{km}\, \mathrm{s}^{-1}$ but evolves in a region that is moving at up to $90\, \mathrm{km}\, \mathrm{s}^{-1}$ relative to the hydrodynamic grid. In the absence of any mitigation, diffusion softens the filaments feeding our galaxy. As a result, gas is unphysically held in the circumgalactic medium around the galaxy for $320\, \mathrm{Myr}$, delaying the onset of star formation until cooling and collapse eventually triggers an initial starburst at z = 9. Using genetic modification, we produce ‘velocity-zeroed’ initial conditions in which the grid-relative streaming is strongly suppressed; by design, the change does not significantly modify the large-scale structure or dark matter accretion history. The resulting simulation recovers a more physical, gradual onset of star formation starting at z = 17. While the final stellar masses are nearly consistent ($4.8 \times 10^6\, \mathrm{M}_{\odot }$ and $4.4\times 10^6\, \mathrm{M}_{\odot }$ for unmodified and velocity-zeroed, respectively), the dynamical and morphological structure of the z = 0 dwarf galaxies are markedly different due to the contrasting histories. Our approach to diffusion suppression is suitable for any AMR zoom cosmological galaxy formation simulations, and is especially recommended for those of small galaxies at high redshift.

Adaptive Mesh Refinement Simulations of Gas Dynamic Flows on Hybrid Meshes

An adaptive mesh refinement algorithm for simulations of the Navier–Stokes equations on unstructured hybrid meshes is presented. Numerical results for compressible supersonic flow around a sphere are given.

Implementation of stellar heating feedback in simulations of star cluster formation: effects on the initial mass function

ABSTRACT Explaining the initial mass function (IMF) of stars is a long-standing problem in astrophysics. The number of complex mechanisms involved in the process of star cluster formation, such as turbulence, magnetic fields, and stellar feedback, make understanding and modelling the IMF a challenging task. In this paper, we aim to assert the importance of stellar heating feedback in the star cluster formation process and its effect on the shape of the IMF. We use an analytical sub-grid model to implement the radiative feedback in fully three-dimensional magnetohydrodynamical (MHD) simulations of star cluster formation, with the ultimate objective of obtaining numerical convergence on the IMF. We compare a set of MHD adaptive mesh refinement simulations with three different implementations of the heating of the gas: (1) a polytropic equation of state, (2) a spherically symmetric stellar heating feedback, and (3) our newly developed polar heating model that takes into account the geometry of the accretion disc and the resulting shielding of stellar radiation by dust. For each of the three heating models, we analyse the distribution of stellar masses formed in 10 molecular cloud simulations with different realizations of the turbulence to obtain a statistically representative IMF. We conclude that stellar heating feedback has a profound influence on the number of stars formed and plays a crucial role in controlling the IMF. We find that the simulations with the polar heating model achieve the best convergence on the observed IMF.

Enabling Adaptive Mesh Refinement for Spectral-Element Simulations of Turbulence Around Wing Sections

The implementation of adaptive mesh refinement (AMR) in the spectral-element method code Nek5000 is used for the first time on the well-resolved large-eddy simulation of the turbulent flow over wings. In particular, the flow over a NACA4412 profile with a 5^circ angle of attack at chord-based Reynolds number {text {Re}}_c=200{,}000 is analyzed in the present work and compared with a previous conformal simulation used as baseline. The mesh, starting from a coarse resolution, is progressively and automatically refined by means of AMR, which allows for high resolution near the wall and wake whereas significantly larger elements are used in the far-field. The resulting mesh, which remains unchanged in the production runs (i.e. AMR is used to create the final mesh, which is then fixed), is of higher resolution than those in previous conformal cases, and it allows for the use of larger computational domains, avoiding the use of precursor RANS simulations to determine the boundary conditions. This is achieved with, approximately, 2 times lower total number of grid points if the same spanwise length is used. Turbulence statistics obtained in the AMR simulation show good agreement with the ones obtained with the conformal mesh, and the pressure-coefficient distribution along the wing surface matches pressure-scan experimental data obtained in the MTL wind tunnel at KTH. The use of AMR is therefore expected to enable the simulation of high-Reynolds numbers turbulent flows over complex geometries (such as wings), thus allowing the study of pressure-gradient effects at high Reynolds numbers relevant for practical applications.

Efficient simulation of turbulent diffusion flames in OpenFOAM using adaptive mesh refinement

We address the challenge of resolving wide spatial scale ranges in fire simulations through the development of a new OpenFOAM-based adaptive mesh refinement (AMR) computational capability for large eddy simulations of turbulent diffusion flames. The AMR approach provides increased resolution in localized regions based on user-defined criteria, resulting in a simulation that dynamically tracks fire spread and reduces computational cost compared to uniform and static mesh approaches. The new AMR-enabled solver, called diffusionFireFoam, is an extension of the fireFoam solver and incorporates dynamic meshing capabilities already available in OpenFOAM. We outline details of the new solver and demonstrate its basic functionality, accuracy, and computational efficiency for a small-scale methane pool fire verification case. We show that both first- and second-order statistics from the AMR simulation are in good agreement with results from a statically refined simulation that has the same fine-scale resolution, but a larger overall mesh. We then show for a larger-scale methane pool fire that an AMR simulation in diffusionFireFoam agrees with results from static mesh simulations, experiments, and prior computational studies. Once again, substantial computational savings are achieved, with roughly 5 times fewer grid cells in the AMR simulations than in prior static mesh simulations.