Adaptive Mesh Refinement Grid Research Articles

An adaptive lattice Green's function method for external flows with two unbounded and one homogeneous directions

We solve the incompressible Navier-Stokes equations using a lattice Green's function (LGF) approach, including immersed boundaries (IB) and adaptive mesh refinement (AMR), for external flows with one homogeneous direction (e.g. infinite cylinders of arbitrary cross-section). We hybridize a Fourier collocation (pseudo-spectral) method for the homogeneous direction with a specially designed, staggered-grid finite-volume scheme on an AMR grid. The Fourier series is also truncated variably according to the refinement level in the other directions. We derive new algorithms to tabulate the LGF of the screened Poisson operator and viscous integrating factor. After adapting other algorithmic details from the fully inhomogeneous case [1], we validate and demonstrate the new method with transitional and turbulent flows over a circular cylinder at Re=300 and Re=12,000, respectively.

κmonty: a Monte Carlo Compton scattering code including non-thermal electrons

ABSTRACT Low-luminosity active galactic nuclei are strong sources of X-ray emission produced by Compton scattering originating from the accretion flows surrounding their supermassive black holes. The shape and energy of the resulting spectrum depend on the shape of the underlying electron distribution function (DF). In this work, we present an extended version of the grmonty code, called κmonty. The grmonty code previously only included a thermal Maxwell–Jütner electron DF. We extend the grmonty code with non-thermal electron DFs, namely the κ and power-law DFs, implement Cartesian Kerr–Schild coordinates, accelerate the code with mpi, and couple the code to the non-uniform adaptive mesh refinement grid data from the general relativistic magnetohydrodynamics code bhac. For the Compton scattering process, we derive two sampling kernels for both DFs. Finally, we present a series of code tests to verify the accuracy of our schemes. The implementation of non-thermal DFs opens the possibility of studying the effect of non-thermal emission on previously developed black hole accretion models.

Forming Gas Giants around a Range of Protostellar M-dwarfs by Gas Disk Gravitational Instability

Recent discoveries of gas giant exoplanets around M-dwarfs from transiting and radial velocity surveys are difficult to explain with core-accretion models. We present here a homogeneous suite of 162 models of gravitationally unstable gaseous disks. These models represent an existence proof for gas giants more massive than 0.1 Jupiter masses to form by the gas disk gravitational instability (GDGI) mechanism around M-dwarfs for comparison with observed exoplanet demographics and protoplanetary disk mass estimates for M-dwarf stars. We use the Enzo 2.6 adaptive mesh refinement (AMR) 3D hydrodynamics code to follow the formation and initial orbital evolution of gas giant protoplanets in gravitationally unstable gaseous disks in orbit around M-dwarfs with stellar masses ranging from 0.1 M ⊙ to 0.5 M ⊙. The gas disk masses are varied over a range from disks that are too low in mass to form gas giants rapidly to those where numerous gas giants are formed, therefore revealing the critical disk mass necessary for gas giants to form by the GDGI mechanism around M-dwarfs. The disk masses vary from 0.01 M ⊙ to 0.05 M ⊙ while the disk to star mass ratios explored the range from 0.04 to 0.3. The models have varied initial outer disk temperatures (10–60 K) and varied levels of AMR grid spatial resolution, producing a sample of expected gas giant protoplanets for each star mass. Broadly speaking, disk masses of at least 0.02 M ⊙ are needed for the GDGI mechanism to form gas giant protoplanets around M-dwarfs.

Interactive steering on in situ particle-based volume rendering framework

The development of supercomputers and multi-scale computational fluid dynamics (CFD) models based on adaptive mesh refinement (AMR) enabled fast, large-scale, and high fidelity CFD simulations. Interactive in situ steering is an effective tool for debugging, searching for optimal solutions, and analyzing inverse problems in such CFD simulations. We propose an interactive in situ steering framework for large-scale CFD simulations on GPU supercomputers. This framework employs in situ particle-based volume rendering (PBVR), in situ data sampling, and a file-based control that enables interactive and asynchronous communication of steering parameters, compressed visualization particle data, and sampled monitoring data between supercomputers and user PCs. The parallelized PBVR is processed on the host CPU to avoid interference with CFD simulations on the GPU. We apply the proposed framework to a real-time plume dispersion analysis code CityLBM, which computes the lattice Boltzmann method on the block AMR grid using GPU supercomputers. In the numerical experiment, we address an inverse problem to find a pollutant source from the observation data at monitoring points and demonstrate the effectiveness of the human-in-the-loop approach via the in situ steering framework.Graphical abstract

Addition of tabulated equation of state and neutrino leakage support to illinoisgrmhd

We have added support for realistic, microphysical, finite-temperature equations of state (EOS) and neutrino physics via a leakage scheme to illinoisgrmhd, an open-source GRMHD code for dynamical spacetimes in the einstein toolkit. These new features are provided by two new, nrpy+-based codes: nrpyeos, which performs highly efficient EOS table lookups and interpolations, and nrpyleakage, which implements a new, adaptive mesh refinement (AMR)-capable neutrino leakage scheme in the einstein toolkit. We have performed a series of strenuous validation tests that demonstrate the robustness of these new codes, particularly on the Cartesian AMR grids provided by carpet. Furthermore, we show results from fully dynamical GRMHD simulations of single unmagnetized neutron stars, and magnetized binary neutron star mergers. This new version of illinoisgrmhd, as well as nrpyeos and nrpyleakage, is pedagogically documented in jupyter notebooks and fully open source. The codes will be proposed for inclusion in an upcoming version of the einstein toolkit.

Eruption and propagation of twisted flux ropes from the base of the solar corona to 1 au

Context.Interplanetary coronal mass ejections (ICMEs) originate from the eruption of complex magnetic structures occurring in our star’s atmosphere. Determining the general properties of ICMEs and the physical processes at the heart of their interactions with the solar wind is a hard task, in particular using only unidimensional in situ profiles. Thus, these phenomena are still not well understood.Aims.In this study we simulate the propagation of a set of flux ropes in order to understand some of the physical processes occurring during the propagation of an ICME, such as their growth or their rotation.Methods.We present simulations of the propagation of a set of flux ropes in a simplified solar wind. We consider different magnetic field strengths and sizes at the initiation of the eruption, and characterize their influence on the properties of the flux ropes during their propagation. We use the 3D magnetohydrodynamics (MHD) module of the PLUTO code on an adaptive mesh refinement grid.Results.The evolution of the magnetic field of the flux rope during the propagation matches evolution law deduced from in situ observations. We also simulate in situ profiles that spacecraft would have measured at the Earth, and we compare these data with the results of statistical studies. We find a good match between simulated in situ profiles and typical profiles obtained in these studies. During their propagation, flux ropes interact with the magnetic field of the wind, but still show realistic signatures of ICMEs when analyzed with synthetic satellite crossings. We also show that flux ropes with different shapes and orientations can lead to similar unidimensional crossings. This warrants some care when extracting the magnetic topology of ICMEs using unidimensional crossings.

A MODIFIED SEQUENTIAL FULLY IMPLICIT METHOD OF COMPOSITIONAL RESERVOIR SIMULATION FOR CO2 FLOODING IN ADAPTIVE MESH REFINEMENT GRIDS

A MODIFIED SEQUENTIAL FULLY IMPLICIT METHOD OF COMPOSITIONAL RESERVOIR SIMULATION FOR CO2 FLOODING IN ADAPTIVE MESH REFINEMENT GRIDS

Magrathea-Pathfinder: a 3D adaptive-mesh code for geodesic ray tracing in N-body simulations

We introduce MAGRATHEA-PATHFINDER, a relativistic ray-tracing framework that can reconstruct the past light cone of observers in cosmological simulations. The code directly computes the 3D trajectory of light rays through the null geodesic equations, with the weak-field limit as its only approximation. This approach offers high levels of versatility while removing the need for many of the standard ray-tracing approximations such as plane-parallel, Born, or multiple-lens. Moreover, the use of adaptive integration steps and interpolation strategies based on adaptive-mesh refinement grids allows MAGRATHEA-PATHFINDER to accurately account for the nonlinear regime of structure formation and fully take advantage of the small-scale gravitational clustering. To handle very large N-body simulations, the framework has been designed as a high-performance computing post-processing tool relying on a hybrid paralleliza-tion that combines MPI tasks with C++11 std::threads. In this paper, we describe how realistic cosmological observables can be computed from numerical simulation using ray-tracing techniques. We discuss in particular the production of simulated catalogues and sky maps that account for all the observational effects considering first-order metric perturbations (such as peculiar velocities, gravitational potential, integrated Sachs-Wolfe, time-delay, and gravitational lensing). We perform convergence tests of our gravitational lensing algorithms and conduct performance benchmarks of the null geodesic integration procedures. MAGRATHEA-PATHFINDER introduces sophisticated ray-tracing tools to make the link between the space of N-body simulations and light-cone observables. This should provide new ways of exploring existing cosmological probes and building new ones beyond standard assumptions in order to prepare for the next generation of large-scale structure surveys.

Fluid-structure interaction simulations of the ASPIRE SR01 supersonic parachute flight test

High-fidelity fluid-structure interaction (FSI) simulations of the ASPIRE SR01 supersonic parachute flight test are performed through the loose coupling of computational fluid dynamics (CFD) and computational structural dynamics (CSD) solvers. The CFD solver employs a Cartesian adaptive mesh refinement (AMR) grid paradigm with a ghost cell immersed boundary method to represent arbitrarily complex geometries, and the CSD solver uses MITC3 triangular shell and Timoshenko beam elements to discretize the parachute canopy and suspension lines. The CFD resolution required to capture the deficit of the dynamic pressure in the wake of the ASPIRE payload and the aerodynamic drag on the parachute canopy is systematically studied via grid refinement study before FSI simulations are conducted. FSI simulations presented consider the inflation of an initially folded parachute canopy in freestream conditions matching the line stretch event during the ASPIRE SR01 flight test. The total pull force at the instance of peak loading is predicted to within 10% of the flight test data. The sensitivity of the total pull force and canopy projected area to the grid resolution in the CFD and CSD domains is systematically studied via another grid refinement study, and grid convergence with respect to the CFD domain resolution is demonstrated. The pull force vs time curve predicted by each CFD and CSD grid resolution varies by less than 1% indicating a high degree of repeatability and low grid-related uncertainty. Remaining differences in the qualitative behavior of the pull force curve and quantitative difference in the peak pull force are thus determined to stem from modeling errors such as the lack of deceleration, and different initial parachute and flow states in the FSI simulations compared to the flight test.

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.

Efficient 2D acoustic wave finite-difference numerical simulation in strongly heterogeneous media using the adaptive mesh refinement technique

The finite-difference method (FDM) is one of the most popular numerical methods to simulate seismic wave propagation in complex velocity models. If a uniform grid is applied in FDM for heterogeneous models, the grid spacing is determined by the global minimum velocity to suppress dispersion and dissipation errors in the numerical scheme, resulting in spatial oversampling in higher velocity zones. Then, the small grid spacing dictates a small time step due to the stability condition of explicit numerical schemes. The spatial oversampling and reduced time step will cause unnecessarily inefficient use of memory and computational resources in simulations for strongly heterogeneous media. To overcome this problem, we have used the adaptive mesh refinement (AMR) technique in the FDM to flexibly adjust the grid spacing following velocity variations. AMR is rarely used in acoustic wave simulations with the FDM due to the increased complexity of implementation, including its data management, grid generation, and computational load balancing on high-performance computing platforms. We implement AMR for 2D acoustic wave simulation in strongly heterogeneous media based on the patch approach with FDM. The AMR grid can be automatically generated for given velocity models. To simplify the implementation, we use a well-developed AMR framework, AMReX, to carry out the complex grid management. Numerical tests determine the stability, accuracy level, and efficiency of the AMR scheme. The computation time is approximately proportional to the number of grid points, and the overhead due to the wavefield exchange and data structure is small.

Cell‐based hybrid adaptive mesh refinement algorithm for immersed boundary method

AbstractThis article proposes a hybrid adaptive mesh refinement (AMR) algorithm for the immersed boundary method (IBM) combination, and the AMR code is split into mesh and physics codes to optimize each part individually. The uniform parent grid solver is used for AMR grids by constructing hanging cells for the high‐order extension. The restrictive spatial refinement in a fully threaded tree (FTT) data structure is explored, and a simplified stencil search algorithm for hanging cells construction is introduced, including current and following child AMR level cells, if any. The proposed AMR method was applied to IBM, which offers flexibility in treating complex geometries in the Cartesian grid, leading to algorithmic simplicity and computational efficiency. Local near immersed boundary refinement is proposed to avoid complex and computationally expensive IBM and AMR algorithms near the solid bodies. Finally, a high‐order flux scheme extension at AMR level transition cells and the proposed method's applicability for steady and transient flows are demonstrated. Besides state and flux variables storage, the proposed hybrid AMR method's additional cost is 4.5 words/cell instead of 3.5 words/cell for 2D and 3.75 words/cell instead of 2.75 words/cell for 3D compared to the conventional FTT‐based AMR method. By comparing the uniform grid, the AMR final grid distribution shows that the optimal cell distribution based on flow physics reduces the cells required by more than 40% to resolve the complex flow features in less computational time. The enhanced performance and accuracy of the proposed AMR method in resolving different scale flow features are validated through benchmark problems.

One-Parameter Optimal Flux Reconstruction Schemes for Adaptive Mesh Refinement

High-order schemes with larger time-step limits can benefit from using adaptive mesh refinement grids. One-parameter optimal flux reconstruction schemes are obtained by minimizing the error associated with wave propagation over the range of resolvable wavenumbers using a novel objective function that accounts for the Courant–Friedrichs–Lewy limit and order of accuracy constraint. The novel schemes are parameterized by the Courant–Friedrichs–Lewy limit, which, if chosen properly, leads to the obtained optimal Courant–Friedrichs–Lewy-like well-known schemes. The schemes are obtained by the differential evolution optimization algorithm, which is combined with the flux reconstruction–discontinuous Galerkin scheme to enlarge the time step limit on adaptive mesh refinement grids. Two numerical experiments were performed to investigate the properties of the schemes, including advection of a Gaussian bump and isentropic Euler vortex. The results show that the new schemes are more suitable for adaptive mesh refinement in terms of accuracy, dissipation, and stability.

High-resolution numerical simulation of the performance of vertical axis wind turbines in urban area: Part II, array of vertical axis wind turbines between buildings

Vertical axis wind turbines can harvest wind energy from every direction, and they are suitable for the complex flow conditions in urban areas. The flow field around buildings consists some high speed regions, and the blockage effect can provide higher wind velocity. Meanwhile, they can be installed at a certain altitude with no interference to pedestrians and vehicles. In this paper, we investigate the characteristics of wind turbines in an array by arranging them between two buildings. For this aim, a high-resolution numerical simulation method is adopted to simulate the accurate flow field and force coefficients. The high-resolution numerical simulation method is composed of adaptive mesh refinement and overset grid techniques. Firstly, there are two array types with wind turbines uniformly arranged in a line, which is perpendicular to the free stream. The result shows that array type A with asymmetric wake achieves a greater mean power coefficient. It reveals that the wake matching phenomenon of array type B causes a loss of wind energy between each couple. Secondly, five column positions between the two buildings are arranged in different positions. The five positions correspond to different flow conditions, and they belong to three typical processes: contraction acceleration process, uniform velocity process, and expansion deceleration process. When mounting array type A in contraction acceleration or expansion deceleration regions, the velocity profile is non-uniform along with the array. The power coefficients of wind turbines in one array are significantly different from each other. The array in the contraction acceleration region reaches the maximum mean power coefficient. Thirdly, in order to evaluate the influence of wind directions in urban area, there are four cases with different wind directions. The simulation results show that the array at α∞=15∘ obtains the maximum mean power coefficient. In summary, the mean output power of the wind turbine array in urban areas is always greater than that of a single wind turbine.

A two-dimensional geometric multigrid model for Poisson equation with interface on structured adaptive mesh refinement grid

In this study, a two-dimensional Geometric Multigrid (GMG) model for Poisson equation with interface on Structured Adaptive Mesh Refinement (SAMR) grid is developed. The model is designed to be combined with Navier-Stokes solvers with staggered arrangements of variables, although solvers with collocated arrangement are also applicable. Based on a general GMG method, special attention for flux conservation is taken on the coarse-fine interface. As large density ratios commonly exist in interface flows such as free surface flows, Galerkin Coarse grid Approximation (GCA) method is adopted to generate coefficients on coarse grids to enhance the robustness and efficiency of the model. Benchmark case is carried out for the validation of the model, and it is demonstrated to obtain 2nd-order accuracy and acceptable efficiency for even the density ratio reaches 104. Point iteration and line relaxation iteration of Gauss-Seidel methods are compared to obtain a better performance. Furthermore, the model is implemented in a developed Navier-Stokes solver to validate its performance in simulating interface problems. The numerical results are compared with theoretical solution or experimental data from reliable sources.

A Numerical Model for Simulating Two-Phase Flow with Adaptive Mesh Refinement

In this study, a numerical model for simulating two-phase flow is developed. The Cartesian grid with Adaptive Mesh Refinement (AMR) is adopted to reduce the computational cost. An explicit projection method is used for the time integration and the Finite Difference Method (FDM) is applied on a staggered grid for the discretization of spatial derivatives. The Volume of Fluid (VOF) method with Piecewise-Linear Interface Calculation (PLIC) is extended to the AMR grid to capture the gas-water interface accurately. A coarse-fine interface treatment method is developed to preserve the flux conservation at the interfaces. Several two-dimensional (2D) and three-dimensional (3D) benchmark cases are carried out for the validation of the model. 2D and 3D shear flow tests are conducted to validate the extension of the VOF method to the AMR grid. A 2D linear sloshing case is considered in which the model is proved to have 2nd-order accuracy in space. The efficiency of applying the AMR grid is discussed with a nonlinear sloshing problem. Finally, 2D solitary wave past stage and 2D/3D dam break are simulated to demonstrate that the model is able to simulate violent interface problems.

GPU-native gas dynamic solver on octree-based AMR grids

GPU implementation of the Godunov-type gas dynamic solver on three-dimensional octree-based grids is proposed. In this implementation, all dynamic adaptive mesh refinement (AMR) procedures are performed entirely on GPU as opposed to most of other implementations where grid metadata is transferred to CPU for further updating. Conducted bench tests show that eliminating regular CPU–GPU grid data transferring in the proposed parallel AMR algorithms makes it possible to reduce the grid modification overhead to lower than 2% on Nvidia Tesla V100. The results concerned with both CUDA and OpenMP implementation performance are also presented.

A full-field simulation methodology for sonic boom modeling on adaptive Cartesian cut-cell meshes

This paper develops a full-field direct numerical simulation methodology of sonic boom in a stratified atmosphere. The entire flow field, ranging from the near field around a supersonic body to the far field extending to the ground, is modeled by the three-dimensional Euler equations with a gravitational source term. Thus far, it has been solved using a structured grid, and an application of previous simulation to complex geometries has been limited. In this study, we realize a full-field simulation by employing the following four numerical approaches: (i) a hierarchical structured adaptive mesh refinement (AMR) method, (ii) a Cartesian cut cell method, (iii) a well-balanced finite volume method, and (iv) a segmentation method of the computational domain. A new well-balanced, MUSCL-Hancock scheme applied over Cartesian AMR and cut cell grids for a stratified atmosphere is formulated. The computational results of an oblique shock wave in a stratified atmosphere agree well with the exact solution. A full-field simulation successfully reproduces the Drop test for Simplified Evaluation of Non-symmetrically Distributed sonic boom (D-SEND) #1, conducted by the Japan Aerospace Exploration Agency (JAXA). The results of this simulation are in good agreement with those of the previous computational study, the waveform parameter method, and flight test measurements. The grid convergence study shows that the mesh size is fine enough to assess pressure signatures over the entire flow field. These results demonstrate that a full-field simulation with AMR and cut cell grids is a powerful tool for extensively analyzing three-dimensional shock wave propagation in a stratified atmosphere.

Modeling non-thermal emission from the jet-launching region of M 87 with adaptive mesh refinement

Context. The galaxy M 87 harbors a kiloparsec-scale relativistic jet, whose origin coincides with a compact source thought to be a supermassive black hole. Observational millimeter very long baseline interferometry campaigns are capable of resolving the jet-launching region at the scale of the event horizon. In order to provide a context for interpreting these observations, realistic general-relativistic magnetohydrodynamical (GRMHD) models of the accretion flow are constructed. Aims. Electrons in the jet are responsible for the observed synchrotron radiation, which is emitted in frequencies ranging from radio to near-infrared (NIR) and optical. The characteristics of the emitted radiation depend on the shape of the electrons’ energy-distribution function (eDF). The dependency on the eDF is omitted in the modeling of the first Event Horizon Telescope results. In this work, we aim to model the M 87 spectral-energy distribution from radio up to optical frequencies using a thermal-relativistic Maxwell–Jüttner distribution, as well as a relativistic κ-distribution function. The power-law index of the eDF is modeled based on sub-grid, particle-in-cell parametrizations for sub-relativistic reconnection. Methods. A GRMHD simulation in Cartesian–Kerr–Schild coordinates, using eight levels of adaptive mesh refinement (AMR), forms the basis of our model. To obtain spectra and images, the GRMHD data was post-processed with the ray-tracing code RAPTOR, which is capable of ray tracing through GRMHD simulation data that is stored in multi-level AMR grids. The resulting spectra and images maps are compared with observations. Results. We obtain radio spectra in both the thermal-jet and κ-jet models consistent with radio observations. Additionally, the κ-jet models also recover the NIR and optical emission. The images show a more extended structure at 43 GHz and 86 GHz and more compact emission at 228 GHz. The models recover the observed source sizes and core shifts and obtain a jet power of ≈1043 ergs s−1. In the κ-jet models, both the accretion rates and jet powers are approximately two times lower than the thermal-jet model. The frequency cut-off observed at ν ≈ 1015 Hz is recovered when the accelerator size is 106 − 108 cm, this could potentially point to an upper limit for plasmoid sizes in the jet of M 87.

Numerical analysis on the effects of a submerged bottom-mounted barrier in the head-on collision of two solitary waves

The collision of solitary waves is closely related to many physical problems. In this paper, the effects of a submerged bottom-mounted barrier in the head-on collision of two solitary waves are analyzed using a self-developed two-dimensional two-phase flow model. Advanced Adaptive Mesh Refinement (AMR) grid is adopted to reduce the computational cost. The free surface is captured with the Volume of Fraction (VOF) method combined with Piecewise Linear Interface Calculation (PLIC). The Immersed Boundary (IB) method is used to account for the existence of the barrier. Several benchmark problems including solitary wave propagation, head-on collision of two solitary waves, and solitary wave past a submerged barrier are considered to validate the accuracy of the model. Then the model is utilized to simulate the head-on collision of two solitary waves with the existence of a submerged bottom-mounted barrier. Both the symmetric (two waves with equal amplitudes) and asymmetric (two waves with unequal amplitudes) head-on collisions are investigated. The results with and without the barrier are compared and analyzed in detail. Special attention is paid to the variations of the wave amplitudes and the vortex sheddings.