Block-structured Adaptive Mesh Refinement Research Articles

Block structured adaptive mesh refinement and strong form elasticity approach to phase field fracture with applications to delamination, crack branching and crack deflection

Fracture is a ubiquitous phenomenon in most composite engineering structures, and is often the responsible mechanism for catastrophic failure. Over the past several decades, many approaches have emerged to model and predict crack failure. The phase field method for fracture uses a surrogate damage field to model crack propagation, eliminating the arduous need for explicit crack meshing. In this work a novel numerical framework is proposed for implementing hybrid phase field fracture in heterogeneous materials. The proposed method is based on the “reflux-free” method for solving, in strong form, the equations of linear elasticity on a block-structured adaptive mesh refinement (BSAMR) mesh. The use of BSAMR enables highly efficient and scalable regridding, facilitates the use of temporal subcycling for explicit time integration, and allows for ultra-high refinement at crack boundaries with minimal computational cost. The method is applied to a variety of simple heterogeneous structures: laminates, wavy interfaces, and circular inclusions. In each case a non-dimensionalized parameter study is performed to identify regions of behavior, varying both the geometry of the problem and the relative fracture energy release rate. In the laminate and wavy interface cases, regions of delamination and fracture correspond to simple analytical predictions. For the circular inclusions, the modulus ratio of the inclusion is varied as well as the delamination energy release rate and the problem geometry. In this case, a wide variety of behaviors was observed, including deflection, splitting, delamination, and pure fracture.

AMReX: Block-structured adaptive mesh refinement for multiphysics applications

Block-structured adaptive mesh refinement (AMR) provides the basis for the temporal and spatial discretization strategy for a number of Exascale Computing Project applications in the areas of accelerator design, additive manufacturing, astrophysics, combustion, cosmology, multiphase flow, and wind plant modeling. AMReX is a software framework that provides a unified infrastructure with the functionality needed for these and other AMR applications to be able to effectively and efficiently utilize machines from laptops to exascale architectures. AMR reduces the computational cost and memory footprint compared to a uniform mesh while preserving accurate descriptions of different physical processes in complex multiphysics algorithms. AMReX supports algorithms that solve systems of partial differential equations in simple or complex geometries and those that use particles and/or particle–mesh operations to represent component physical processes. In this article, we will discuss the core elements of the AMReX framework such as data containers and iterators as well as several specialized operations to meet the needs of the application projects. In addition, we will highlight the strategy that the AMReX team is pursuing to achieve highly performant code across a range of accelerator-based architectures for a variety of different applications.

超音速探测器-刚性盘-缝-带型降落伞系统的大涡模拟研究

The influences of the aerodynamic deceleration performance and the flow field structure characteristics of the capsule-rigid disk-gap-band parachute system at an initial Mach number of 2.0 and different block-structured adaptive mesh refinement were studied. In the unsteady compressible fluid, the hybrid WENO (weighted essentially non-oscillatory) and TCD (tuned center difference) schemes were used to simulate the shock wave and the smooth continuous flow field. The large-eddy simulation method with the stretched vortex subgrid model was used to deal with the turbulence. The results show that, at a low resolution of the block-structured adaptive mesh refinement, it is difficult to accurately simulate the important aerodynamic drag coefficient and capture the flow field characteristics of the parachute system. Subsequently, the convergence of the adaptive mesh refinement of the flow field was verified.

Massively parallel finite difference elasticity using block-structured adaptive mesh refinement with a geometric multigrid solver

Computationally solving the equations of elasticity is a key component in many materials science and mechanics simulations. Phenomena such as deformation-induced microstructure evolution, microfracture, and microvoid nucleation are examples of applications for which accurate stress and strain fields are required. A characteristic feature of these simulations is that the problem domain is simple (typically a rectilinear representative volume element (RVE)), but the evolution of internal topological features is extremely complex. Traditionally, the finite element method (FEM) is used for elasticity calculations; FEM is nearly ubiquitous due to (1) its ability to handle meshes of complex geometry using isoparametric elements, and (2) the weak formulation which eschews the need for computation of second derivatives. However, variable topology problems (e.g. microstructure evolution) require either remeshing, or adaptive mesh refinement (AMR) - both of which can cause extensive overhead and limited scaling. Block-structured AMR (BSAMR) is a method for adaptive mesh refinement that exhibits good scaling and is well-suited for many problems in materials science. Here, it is shown that the equations of elasticity can be efficiently solved using BSAMR using the finite difference method. The boundary operator method is used to treat different types of boundary conditions, and the “reflux-free” method is introduced to efficiently and easily treat the coarse-fine boundaries that arise in BSAMR. Examples are presented that demonstrate the use of this method in a variety of cases relevant to materials science: Eshelby inclusions, fracture, and microstructure evolution. Reasonable scaling is demonstrated up to ∼4000 processors with tens of millions of grid points, and good AMR efficiency is observed.

A lattice Boltzmann modeling of viscoelastic drops’ deformation and breakup in simple shear flows

The deformation and breakup of viscoelastic drops in simple shear flows of Newtonian liquids are studied numerically. Our three-dimensional numerical scheme, extended from our previous two-dimensional algorithm, employs a diffusive-interface lattice Boltzmann method together with a lattice advection–diffusion scheme, the former to model the macroscopic hydrodynamic equations for multiphase fluids and the latter to describe the polymer dynamics modeled by the Oldroyd-B constitutive model. A block-structured adaptive mesh refinement technique is implemented to reduce the computational cost. The multiphase model is validated by a simulation of Newtonian drop deformation and breakup under an unconfined steady shear, while the coupled algorithm is validated by simulating viscoelastic drop deformation in the shear flow of a Newtonian matrix. The results agree with the available numerical and experimental results from the literature. We quantify the drop response by changing the polymer relaxation time λ and the concentration of the polymer c. The viscoelasticity in the drop phase suppresses the drop deformation, and the steady-state drop deformation parameter D exhibits a non-monotonic behavior with the increase in Deborah number De (increase in λ) at a fixed capillary number Ca. This is explained by the two distribution modes of the polymeric elastic stresses that depend on the polymer relaxation time. As the concentration of the polymer c increases, the degree of suppression of deformation becomes stronger and the transient result of D displays an overshoot. The critical capillary number for unconfined drop breakup increases due to the inhibitive effects of viscoelasticity. Different distribution modes of elastic stresses are reported for different De.

Analysis and Performance Evaluation of Adjoint-guided Adaptive Mesh Refinement for Linear Hyperbolic PDEs Using Clawpack

Adaptive mesh refinement (AMR) is often used when solving time-dependent partial differential equations using numerical methods. It enables time-varying regions of much higher resolution, which can selectively refine areas to track discontinuities in the solution. The open source Clawpack software implements block-structured AMR to refine around propagating waves in the AMRClaw package. For problems where the solution must be computed over a large domain but is only of interest in a small area, this approach often refines waves that will not impact the target area. We seek a method that enables the identification and refinement of only the waves that will influence the target area. Here we show that solving the time-dependent adjoint equation and using a suitable inner product allows for a more precise refinement of the relevant waves. We present the adjoint methodology in general and give details on the implementation of this method in AMRClaw. Examples and a computational performance analysis for linear acoustics equations are presented. The adjoint method is compared to AMR methods already available in AMRClaw, and the advantages and disadvantages are discussed. The approach presented here is implemented in Clawpack, in Version 5.6.1, and code for all examples presented is archived on Github.

MAESTROeX: A Massively Parallel Low Mach Number Astrophysical Solver

Abstract We present MAESTROeX, a massively parallel solver for low Mach number astrophysical flows. The underlying low Mach number equation set allows for efficient, long-time integration for highly subsonic flows compared to compressible approaches. MAESTROeX is suitable for modeling full spherical stars as well as well as planar simulations of dynamics within localized regions of a star, and can robustly handle several orders of magnitude of density and pressure stratification. Previously, we have described the development of the predecessor of MAESTROeX, called MAESTRO, in a series of papers. Here, we present a new, greatly simplified temporal integration scheme that retains the same order of accuracy as our previous approaches. We also explore the use of alternative spatial mapping of the one-dimensional base state onto the full Cartesian grid. The code leverages the new AMReX software framework for block-structured adaptive mesh refinement (AMR) applications, allowing for scalability to large fractions of leadership-class machines. Using our previous studies on the convective phase of single-degenerate progenitor models of SNe Ia as a guide, we characterize the performance of the code and validate the new algorithmic features. Like MAESTRO, MAESTROeX is fully open source.

A formulation for high-fidelity simulations of pool boiling in low gravity

Direct numerical simulation of pool boiling under varying gravity environments was performed and compared with experimental data. The three dimensional solver is fully explicit in time and uses a fractional step method for Navier-Stokes, energy and mass transfer equations. A level-set technique is used to represent and advect the interface. Sharp jumps are applied to the diffusion terms using a ghost-fluid method and the advection terms are discretized using a third order weighted essentially non-oscillatory scheme. A multi-level, block-structured adaptive mesh refinement is used to selectively refine the grid around the interface and thermal boundary layer. The latter contributes towards accurate calculation of evaporative heat flux. The pressure Poisson solver uses Hypre to solve the linear system on the coarsest level and geometric multi-grid method to prolong-restrict the solution between successive refinements. Parallelization is achieved using MPI on distributed memory systems and a dynamic contact line model is implemented to account for inertial effects on vapor bubbles due to wall adhesion force. Validation cases are presented to test the accuracy of the solver in comparison to analytical and experimental results. Replicability is also demonstrated by comparing results with already published data. A simple mathematical model is used to account for nucleation site density and results of pool boiling simulations are compared with experimental results to illustrate the effects of subcooling and gravity.

LES study on aerodynamics of auto-rotating square flat plate by IBM and SAMR

Windborne debris is caused by severe wind events, such as typhoons and tornadoes. Among the various shapes, sheet-shaped debris has especially complex flight behavior due to the Magnus effect induced by autorotation. In this study, we simulate flows past an autorotating flat square plate pinned with a freely rotatable axis (one degree-of-freedom) and a free-flight flat square plate (six degrees-of-freedom). Therefore, the coupled model for fluid flow and a rigid body based on large-eddy simulation has been developed using the immersed-boundary method and block-structured adaptive mesh refinement to capture details of the vortex structures around the moving plate. This model has such efficiency of computation that the boundary of the moving plate can be treated as passing through a fixed mesh pattern represented by sufficiently fine Cartesian grids, avoiding time-dependent grid generation in a boundary-fitted manner. The aerodynamics of the auto-rotating flat plate was examined and confirmed to validate the present model. Moreover, the unsteady forces based on wake vortices in the process of successive deformation are identified, and their roles on autorotation are clarified. In the case of free flight, the sensitive instability of the axis during autorotation and the effects of translational motion on rotational motion are discussed.

AMReX: a framework for block-structured adaptive mesh refinement

Author(s): Zhang, Weiqun; Almgren, Ann; Beckner, Vince; Bell, John; Blaschke, Johannes; Chan, Cy; Day, Marcus; Friesen, Brian; Gott, Kevin; Graves, Daniel; Katz, Max; Myers, Andrew; Nguyen, Tan; Nonaka, Andrew; Rosso, Michele; Williams, Samuel; Zingale, Michael

A fourth-order adaptive mesh refinement algorithm for the multicomponent, reacting compressible Navier–Stokes equations

In this paper, we present a fourth-order in space and time block-structured adaptive mesh refinement algorithm for the compressible multicomponent reacting Navier–Stokes equations. The algorithm uses a finite-volume approach that incorporates a fourth-order discretisation of the convective terms. The time-stepping algorithm is based on a multi-level spectral deferred corrections method that enables explicit treatment of advection and diffusion coupled with an implicit treatment of reactions. The temporal scheme is embedded in a block-structured adaptive mesh refinement algorithm that includes subcycling in time with spectral deferred correction sweeps applied on levels. Here we present the details of the multi-level scheme paying particular attention to the treatment of coarse–fine boundaries required to maintain fourth-order accuracy in time. We then demonstrate the convergence properties of the algorithm on several test cases including both non-reacting and reacting flows. Finally we present simulations of a vitiated dimethyl ether jet in 2D and a turbulent hydrogen jet in 3D, both with detailed kinetics and transport.

CPU Isosurface Ray Tracing of Adaptive Mesh Refinement Data.

Adaptive mesh refinement (AMR) is a key technology for large-scale simulations that allows for adaptively changing the simulation mesh resolution, resulting in significant computational and storage savings. However, visualizing such AMR data poses a significant challenge due to the difficulties introduced by the hierarchical representation when reconstructing continuous field values. In this paper, we detail a comprehensive solution for interactive isosurface rendering of block-structured AMR data. We contribute a novel reconstruction strategy-the octant method-which is continuous, adaptive and simple to implement. Furthermore, we present a generally applicable hybrid implicit isosurface ray-tracing method, which provides better rendering quality and performance than the built-in sampling-based approach in OSPRay. Finally, we integrate our octant method and hybrid isosurface geometry into OSPRay as a module, providing the ability to create high-quality interactive visualizations combining volume and isosurface representations of BS-AMR data. We evaluate the rendering performance, memory consumption and quality of our method on two gigascale block-structured AMR datasets.

Block-based adaptive mesh refinement for fluid–structure interactions in incompressible flows

In this study, an immersed boundary (IB) approach on the basis of moving least squares (MLS) interpolation is proposed for analyzing the dynamic response of a rigid body immersed in incompressible flows. An improved mapping strategy is proposed for a quick update of the signed distance field. A CIP-CSL (constraint interpolation profile - semi-Lagrangian) scheme with a compact stencil is adopted for the convective term in momentum equation. Fluid–structure interaction problems can be solved by either the weak or the strong coupling schemes according to the density ratio of the solid and fluid. This research is based on our previous studies on block-structured adaptive mesh refinement (AMR) method for incompressible flows (Liu & Hu, 2018). Present AMR-FSI solver is proved to be accurate and robust in predicting dynamics of VIV (vortex induced vibration) problems. The efficiency of the adaptive method is demonstrated by the 2D simulation of a freely falling plate with the comparison to other numerical methods. Finally, the freely falling and rising 3D sphere are computed and compared with corresponding experimental measurement.

Meeting the Challenges of Modeling Astrophysical Thermonuclear Explosions: Castro, Maestro, and the AMReX Astrophysics Suite

We describe the AMReX suite of astrophysics codes and their application to modeling problems in stellar astrophysics. Maestro is tuned to efficiently model subsonic convective flows while Castro models the highly compressible flows associated with stellar explosions. Both are built on the block-structured adaptive mesh refinement library AMReX. Together, these codes enable a thorough investigation of stellar phenomena, including Type Ia supernovae and X-ray bursts. We describe these science applications and the approach we are taking to make these codes performant on current and future many-core and GPU-based architectures.

Neutron transport solution of lattice Boltzmann method and streaming-based block-structured adaptive mesh refinement

Simulation of neutron transport problem is the kernel of nuclear reactor physics, whose application, however, is limited by the exorbitant computational cost and complex geometry structure. This paper presents a lattice Boltzmann method (LBM) for multi-group neutron transport process and proposes a streaming-based block-structured adaptive-mesh-refinement (SSAMR) technique. The neutron lattice Boltzmann equation is deduced from the neutron transport equation and the macroscopic neutron diffusion equation can be recovered from neutron lattice Boltzmann equation via the Chapman-Enskog expansion, which makes the kinetic significance of lattice Boltzmann equation clearly. The significance of relaxation time for neutron LBM is further discussed for the first time, and the factors affecting the neutron relaxation process are studied deeply also. After establishing the neutron LBM, the SSAMR technique is applied to efficiently utilizing the computational resources of proposed LBM. To simply achieve the data communication between different meshes and eliminate the discontinuity of scalar neutron flux, a data exchange technique based on the streaming process of LBM is adopted. Simulation results show that the proposed LBM can be applied to solving neutron transport process in all dimensions, and the SSAMR technique can not only effectively reduce the computational cost, but also be easily implemented. This work may provide some new perspectives for solving the neutron transport process and a powerful thought for large and complex engineering calculation.

An ideal compressible magnetohydrodynamic solver with parallel block-structured adaptive mesh refinement

We present an adaptive parallel solver for the numerical simulation of ideal magnetohydrodynamics in two and three space dimensions. The discretisation uses a finite volume scheme based on a Cartesian mesh and an explicit compact Runge–Kutta scheme for time integration. Numerically, a generalized Lagrangian multiplier approach with a mixed hyperbolic-parabolic correction is used to guarantee a control on the incompressibility of the magnetic field. We implement the solver in the AMROC (Adaptive Mesh Refinement in Object-oriented C++) framework that uses a structured adaptive mesh refinement (SAMR) method discretisation-independent and is fully parallelised for distributed memory systems. Moreover, AMROC is a modular framework providing manageability, extensibility and efficiency. In this paper, we give an overview of the ideal magnetohydrodynamics solver developed in this framework and its capabilities. We also include an example of this solver’s verification with other codes and its numerical and computational performance.

Extreme-Scale Block-Structured Adaptive Mesh Refinement

In this article, we present a novel approach for block-structured adaptive mesh refinement (AMR) that is suitable for extreme-scale parallelism. All data structures are designed such that the size of the meta data in each distributed processor memory remains bounded independent of the processor number. In all stages of the AMR process, we use only distributed algorithms. No central resources such as a master process or replicated data are employed, so that an unlimited scalability can be achieved. For the dynamic load balancing in particular, we propose to exploit the hierarchical nature of the block-structured domain partitioning by creating a lightweight, temporary copy of the core data structure. This copy acts as a local and fully distributed proxy data structure. It does not contain simulation data, but only provides topological information about the domain partitioning into blocks. Ultimately, this approach enables an inexpensive, local, diffusion-based dynamic load balancing scheme. We demonstrate the excellent performance and the full scalability of our new AMR implementation for two architecturally different petascale supercomputers. Benchmarks on an IBM Blue Gene/Q system with a mesh containing 3.7 trillion unknowns distributed to 458,752 processes confirm the applicability for future extreme-scale parallel machines. The algorithms proposed in this article operate on blocks that result from the domain partitioning. This concept and its realization support the storage of arbitrary data. In consequence, the software framework can be used for different simulation methods, including mesh based and meshless methods. In this article, we demonstrate fluid simulations based on the lattice Boltzmann method.

Relativistic Vlasov-Maxwell modelling using finite volumes and adaptive mesh refinement

The dynamics of collisionless plasmas can be modelled by the Vlasov-Maxwell system of equations. An Eulerian approach is needed to accurately describe processes that are governed by high energy tails in the distribution function, but is of limited efficiency for high dimensional problems. The use of an adaptive mesh can reduce the scaling of the computational cost with the dimension of the problem. Here, we present a relativistic Eulerian Vlasov-Maxwell solver with block-structured adaptive mesh refinement in one spatial and one momentum dimension. The discretization of the Vlasov equation is based on a high-order finite volume method. A flux corrected transport algorithm is applied to limit spurious oscillations and ensure the physical character of the distribution function. We demonstrate a speed-up by a factor of 7 × in a typical scenario involving laser pulse interaction with an underdense plasma due to the use of an adaptive mesh.Graphical abstract

A versatile embedded boundary adaptive mesh method for compressible flow in complex geometry

We present an embedded ghost fluid method for numerical solutions of the compressible Navier Stokes (CNS) equations in arbitrary complex domains. A PDE multidimensional extrapolation approach is used to reconstruct the solution in the ghost fluid regions and imposing boundary conditions on the fluid–solid interface, coupled with a multi-dimensional algebraic interpolation for freshly cleared cells. The CNS equations are numerically solved by the second order multidimensional upwind method. Block-structured adaptive mesh refinement, implemented with the Chombo framework, is utilized to reduce the computational cost while keeping high resolution mesh around the embedded boundary and regions of high gradient solutions. The versatility of the method is demonstrated via several numerical examples, in both static and moving geometry, ranging from low Mach number nearly incompressible flows to supersonic flows. Our simulation results are extensively verified against other numerical results and validated against available experimental results where applicable. The significance and advantages of our implementation, which revolve around balancing between the solution accuracy and implementation difficulties, are briefly discussed as well.

Application of Block-structured Adaptive Mesh Refinement to Particle Simulation

We implemented the particle treatment in the block-structured adaptive mesh refinement (AMR) framework which we have developed. In the AMR framework, the simulation domain is divided into multiple sub-domains and they are assigned to a number of processes for parallel calculation using MPI. A sub-domain is composed of multiple block-structured regions each of which has the fixed number of grids. When high resolution is required at a certain region in the sub-domain, a block-structured region with refined grids, which is called child block, is locally created. To apply this AMR framework to the particle simulations such as particle-in-cell simulation, we set up several arrays for the particle treatment for each sub-domain assigned to one process. These arrays are shared among all the blocks consisting of the corresponding sub-domain. For the particle calculation in each block, we also set up several other arrays which are privately defined and used in each block. The functions for these arrays for the particle treatment are described in this paper. To test the implementation of the particle treatment in the AMR framework, we performed test simulations by adopting the sugarscape model which was proposed for the simulation of an artificial society by using many agents representing inhabitants in a certain area. We treated the inhabitants as a bunch of particles and assign the sugar amount at each grid as the environment in a two-dimensional simulation domain. In the simulation, we initially place two peaks of sugar and randomly distribute the inhabitants. For simplicity, we examined the motions of the inhabitants agents by assuming no temporal variation of the sugar. The simulation results show that the inhabitant agents were accelerated and gathered to the two sugar peaks as we expected. When the inhabitant density exceeded a certain criteria, child blocks with refined grids were adaptively created at the corresponding region. We confirmed that the motions of the inhabitants were not influenced by the block boundaries, which ensures that the particle treatment to the AMR framework has been properly implemented.