Block-structured Adaptive Mesh Refinement Research Articles

Adjoint Methods for Guiding Adaptive Mesh Refinement in Tsunami Modeling

One difficulty in developing numerical methods for tsunami modeling is the fact that solutions contain time-varying regions where much higher resolution is required than elsewhere in the domain, particularly when tracking a tsunami propagating across the ocean. The open source GeoClaw software deals with this issue by using block-structured adaptive mesh refinement to selectively refine around propagating waves. For problems where only a target area of the total solution is of interest (e.g., one coastal community), a method that allows identifying and refining the grid only in regions that influence this target area would significantly reduce the computational cost of finding a solution. In this work, we show that solving the time-dependent adjoint equation and using a suitable inner product with the forward solution allows more precise refinement of the relevant waves. We present the adjoint methodology first in one space dimension for illustration and in a broad context since it could also be used in other adaptive software, and potentially for other tsunami applications beyond adaptive refinement. We then show how this adjoint method has been integrated into the adaptive mesh refinement strategy of the open source GeoClaw software and present tsunami modeling results showing that the accuracy of the solution is maintained and the computational time required is significantly reduced through the integration of the adjoint method into adaptive mesh refinement.

Impact of the bluff-body material on the flame leading edge structure and flame–flow interaction of premixed CH4/air flames

In this paper we investigate the interaction between the flame structure, the flow field and the coupled heat transfer with the flame holder of a laminar lean premixed CH4/air flame stabilized on a heat conducting bluff body in a channel. The study is conducted with a 2-D direct numerical simulation with detailed chemistry and species transport and with no artificial flame anchoring boundary conditions. Capturing the multiple time scales, length scales and flame-wall thermal interaction was done using a low Mach number operator-split projection algorithm, coupled with a block-structured adaptive mesh refinement and an immersed boundary method for the solid body. The flame structure displays profiles of the main species and atomic ratios similar to previously published experimental measurements on an annular bluff body configuration for both laminar and turbulent flow, demonstrating generality of the resolved flame leading edge structure for flames that stabilize on a sudden expansion. The flame structure near the bluff body and further downstream shows dependence on the thermal properties of the bluff body. We analyze the influence of flow strain and heat losses on the flame, and show that the flame stretch increases sharply at the flame leading edge, and this high stretch rate, together with heat losses, dictate the flame anchoring location. By analyzing the impact of the flame on the flow field we reveal that the strong dependence of vorticity dilatation on the flame location leads to high impact of the flame anchoring location on the flow and flame stretch downstream. This study sheds light on the impact of heat losses to the flame holder on the flame–flow feedback mechanism in lean premixed flames.

An Embedded Ghost-Fluid 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. The PDE multidimensional extrapolation approach of Aslam [1] is used to reconstruct the solution in the ghost-fluid regions and impose boundary conditions at the fluid-solid interface. The CNS equations are numerically solved by the second order multidimensional upwind method of Colella [2] and Saltzman [3]. Block-structured adaptive mesh refinement implemented under 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. Numerical examples with different Reynolds numbers for low and high Mach number flow will be presented. We compare our simulation results with other reported experimental and computational results. The significance and advantages of our implementation, which revolve around balancing between the solution accuracy and implementation difficulties, are briefly discussed as well.

BoxLib with Tiling: An Adaptive Mesh Refinement Software Framework

In this paper we introduce a block-structured adaptive mesh refinement software framework that incorporates tiling, a well-known loop transformation. Because the multiscale, multiphysics codes built in BoxLib are designed to solve complex systems at high resolution, performance on current and next generation architectures is essential. With the expectation of many more cores per node on next generation architectures, the ability to effectively utilize threads within a node is essential, and the current model for parallelization will not be sufficient. We describe a new version of BoxLib in which the tiling constructs are embedded so that BoxLib-based applications can easily realize expected performance gains without extra effort on the part of the application developer. We also discuss a path forward to enable future versions of BoxLib to take advantage of NUMA-aware optimizations using the TiDA portable library.

Modeling gravitational instabilities in self-gravitating protoplanetary disks with adaptive mesh refinement techniques

The astonishing diversity in the observed planetary population requires theoretical efforts and advances in planet formation theories. Numerical approaches provide a method to tackle the weaknesses of current planet formation models and are an important tool to close gaps in poorly constrained areas. We present a global disk setup to model the first stages of giant planet formation via gravitational instabilities (GI) in 3D with the block-structured adaptive mesh refinement (AMR) hydrodynamics code ENZO. With this setup, we explore the impact of AMR techniques on the fragmentation and clumping due to large-scale instabilities using different AMR configurations. Additionally, we seek to derive general resolution criteria for global simulations of self-gravitating disks of variable extent. We run a grid of simulations with varying AMR settings, including runs with a static grid for comparison, and study the effects of varying the disk radius. Adopting a marginally stable disk profile (Q_init=1), we validate the numerical robustness of our model for different spatial extensions, from compact to larger, extended disks (R_disk = 10, 100 and 300 AU, M_disk ~ 0.05 M_Sun, M_star = 0.646 M_Sun). By combining our findings from the resolution and parameter studies we find a lower limit of the resolution to be able to resolve GI induced fragmentation features and distinct, turbulence inducing clumps. Irrespective of the physical extension of the disk, topologically disconnected clump features are only resolved if the fragmentation-active zone of the disk is resolved with at least 100 cells, which holds as a minimum requirement for all global disk setups. Our simulations illustrate the capabilities of AMR-based modeling techniques for planet formation simulations and underline the importance of balanced refinement settings to reproduce fragmenting structures.

Compressibility Effects on Dielectric Barrier Discharge Actuation and Boundary-Layer Receptivity

Dielectric barrier discharge actuators are promising candidates for supersonic boundary-layer transition control because of their ability to concentrate energy transfer in receptive regions in the depth of the boundary layer. A detailed understanding of the plasma–flow coupling mechanisms and optimum scaling in compressible flows is necessary to develop efficient actuation schemes. In this work, the dielectric barrier discharge momentum transfer to an unstable laminar boundary layer over a flat plate under different Reynolds and freestream Mach numbers is studied. A new coupled plasma–compressible flow solver using a block-structured adaptive mesh refinement algorithm is presented, which was developed to model the force field generated by the actuator. The spectral components of the force are used as source terms for the study of the influence of flow conditions and length scales on linear receptivity.

Effects of a hot jet on detonation initiation and propagation in supersonic combustible mixtures

The effects of a hot jet on detonation initiation and propagation in supersonic combustible mixtures has been studied with two-dimensional numerical simulations with the open-source program AMROC that uses a block-structured adaptive mesh refinement method. Results indicate that the hot jet could ignite the detonation effectively in supersonic combustible mixtures like a pneumatic ramp. After the realization of the detonation initiation, the hot jet can still play an important role on the detonation propagation during its continuous ejection. For a hot jet with certain diameter, it can result in an overdriven detonation with almost constant overdrive degree. After the shutdown of the hot jet, the stable CJ detonation combustion was realized finally in the supersonic combustible mixtures. With the re-ejection of the hot jet, the failed detonation could be reinitiated quickly. Through the control of the re-ejection of the hot jet, it plays a key role not only in the initiation process, but also in the subsequent continuous detonation combustion period.

Adaptive executions of hyperbolic block-structured AMR applications on GPU systems

A block-structured adaptive mesh refinement (AMR) technique has been used to obtain numerical solutions for many scientific applications. Some block-structured AMR approaches have focused on forming patches of non-uniform sizes where the size of a patch can be tuned to the geometry of a region of interest. In this paper, we develop strategies for adaptive execution of block-structured AMR applications on GPUs, for hyperbolic directionally split solvers. While effective hybrid execution strategies exist for applications with uniform patches, our work considers efficient execution of non-uniform patches with different workloads. Our techniques include bin-packing work units to load balance GPU computations, adaptive asynchronism between CPU and GPU executions using a knapsack formulation, and scheduling communications for multi-GPU executions. Our experiments with synthetic and real data, for single-GPU and multi-GPU executions, on Tesla S1070 and Fermi C2070 clusters, show that our strategies result in up to a 3.23 speedup in performance over existing strategies.

A survey of high level frameworks in block-structured adaptive mesh refinement packages

Over the last decade block-structured adaptive mesh refinement (SAMR) has found increasing use in large, publicly available codes and frameworks. SAMR frameworks have evolved along different paths. Some have stayed focused on specific domain areas, others have pursued a more general functionality, providing the building blocks for a larger variety of applications. In this survey paper we examine a representative set of SAMR packages and SAMR-based codes that have been in existence for half a decade or more, have a reasonably sized and active user base outside of their home institutions, and are publicly available. The set consists of a mix of SAMR packages and application codes that cover a broad range of scientific domains. We look at their high-level frameworks, their design trade-offs and their approach to dealing with the advent of radical changes in hardware architecture. The codes included in this survey are BoxLib, Cactus, Chombo, Enzo, FLASH, and Uintah.

A second-order coupled immersed boundary-SAMR construction for chemically reacting flow over a heat-conducting Cartesian grid-conforming solid

In this paper, we present a second-order numerical method for simulations of reacting flow around heat-conducting immersed solid objects. The method is coupled with a block-structured adaptive mesh refinement (SAMR) framework and a low-Mach number operator-split projection algorithm. A “buffer zone” methodology is introduced to impose the solid–fluid boundary conditions such that the solver uses symmetric derivatives and interpolation stencils throughout the interior of the numerical domain; irrespective of whether it describes fluid or solid cells. Solid cells are tracked using a binary marker function. The no-slip velocity boundary condition at the immersed wall is imposed using the staggered mesh. Near the immersed solid boundary, single-sided buffer zones (inside the solid) are created to resolve the species discontinuities, and dual buffer zones (inside and outside the solid) are created to capture the temperature gradient discontinuities. The development discussed in this paper is limited to a two-dimensional Cartesian grid-conforming solid. We validate the code using benchmark simulations documented in the literature. We also demonstrate the overall second-order convergence of our numerical method. To demonstrate its capability, a reacting flow simulation of a methane/air premixed flame stabilized on a channel-confined bluff-body using a detailed chemical kinetics model is discussed.

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 1, 2, and 3 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 code's parallel performance, and discuss the Enzo collaboration's code development methodology.

Construction of Thermodynamic Properties Look-Up Table with Block-Structured Adaptive Mesh Refinement Method

An efficient procedure for evaluating the thermodynamic and transport properties of real fluids was presented. Block-structured adaptive mesh refinement was used to construct the equations of state look-up table, which provides uniform accuracy over a selected thermodynamic plane with fewer grids. An overlapping uniform index domain was developed to provide fast search capability. Properties can be evaluated by bilinear, bicubic, and biquintic interpolation to achieve different levels of function continuity and thermodynamic consistency. Reconstruction discontinuity may appear across the interface of unequally sized blocks, but the level of discontinuity decreases when reconstruction is based on structured grids on each block. The effectiveness and efficiency of the method was demonstrated by comparing the storage, data retrieval, and computational fluid dynamics samples. The storage requirement decreases by 20 to 80% compared to the table constructed with uniform mesh. The overlapping uniform index domain is 14 to 19% faster than the tree data-structure in computational fluid dynamics calculations with the table of 0.1% accuracy. When reconstructed property is within 0.1% of the exact value, the degree of discontinuity is small enough to obtain a convergent solution in computational fluid dynamics cases. An equation of state table look-up method is as efficient as ideal gas equations of state and two orders of magnitude faster than the complex thermodynamic database.

Adaptive Mesh Refinement–Based Numerical Simulation of Detonation Initiation in Supersonic Combustible Mixtures Using a Hot Jet

An open-source program implementing a block-structured adaptive mesh refinement method was adopted for the fine structure numerical simulation of detonation initiation in supersonic combustible mixtures. Simulations were conducted on a nested parallel computing system. The initiation process was specified as three stages, and their respective flow field characteristics were analyzed. Results indicate that a hot jet under specific conditions can have a similar effect as a pneumatic oblique bevel for inducing periodical shock-induced detonative combustion by a bow shock. The interaction of bow shock–induced combustion with the local detonation wave, produced by the reflection shock on the upper wall, can create a structure with two triple-wave points. The hot jet not only plays a role in the detonation initiation but also acts as a stabilizing control mechanism for detonation propagation. In the simulations in this study, the detonation wave propagates in an overdriven state initially and achieves self-sustaining motion after the shutdown of the hot jet. Subsequently, the final pisiform structure of typical stable Chapman-Jouguet detonation cells is formed.

Nyx: A MASSIVELY PARALLEL AMR CODE FOR COMPUTATIONAL COSMOLOGY

We present a new N-body and gas dynamics code, called Nyx, for large-scale cosmological simulations. Nyx follows the temporal evolution of a system of discrete dark matter particles gravitationally coupled to an inviscid ideal fluid in an expanding universe. The gas is advanced in an Eulerian framework with block-structured adaptive mesh refinement (AMR); a particle-mesh (PM) scheme using the same grid hierarchy is used to solve for self-gravity and advance the particles. Computational results demonstrating the validation of Nyx on standard cosmological test problems, and the scaling behavior of Nyx to 50,000 cores, are presented.

Block-structured adaptive mesh refinement algorithms for Vlasov simulation

Direct discretization of continuum kinetic equations, like the Vlasov equation, are under-utilized because the distribution function generally exists in a high-dimensional (>3D) space and computational cost increases geometrically with dimension. We propose to use high-order finite-volume techniques with block-structured adaptive mesh refinement (AMR) to reduce the computational cost. The primary complication comes from a solution state comprised of variables of different dimensions. We develop the algorithms required to extend standard single-dimension block structured AMR to the multi-dimension case. Specifically, algorithms for reduction and injection operations that transfer data between mesh hierarchies of different dimensions are explained in detail. In addition, modifications to the basic AMR algorithm that enable the use of high-order spatial and temporal discretizations are discussed. Preliminary results for a standard 1D+1V Vlasov–Poisson test problem are presented. Results indicate that there is potential for significant savings for some classes of Vlasov problems.

High-order schemes for predicting computational aeroacoustic propagation with adaptive mesh refinement

High-order schemes based on block-structured adaptive mesh refinement method are prepared to solve computational aeroacoustic (CAA) problems with an aim at improving computational efficiency. A number of numerical issues associated with high-order schemes on an adaptively refined mesh, such as stability and accuracy are addressed. Several CAA benchmark problems are used to demonstrate the feasibility and efficiency of the approach.

A Block-Structured Adaptive Mesh Refinement Solver for Morphodynamic Modeling

ABSTRACT Cowles, G.W., 2013. A block-structured adaptive mesh refinement solver for morphodynamic modeling. An adaptive solver for two-dimensional horizontal morphodynamic modeling studies is presented. The method employs an established augmented Riemann solver to compute unsteady, two-dimensional flows over arbitrary topography. An Exner equation is used to model the evolution of the bed using several common load formulas. The morphodynamic coupling is stabilized using an upwind approach. The scheme is implemented in a highly scalable block-structured adaptive mesh refinement framework. The resulting solver is well balanced and resolves the dry state while maintaining nonnegative depth. Idealized tests include comparison with exact Riemann solutions for dam break problems and an analytical solution for the migration of a one-dimensional sinusoidal bedform. Practical tests include the migration of a Gaussian perturbation and the evolution of flood and ebb shoals in a tidal inlet. The solver is benchmarked...

CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. III. MULTIGROUP RADIATION HYDRODYNAMICS

We present a formulation for multigroup radiation hydrodynamics that is correct to order $O(v/c)$ using the comoving-frame approach and the flux-limited diffusion approximation. We describe a numerical algorithm for solving the system, implemented in the compressible astrophysics code, CASTRO. CASTRO uses an Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically-rectangular variable-sized grids with simultaneous refinement in both space and time. In our multigroup radiation solver, the system is split into three parts, one part that couples the radiation and fluid in a hyperbolic subsystem, another part that advects the radiation in frequency space, and a parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem and the frequency space advection are solved explicitly with high-order Godunov schemes, whereas the parabolic part is solved implicitly with a first-order backward Euler method. Our multigroup radiation solver works for both neutrino and photon radiation.

Coupled Level-Set/Volume-of-Fluid Method for Simulation of Injector Atomization

This paper presents results of a multiphase computational fluid dynamics code using a coupled level-set/volume-of-fluid method to simulate liquid atomization. This interface-capturing approach combines the mass conservation properties of the volume-of-fluid method with the accurate surface reconstruction properties of the level-set method, and it includes surface tension as a volume force calculated with second-order accuracy. Developed by one of the authors, the multiphase code builds upon the combined level-set/volume-of-fluid methodology to enable bubbly flow, liquid breakup, and phase-change simulations. The extension presented in this paper couples a Lagrangian dispersed phase model for postbreakup tracking of droplets with block-structured adaptive mesh refinement on the Eulerian grid. Under an appropriate set of criteria, the transfer of droplets representation from the Eulerian to the Lagrangian discretization enables the simulation of sprays on larger domains and for longer physical times without degrading the overall accuracy of the calculation. A demonstration for like-on-like jet impingement of relevance to cold startup of liquid rocket engines is presented here at low, moderate, and high injection velocities, including validation with experimental data.

A high-resolution method for compressible two-fluid flows and simulation of three-dimensional shock-bubble interactions

SUMMARY A high-resolution method is developed to capture the material interfaces of compressible two-fluid flows in multiple dimensions. A fluid mixture model system with single velocity and pressure is used, and viscous effect can also be taken into account. A consistent thermodynamic law based on the assumption of pressure equilibrium is employed to describe the thermodynamic behaviors of the pure fluids and mixture of two components. The splitting and unsplit Eulerian formulations of piecewise parabolic method are extended to numerically integrate the hyperbolic part of the model system, whereas the system of diffusion equations is solved using an explicit, central difference scheme. The block-structured adaptive mesh refinement (AMR) capability is built in the hydrodynamic code to locally improve grid resolution. The resulting method is verified to be at least second-order accurate in space. Numerical results show that the discontinuities, particularly contact discontinuities, can be resolved sharply. The use of AMR allows flow features at disparate scales to be resolved sufficiently. In addition, three-dimensional shock–bubble interactions are simulated to investigate effects of Mach number on bubble evolution. The flow structures including those peculiar to three-dimensional bubble are resolved correctly, and some physical phenomena with increasing Mach number are reported. Copyright © 2012 John Wiley & Sons, Ltd.