SEARCH · Engineering Papers

Results for “Mesh Refinement”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2

All sources NASA NTRS DOE OSTI

DOE OSTI2021

Structured Adaptive Mesh Refinement Adaptations to Retain Performance Portability With Increasing Heterogeneity

Adaptive mesh refinement (AMR) is an important method that enables many mesh-based applications to run at effectively higher resolution within limited computing resources by allowing high resolution only where really needed. This advantage comes at a cost, however: greater complexity in the mesh management machinery and challenges with load distribution. With the current trend of increasing heterogeneity in hardware architecture, AMR presents an orthogonal axis of complexity. Additionally, the usual techniques, such as asynchronous communication and hierarchy management for parallelism and memory that are necessary to obtain reasonable performance are very challenging to reason about with AMR. Different groups working with AMR are bringing different approaches to this challenge. Here, we examine the design choices of several AMR codes and also the degree to which demands placed on them by their users influence these choices.

42 ENGINEERING↗

NASA NTRS2001

Highly parallel structured adaptive mesh refinement using parallel language-based approaches

Adaptive mesh refinement (AMR) calculations carried out on structured meshes play an exceedingly important role in several areas of science and engineering. A strategy for using Fortran 90 in an object-oriented fashion is presented. This permits AMR applications to be expressed in terms of familiar abstractions that are natural to the process of solving AMR hierarchies. The OpenMP features that are useful for parallel processing of AMR hierarchies in a load balanced fashion on multiprocessors is described.

computational↗

DOE OSTI2020

Source Discretization Near Curvilinear Mesh Refinements in One Dimeions (Summer Internship Final Report)

Lawrence Livermore National Lab developed the seismic wave code SW4 for earthquake simulations, and has recently added the ability to specify mesh-refinement interfaces in the curvilinear mesh. The primary purpose of this is to allow for high resolution near the surface, with relatively fewer total points in the mesh leading to shorter computation time. Presently, the code does not allow for point-source forcing terms (commonly used in seismic simulations) to be located near these curvilinear mesh refinement interfaces. The goal of this internship was to investigate the discretization of point-source forcing terms in the seismic wave equation when the sources are located near the interfaces between two curvilinear meshes. Ultimately this will be incorporated into SW4 to allow for more realistic simulations to be carried out in this faster implementation.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1994

Error estimation and adaptive mesh refinement for parallel analysis of shell structures

The formulation and application of element-level, element-independent error indicators is investigated. This research culminates in the development of an error indicator formulation which is derived based on the projection of element deformation onto the intrinsic element displacement modes. The qualifier 'element-level' means that no information from adjacent elements is used for error estimation. This property is ideally suited for obtaining error values and driving adaptive mesh refinements on parallel computers where access to neighboring elements residing on different processors may incur significant overhead. In addition such estimators are insensitive to the presence of physical interfaces and junctures. An error indicator qualifies as 'element-independent' when only visible quantities such as element stiffness and nodal displacements are used to quantify error. Error evaluation at the element level and element independence for the error indicator are highly desired properties for computing error in production-level finite element codes. Four element-level error indicators have been constructed. Two of the indicators are based on variational formulation of the element stiffness and are element-dependent. Their derivations are retained for developmental purposes. The second two indicators mimic and exceed the first two in performance but require no special formulation of the element stiffness mesh refinement which we demonstrate for two dimensional plane stress problems. The parallelizing of substructures and adaptive mesh refinement is discussed and the final error indicator using two-dimensional plane-stress and three-dimensional shell problems is demonstrated.

Keating, Scott C.↗

NASA NTRS1995

Parallel adaptive mesh refinement within the PUMAA3D Project

To enable the solution of large-scale applications on distributed memory architectures, we are designing and implementing parallel algorithms for the fundamental tasks of unstructured mesh computation. In this paper, we discuss efficient algorithms developed for two of these tasks: parallel adaptive mesh refinement and mesh partitioning. The algorithms are discussed in the context of two-dimensional finite element solution on triangular meshes, but are suitable for use with a variety of element types and with h- or p-refinement. Results demonstrating the scalability and efficiency of the refinement algorithm and the quality of the mesh partitioning are presented for several test problems on the Intel DELTA.

Freitag, Lori↗

DOE OSTI2025

Dominant balance-based adaptive mesh refinement for incompressible fluid flows

This work introduces a novel adaptive mesh refinement (AMR) method that utilizes dominant balance analysis (DBA) for efficient and accurate grid adaptation in computational fluid dynamics (CFD) simulations. The proposed method leverages a Gaussian mixture model (GMM) to classify grid cells into active and passive regions based on the dominant physical interactions within the equation space. By modeling truncation error probabilistically from discretized terms, the method identifies regions of high interaction where numerical accuracy is most sensitive to resolution. Unlike traditional AMR strategies, this approach does not rely on heuristic-based sensors or user-defined thresholds, providing a fully automated and problem-independent framework for AMR. Applied to the incompressible Navier-Stokes equations for steady and unsteady flow past a cylinder, the DBA-based AMR method achieves comparable accuracy to high-resolution grids while reducing computational costs by up to 70 %. The validation highlights the method’s effectiveness in capturing complex flow features while minimizing grid cells, directing computational resources toward regions with the most critical dynamics. This modular and scalable strategy is adaptable to a wide range of applications, presenting a promising tool for efficient high-fidelity simulations in CFD and other multiphysics domains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

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.

Zhang, Weiqun↗

DOE OSTI2024

Adaptive mesh refinement in binary black holes simulations

Abstract We discuss refinement criteria for the Berger–Rigoutsos (block-based) refinement algorithm in our numerical relativity code GR-Athena++ in the context of binary black hole (BBH) merger simulations. We compare three different strategies: the ‘box-in-box’ approach, the ‘sphere-in-sphere’ approach and a local criterion for refinement based on the estimation of truncation error of the finite difference scheme. We extract and compare gravitational waveforms using the three different mesh refinement methods and compare their accuracy against a calibration waveform and demonstrate that the sphere-in-sphere approach provides the best strategy overall when considering computational cost and the waveform accuracy. Ultimately, we demonstrate the capability of each mesh refinement method in accurately simulating gravitational waves from BBH systems—a crucial aspect for their application in next-generation detectors. We quantify the mismatch achievable with the different strategies by extrapolating the gravitational wave mismatch to higher resolution.

Astronomy & Astrophysics↗

NASA NTRS1985

Stability of interfaces with mesh refinement

A study is conducted of the stability of mesh refinement in space and time for several different interface equations and finite-difference approximations. First, a root condition which implies stability for the initial-boundary value problem for this type of interface is derived. From the root condition, the stability of several interface equations is proved, using the maximum principle. In some cases, the final verification steps can be done analytically; in other cases, a simple computer program has been written to check the condition for values of a parameter along the boundary of the unit circle. Using this method, stability for Lax-Wendroff with all the interface conditions considered, and for Leapfrog with interpolation interface conditions when the fine and coarse grids overlap is proved.

Berger, M. J.↗

NASA NTRS1994

Computations of Unsteady Viscous Compressible Flows Using Adaptive Mesh Refinement in Curvilinear Body-fitted Grid Systems

A methodology for accurate and efficient simulation of unsteady, compressible flows is presented. The cornerstones of the methodology are a special discretization of the Navier-Stokes equations on structured body-fitted grid systems and an efficient solution-adaptive mesh refinement technique for structured grids. The discretization employs an explicit multidimensional upwind scheme for the inviscid fluxes and an implicit treatment of the viscous terms. The mesh refinement technique is based on the AMR algorithm of Berger and Colella. In this approach, cells on each level of refinement are organized into a small number of topologically rectangular blocks, each containing several thousand cells. The small number of blocks leads to small overhead in managing data, while their size and regular topology means that a high degree of optimization can be achieved on computers with vector processors.

Steinthorsson, E.↗

NASA NTRS1995

Some observations on mesh refinement schemes applied to shock wave phenomena

This workshop's double-wedge test problem is taken from one of a sequence of experiments which were performed in order to classify the various canonical interactions between a planar shock wave and a double wedge. Therefore to build up a reasonably broad picture of the performance of our mesh refinement algorithm we have simulated three of these experiments and not just the workshop case. Here, using the results from these simulations together with their experimental counterparts, we make some general observations concerning the development of mesh refinement schemes for shock wave phenomena.

Quirk, James J.↗

NASA NTRS2000

Local Mesh Refinement in the Space-Time CE/SE Method

A local mesh refinement procedure for the CE/SE method which does not use an iterative procedure in the treatments of grid-to-grid communications is described. It is shown that a refinement ratio higher than ten can be applied successfully across a single coarse grid/fine grid interface.

Chang, Sin-Chung↗

NASA NTRS2002

Interface Conditions for Wave Propagation Through Mesh Refinement Boundaries

We study the propagation of waves across fixed mesh refinement boundaries in linear and nonlinear model equations in 1-D and 2-D, and in the 3-D Einstein equations of general relativity. We demonstrate that using linear interpolation to set the data in guard cells leads to the production of reflected waves at the refinement boundaries. Implementing quadratic interpolation to fill the guard cells eliminates these spurious signals.

Choi, Dae-II↗

NASA NTRS2004

Evolving a Puncture Black Hole with Fixed Mesh Refinement

We present a detailed study of the effects of mesh refinement boundaries on the convergence and stability of simulations of black hole spacetimes. We find no technical problems. In our applications of this technique to the evolution of puncture initial data, we demonstrate that it is possible to simulaneously maintain second order convergence near the puncture and extend the outer boundary beyond 100M, thereby approaching the asymptotically flat region in which boundary condition problems are less difficult.

Imbiriba, Breno↗

NASA NTRSDate not supplied

The Influence of Adaptive Mesh Refinement on the Prediction of Vortex Interactions about a Generic Missile Airframe

The complex interaction of forebody and wing vortices significantly impacts missile aerodynamics. The formation of these vortices involves smooth regions of the geometry or geometric discontinuities like leading edges, trailing edges, tips, and corners. Regions of supersonic flow and complex shock topologies interact with boundary layers and vortices. Smooth-body separation and 3D viscous effects strain current Reynolds-averaged Navier-Stokes (RANS) techniques. The quantification and control of discretization error is critical to obtaining reliable simulation results and often turbulence model assessments are made in the presence of unquantified (and potentially large) discretization errors. Two mesh adaptation schemes are applied to steady RANS simulations. Multiscale unstructured mesh adaptation is applied to control interpolation error estimates of the Mach field, which resolves boundary layers, vortices, and shocks. A dual-mesh approach with overset communication is applied between an expert-crafted near-body unstructured mesh and an adaptive off-body Cartesian mesh refined with Q-criterion scaled by the strain tensor magnitude. A generic missile configuration is examined in a supersonic flow field to show the interaction of mesh adaptation and turbulence model. Turbulence model modifications for rotational correction and a quadratic constitutive relationship show a strong influence on adaptive mesh refinement and predicted rolling moment.

slender body aerodynamics↗

DOE OSTI2023

Mesh refinement for anisotropic diffusion in magnetized plasmas

Highly accurate simulation of plasma transport is needed to drive the successful design and operation of magnetically confined fusion reactors. Unfortunately, the extreme anisotropy present in magnetized plasmas results in thin boundary layers that are expensive to resolve. Here, this work investigates how various mesh refinement strategies might reduce that expense to allow for more efficient simulation by comparing standard variable refinement approaches that use a field quantity to an adaptive approach that uses an error estimator. It is first verified that higher order discretization only realizes the proper rate of convergence once the mesh resolves the thin boundary layer, therefore motivating the focusing of refinement on the boundary layer. For three two-dimensional test cases that contain characteristic features of tokamak magnetic fields, an exponential refinement strategy based on the magnetic flux function, which is the standard refinement approach in the field, is compared to an adaptive strategy utilizing the established Zienwiekicz and Zhu error estimator. The adaptive mesh refinement strategy consistently achieves the same accuracy using orders of magnitude less degrees of freedom than either exponential or uniform refinement. This result makes the adaptive refinement strategy more efficient than the exponential refinement strategy while also being more generalizable to problems with complex magnetic geometries. Scaling laws are derived that quantify the improvement in cost of the adaptive refinement strategy over other refinement approaches in 2D and 3D.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

GR-Athena++: Puncture Evolutions on Vertex-centered Oct-tree Adaptive Mesh Refinement

Numerical relativity is central to the investigation of astrophysical sources in the dynamical and strong-field gravity regime, such as binary black hole and neutron star coalescences. Current challenges set by gravitational-wave and multimessenger astronomy call for highly performant and scalable codes on modern massively parallel architectures. We present GR-Athena++, a general-relativistic, high-order, vertex-centered solver that extends the oct-tree, adaptive mesh refinement capabilities of the astrophysical (radiation) magnetohydrodynamics code Athena++. To simulate dynamical spacetimes, GR-Athena++ uses the Z4c evolution scheme of numerical relativity coupled to the moving puncture gauge. We demonstrate stable and accurate binary black hole merger evolutions via extensive convergence testing, cross-code validation, and verification against state-of-the-art effective-one-body waveforms. GR-Athena++ leverages the task-based parallelism paradigm of Athena++ to achieve excellent scalability. We measure strong-scaling efficiencies above 95% for up to ~1.2 × 10 4 CPUs and excellent weak scaling is shown up to ~10 5 CPUs in a production binary black hole setup with adaptive mesh refinement. GR-Athena++ thus allows for the robust simulation of compact binary coalescences and offers a viable path toward numerical relativity at exascale.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Dark matter from axion strings with adaptive mesh refinement

Abstract 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.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗