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At least 343 records · Page 19

Systematic generation of nonlinear discretized dynamic equilibrium equations of spinning cantilevers

General nonlinear discretized governing equations of motion of spinning elastic solids and structures are adjusted for the case of a spinning cantilever with initial geometric imperfections. Consideration is given to second degree nonlinearities in the strain-displacement and velocity-displacement relationships. Parameters of the discretization are developed to include the type and number of the coordinate functions used in the admissible trial solution in order to unify the discretization approaches associated with stationarity principles. The coordinate functions comprise both sets of continuous and piecewise continuous functions employed in the Rayleigh-Ritz and the finite element methods, respectively. Coefficient matrices are provided which contain the energy density expressions and which are adaptable to computer programming.

El-Essawi, M.↗

An error estimation procedure for plate bending elements

Procedures for identifying and eliminating errors inherent in individual finite elements and those due to the discretization of the continuum are presented. The elemental errors are identified through the use of an element formulation procedure based on physically interpretable strain gradient interpolation functions. The use of physically interpretable notation allows these errors to be eliminated using rational arguments. The discretization errors are identified by comparing the finite-element solution with a smoothed superconvergent solution. The errors thus identified are used to guide an adaptive mesh refinement procedure which produces improved results.

Dow, John O.↗

Adaptive implicit-explicit and parallel element-by-element iteration schemes

Adaptive implicit-explicit (AIE) and grouped element-by-element (GEBE) iteration schemes are presented for the finite element solution of large-scale problems in computational mechanics and physics. The AIE approach is based on the dynamic arrangement of the elements into differently treated groups. The GEBE procedure, which is a way of rewriting the EBE formulation to make its parallel processing potential and implementation more clear, is based on the static arrangement of the elements into groups with no inter-element coupling within each group. Various numerical tests performed demonstrate the savings in the CPU time and memory.

Tezduyar, T. E.↗

A-Posteriori Error Estimation for Hyperbolic Conservation Laws with Constraint

This lecture considers a-posteriori error estimates for the numerical solution of conservation laws with time invariant constraints such as those arising in magnetohydrodynamics (MHD) and gravitational physics. Using standard duality arguments, a-posteriori error estimates for the discontinuous Galerkin finite element method are then presented for MHD with solenoidal constraint. From these estimates, a procedure for adaptive discretization is outlined. A taxonomy of Green's functions for the linearized MHD operator is given which characterizes the domain of dependence for pointwise errors. The extension to other constrained systems such as the Einstein equations of gravitational physics are then considered. Finally, future directions and open problems are discussed.

Barth, Timothy↗

Surface Remeshing with Robust High-Order Reconstruction

Remeshing is an important problem in variety of applications, such as finite element methods and geometry processing. Surface remeshing poses some unique challenges, as it must deliver not only good mesh quality but also good geometric accuracy. For applications such as finite elements with high-order elements (quadratic or cubic elements), the geometry must be preserved to high-order (third-order or higher) accuracy, since low-order accuracy may undermine the convergence of numerical computations. The problem is particularly challenging if the CAD model is not available for the underlying geometry, and is even more so if the surface meshes contain some inverted elements. We describe remeshing strategies that can simultaneously produce high-quality triangular meshes, untangling mildly folded triangles and preserve the geometry to high-order of accuracy. Our approach extends our earlier works on high-order surface reconstruction and mesh optimization by enhancing its robustness with a geometric limiter for under-resolved geometries. We also integrate high-order surface reconstruction with surface mesh adaptation techniques, which alter the number of triangles and nodes. We demonstrate the utilization of our method to meshes for high-order finite elements, biomedical image-based surface meshes, and complex interface meshes in fluid simulations.

Ray, Navamita↗

A Robust and Scalable Software Library for Parallel Adaptive Refinement on Unstructured Meshes

The design and implementation of Pyramid, a software library for performing parallel adaptive mesh refinement (PAMR) on unstructured meshes, is described. This software library can be easily used in a variety of unstructured parallel computational applications, including parallel finite element, parallel finite volume, and parallel visualization applications using triangular or tetrahedral meshes. The library contains a suite of well-designed and efficiently implemented modules that perform operations in a typical PAMR process. Among these are mesh quality control during successive parallel adaptive refinement (typically guided by a local-error estimator), parallel load-balancing, and parallel mesh partitioning using the ParMeTiS partitioner. The Pyramid library is implemented in Fortran 90 with an interface to the Message-Passing Interface (MPI) library, supporting code efficiency, modularity, and portability. An EM waveguide filter application, adaptively refined using the Pyramid library, is illustrated.

Lou, John Z.↗

High-Order Mesh Morphing for Boundary and Interface Fitting to Implicit Geometries

Here, we propose a method that morphs high-order meshes such that their boundaries and interfaces coincide/align with implicitly defined geometries. Our focus is particularly on the case when the target surface is prescribed as the zero isocontour of a smooth discrete function. Common examples of this scenario include using level set functions to represent material interfaces in multimaterial configurations, and evolving geometries in shape and topology optimization. The proposed method formulates the mesh optimization problem as a variational minimization of the sum of a chosen mesh-quality metric using the Target-Matrix Optimization Paradigm (TMOP) and a penalty term that weakly forces the selected faces of the mesh to align with the target surface. The distinct features of the method are use of a source mesh to represent the level set function with sufficient accuracy, and adaptive strategies for setting the penalization weight and selecting the faces of the mesh to be fit to the target isocontour of the level set field. We demonstrate that the proposed method is robust for generating boundary- and interface-fitted meshes for curvilinear domains using different element types in 2D and 3D.

97 MATHEMATICS AND COMPUTING↗

End-to-end GPU acceleration of low-order-refined preconditioning for high-order finite element discretizations

In this article, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of effective preconditioners for high-order problems with optimal memory usage and computational complexity. The preconditioners are based on the construction of a spectrally equivalent low-order discretization on a refined mesh, which is then amenable to, for example, algebraic multigrid preconditioning. The constants of equivalence are independent of mesh size and polynomial degree. For vector finite element problems in H(curl) and H(div) (e.g., for electromagnetic or radiation diffusion problems), a specially constructed interpolation–histopolation basis is used to ensure fast convergence. Detailed performance studies are carried out to analyze the efficiency of the GPU algorithms. The kernel throughput of each of the main algorithmic components is measured, and the strong and weak parallel scalability of the methods is demonstrated. The different relative weighting and significance of the algorithmic components on GPUs and CPUs is discussed. Results on problems involving adaptively refined nonconforming meshes are shown, and the use of the preconditioners on a large-scale magnetic diffusion problem using all spaces of the finite element de Rham complex is illustrated.

97 MATHEMATICS AND COMPUTING↗

Meshfree Methods

Meshfree methods have undergone substantial development and have received much attention in the last two decades. This new family of numerical methods is designed to inherit the main advantages of the finite element method such as compact supports of shape functions and good approximation properties while, at the same time, overcome the main disadvantages of the finite element method caused by the mesh dependence. The meshfree methods share a common feature that no mesh is needed and shape functions are constructed from sets of points, thus eliminating the need for time consuming mesh generation. The most significant advantage of meshfree methods is the flexibility in customizing approximation functions for desired regularity and for capturing essential physics and features of the particular problems of interest. Adaptivity formulation and multiple-scale solution strategies also can be implemented with relative ease. It has become clear that the meshfree methods provide considerable advantages over the conventional finite element methods in solving problems involving moving discontinuities, evolving material interfaces, multiple-scale phenomena, large material distortion and structural deformation, and fracture and damage processes. This Chapter gives an overview of many classes of meshfree methods, with more detailed discussions on Smoothed Particle Hydrodynamics (SPH), the Reproducing Kernel Particle Method (RKPM), Peridynamics (PD), the Material Point Method (MPM), as well as their applications in various challenging engineering problems.2

Chen, Jiun-Shyan↗

Single-Bubble Flow Boiling Phenomena - Interface Tracking Simulation

Boiling, as one of the most efficient heat transfer mechanisms, is widely used in various engineering systems. Better understanding and modeling of this process remains a major challenge in multiphase flow research. The distribution of vapor in boiling system affects the heat transfer rate and may cause unfavorable conditions, such as heater burn-out. A number of flow regimes have been observed experimentally. In general, there are three regimes under boiling conditions: nucleate boiling, transition boiling, and film boiling. The nucleate boiling regime is categorized into partial boiling regime and fully developed nucleate boiling, according to behavior of bubble dynamics and heat transfer characteristics. In the first region, as the wall temperature increases, the fraction of the wall surface subject to nucleate boiling increases until bubble formation occupies the entire heated surface. Heat transfer in this region is a complex mixture of single-phase forced convection and nucleate boiling. As bubble density increases, bubbles turn to coalesce and form insulating vapor patches, which impedes liquid flow back to the surface. The heat transfer rate under this condition reduces dramatically. This point is called Critical Heat Flux (CHF), which leads to boiling crisis. The behavior of boiling crisis is dependent on local fluid conditions due to bubble growth and departure. Experiments are the ultimate tool for boiling model development and verification, but they still lack some capabilities needed for better understanding of the local mechanism of this phenomena. It's difficult to capture many important details at the pressure/temperature conditions of interest using experimental techniques, such as full three dimensional measurements of velocity and temperature distribution and estimates of heat flux partitioning during the boiling process. The interface tracking simulation (ITS) is one of the promising approaches to describe heat transfer of boiling phenomena and their underlying mechanisms. The advances of high performance computing (HPC) in recent years made it possible to apply DNS to a wide variety of adiabatic flows. Some work has been done to implement evaporation / condensation models as well. Lee and Nydahl performed a numerical simulation of bubble growth and departure assuming that the bubble has the shape of a truncated sphere and a micro-layer exists during bubble growth. A 2-D cylindrical bubbles simulation has been done by Son with a simplified model to predict the heat flux in a thin liquid micro-layer. A direct simulation of 2D film boiling is conducted by Juric and Tryggvason. The film boiling, below critical pressure with a modified Level Set Method, is studied by Son and Dhir. Ose and Kunugi have developed a boiling and condensation model on subcooled boiling phenomena. Fuchs performed numerical simulations of bubble growth and departure considering wall conduction effects. Fully transient heat and fluid flow is modeled with a free surface of a rising bubble and a periodic calculation of the whole cycling of a growing, detaching, and rising bubble. Mukherjee and Kandikar have done a numerical simulation of an evaporating meniscus on a moving heated surface with level set method. The heat transfer associated with the advancing and receding contact angle has been studied. To develop the capability of physics-based boiling process, in the presented work the energy and momentum equations are coupled to simulate single-bubble growth scenarios. For a single bubble simulation in infinite liquid, the analytical solution exists and can be compared with the numerical results for verification purposes. The presented capabilities will be utilized in the large scale DNS of boiling flows in the future. The finite-element based code, PHASTA is used for the simulation. It is a parallel, hierarchic, higher-order accurate, adaptive, stabilized, transient analysis flow solver, which has been shown to be an effective tool for a wide range of single and two-phase flow problems. It has been shown to be highly scalable on top supercomputers ({approx}85% scaling on up to 3 million mesh partitions using a 92 billion element mesh . PHASTA has been shown to reliably predict the details of adiabatic bubbly flows as well as single-phase flows with heat transfer. To develop the capability of physics-based boiling process, in the presented work the energy and momentum equations are coupled to simulate a single-bubble growth scenario. For a single bubble growth in superheated water, the analytical solution exists and can be compared with the numerical results for verification purposes. The second-order accurate spatial and time discretization is used for the flow solver in the presented work. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

A least-squares finite element method based on the Helmholtz decomposition for hyperbolic balance laws

In this paper, a least-squares finite element method for scalar nonlinear hyperbolic balance laws is proposed and studied. The approach is based on a formulation that utilizes an appropriate Helmholtz decomposition of the flux vector and is related to the standard notion of a weak solution. This relationship, together with a corresponding connection to negative-norm least-squares, is described in detail. As a consequence, an important numerical conservation theorem is obtained, similar to the famous Lax–Wendroff theorem. The numerical conservation properties of the method in this paper do not fall precisely in the framework introduced by Lax and Wendroff, but they are similar in spirit as they guarantee that when L 2 convergence holds, the resulting approximations approach a weak solution to the hyperbolic problem. The least-squares functional is continuous and coercive in an H -1 -type norm, but not L 2 -coercive. Nevertheless, the L 2 convergence properties of the method are discussed. Convergence can be obtained either by an explicit regularization of the functional, that provides control of the L 2 norm, or by properly choosing the finite element spaces, providing implicit control of the L 2 norm. Numerical results for the inviscid Burgers equation with discontinuous source terms are shown, demonstrating the L 2 convergence of the obtained approximations to the physically admissible solution. The numerical method utilizes a least-squares functional, minimized on finite element spaces, and a Gauss–Newton technique with nested iteration. Finally, we believe that the linear systems encountered with this formulation are amenable to multigrid techniques and combining the method with adaptive mesh refinement would make this approach an efficient tool for solving balance laws (this is the focus of a future study).

97 MATHEMATICS AND COMPUTING↗

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↗

NASA/CARES dual-use ceramic technology spinoff applications

NASA has developed software that enables American industry to establish the reliability and life of ceramic structures in a wide variety of 21st Century applications. Designing ceramic components to survive at higher temperatures than the capability of most metals and in severe loading environments involves the disciplines of statistics and fracture mechanics. Successful application of advanced ceramics material properties and the use of a probabilistic brittle material design methodology. The NASA program, known as CARES (Ceramics Analysis and Reliability Evaluation of Structures), is a comprehensive general purpose design tool that predicts the probability of failure of a ceramic component as a function of its time in service. The latest version of this software, CARESALIFE, is coupled to several commercially available finite element analysis programs (ANSYS, MSC/NASTRAN, ABAQUS, COSMOS/N4, MARC), resulting in an advanced integrated design tool which is adapted to the computing environment of the user. The NASA-developed CARES software has been successfully used by industrial, government, and academic organizations to design and optimize ceramic components for many demanding applications. Industrial sectors impacted by this program include aerospace, automotive, electronic, medical, and energy applications. Dual-use applications include engine components, graphite and ceramic high temperature valves, TV picture tubes, ceramic bearings, electronic chips, glass building panels, infrared windows, radiant heater tubes, heat exchangers, and artificial hips, knee caps, and teeth.

Powers, Lynn M.↗

Measurement and Prediction of the Thermomechanical Response of Shape Memory Alloy Hybrid Composite Beams

An experimental and numerical investigation into the static and dynamic responses of shape memory alloy hybrid composite (SMAHC) beams is performed to provide quantitative validation of a recently commercialized numerical analysis/design tool for SMAHC structures. The SMAHC beam specimens consist of a composite matrix with embedded pre-strained SMA actuators, which act against the mechanical boundaries of the structure when thermally activated to adaptively stiffen the structure. Numerical results are produced from the numerical model as implemented into the commercial finite element code ABAQUS. A rigorous experimental investigation is undertaken to acquire high fidelity measurements including infrared thermography and projection moire interferometry for full-field temperature and displacement measurements, respectively. High fidelity numerical results are also obtained from the numerical model and include measured parameters, such as geometric imperfection and thermal load. Excellent agreement is achieved between the predicted and measured results of the static and dynamic thermomechanical response, thereby providing quantitative validation of the numerical tool.

Davis, Brian↗

Computational Models of the Eye and their Applications in Long Duration Space Flight

Astronauts are exposed to cephalad fluid shift, increased carbon dioxide levels and other environmental factors during space flight. As a result of these conditions, it is believed that they are at risk of developing increased intracranial pressure (ICP) and intraocular pressure (IOP), which in turn may cause papilledema and other disorders of the eye that can lead to temporary or permanent changes in vision. However, the mechanisms behind this risk are not fully understood. Ground analog and flight studies pose challenges because there are limited non-invasive methods that can be used to study the eye and intracranial space. Therefore it is proposed that computational models can be applied to help address this gap by providing a low cost method for studying the effects of IOP, ICP and various properties of the eye on these diseases. The information presented by the authors provides a summary of several models found in literature that could potentially be augmented and applied to inform research. Specifically, finite element models of the optic nerve head, sclera and other structures of the eye can be readily adapted as potential building blocks. These models may also be integrated with a brain/cerebrospinal fluid (CSF) model which will take into account the interaction between the CSF fluid and its pressure on the optic nerve. This integration can enable the study of the effects of microgravity on the interaction between the vasculature system and CSF system and can determine the effects of these changes on the optic nerve, and in turn the eye. Ultimately, it can help pinpoint the influences of long-term exposure to microgravity on vision and inform the future research into countermeasure development. In addition to spaceflight, these models can provide deeper understanding of the mechanisms of glaucoma, papilledema and other eye disorders observed in terrestrial conditions.

Chen, Richard↗

Coupling Carbon Oxidation and Surface Recession in Direct-Simulation Monte Carlo Code, SPARTA

Ablative thermal protection system (TPS) materials for spacecraft are composites that are often made out of carbon-based reinforcement and a polymeric matrix. They endure high-temperature oxidation and surface recession when re-entering Earth’s atmosphere. Ablation is the result of many coupled and competing thermal, mechanical, and chemical phenomena, and it is difficult to isolate the role of each on the overall degradation of the TPS. Here we develop an ablation model for material recession coupled explicitly to finite rate carbon oxidation in complex microstructures. In this work, Stochastic PArallel Rarified-gas Time-accurate Analyzer (SPARTA), a direct-simulation Monte Carlo (DSMC) code, is modified to allow oxidation-driven ablation of implicitly defined carbon surfaces. In SPARTA, implicit surfaces are generated from the grid corner point values via a marching cubes algorithm, therefore creating a new set of surface elements every time ablation is performed. The finite-rate oxidation model developed by Gopalan et. al, was adapted to tally surface reactions and other surface data on a per-grid cell basis. The ablation functionality was also adjusted so once the reactions have occurred, the number of reactions leading to CO formation can be converted to corner point reduction values; therefore, carbon removal is directly proportional to surface recession. We also develop robust algorithms which handle the evolution of the flow cells and solid material regions, including split cells (flow cell divided in two by a solid surface). Finally, we demonstrate our implicit chemistry model for 2D and 3D geometries by producing reaction statistics and detailed visualization of oxidation-induced material recession at the microscale.

V Arias↗

Additive Manufacturing for Powering the Blue Economy Applications: A Tidal Turbine Blade Case Study: Preprint

As the marine renewable energy industry continues to expand, innovation in the manufacturing space must grow accordingly to reduce costs and ensure the economic feasibility of new technologies. Additive manufacturing, more commonly known as 3D printing, provides an alternative for rapid prototyping of marine hydrokinetic technologies, particularly supporting Powering the Blue Economy initiatives of the U.S. Department of Energy Water Power Technologies Office. This study explores the application of additive manufacturing in the development of marine hydrokinetic structures, focusing on material and printing method selection, design, and analysis of a 3D-printed spar for an axial-flow tidal turbine blade. Corrosion-resistant metals were deemed ideal due to the loads and harsh marine environment the blade would experience. Laser metal deposition methods were determined to be the most effective and scalable for the considered scale. The designed spar adapts its geometry to the blade - a feature uniquely suited to additive manufacturing - and is intended to serve as the blade's primary structural component. A finite element model was used to study stresses and deformations under loading conditions. The spar was manufactured using 316L stainless steel through direct energy deposition, and defects were assessed and recorded. Future efforts will include mechanical testing of the spar. This research establishes a benchmark process for using additive manufacturing in developing marine hydrokinetic structures, paving the way for future optimization and techno-economic analysis.

additive manufacturing↗

Investigation of transonic flow in a cascade using an adaptive mesh

The solution of two-dimensional full potential equation for the analysis of steady transonic flow through cascades is investigated. Finite element method is employed in the analysis. Accuracy and efficiency of the obtained numerical solutions are discussed in terms of the employed computational grid. Accurate modeling of subsonic and supersonic flow regions together with the shock is discussed. The choice of artificial viscosity and relaxation factors are examined and related to the design of a computational grid. Shock capturing and shock fitting procedures are compared for improved accuracy and efficiency. Numerical results include cascades of Gostelow and NACA 0012 airfoils.

Ecer, A.↗