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At least 73 records · Page 4

Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part I

In this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes—wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries—and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid–structure interaction, and free surface flow. A class of techniques known as interfacial gauge methods is adopted to solve the corresponding incompressible Navier–Stokes equations, which, compared to archetypical projection methods, have a weaker coupling between fluid velocity, pressure, and interface position, and allow high-order accurate numerical methods to be developed more easily. Convergence analyses conducted throughout the work demonstrate high-order accuracy in the maximum norm for all of the applications considered; for example, fourth-order spatial accuracy in fluid velocity, pressure, and interface location is demonstrated for surface tension-driven two phase flow in 2D and 3D. Specific application examples include: vortex shedding in nontrivial geometry, capillary wave dynamics revealing fine-scale flow features, falling rigid bodies tumbling in unsteady flow, and free surface flow over a submersed obstacle, as well as high Reynolds number soap bubble oscillation dynamics and vortex shedding induced by a type of Plateau–Rayleigh instability in water ripple free surface flow. In conclusion, these last two examples compare numerical results with experimental data and serve as an additional means of validation; they also reveal physical phenomena not visible in the experiments, highlight how small-scale interfacial features develop and affect macroscopic dynamics, and demonstrate the wide range of spatial scales often at play in interfacial fluid flow.

97 MATHEMATICS AND COMPUTING↗

Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part II

Here, in this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes—wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries—and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid–structure interaction, and free surface flow. A class of techniques known as interfacial gauge methods is adopted to solve the corresponding incompressible Navier–Stokes equations, which, compared to archetypical projection methods, have a weaker coupling between fluid velocity, pressure, and interface position, and allow high-order accurate numerical methods to be developed more easily. Convergence analyses conducted throughout the work demonstrate high-order accuracy in the maximum norm for all of the applications considered; for example, fourth-order spatial accuracy in fluid velocity, pressure, and interface location is demonstrated for surface tension-driven two phase flow in 2D and 3D. Specific application examples include: vortex shedding in nontrivial geometry, capillary wave dynamics revealing fine-scale flow features, falling rigid bodies tumbling in unsteady flow, and free surface flow over a submersed obstacle, as well as high Reynolds number soap bubble oscillation dynamics and vortex shedding induced by a type of Plateau–Rayleigh instability in water ripple free surface flow. In these last two examples compare numerical results with experimental data and serve as an additional means of validation; they also reveal physical phenomena not visible in the experiments, highlight how small-scale interfacial features develop and affect macroscopic dynamics, and demonstrate the wide range of spatial scales often at play in interfacial fluid flow.

97 MATHEMATICS AND COMPUTING↗

Lattice-statics approach to fracture and plasticity

The lattice-statics approach to the problem of providing a quantitative description of the microstructure near a defect is outlined. The method deals with an effectively infinite lattice and hence avoids interface problems; the lattice-statics method is not restricted by the range of the potential. The lattice-statics solution requires a harmonic solution for the lattice which is shown to be always obtainable by suitable Fourier transforms. Applications of the method to fracture and dislocations are discussed and areas that warrant further research are specified.

Esterling, D. M.↗

Direct discontinuous Galerkin method and its variations for second order elliptic equations

In this study, we study direct discontinuous Galerkin method (Liu and Yan in SIAM J Numer Anal 47(1):475–698, 2009) and its variations (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010; Vidden and Yan in J Comput Math 31(6):638–662, 2013; Yan in J Sci Comput 54(2–3):663–683, 2013) for 2nd order elliptic problems. A priori error estimate under energy norm is established for all four methods. Optimal error estimate under L 2 norm is obtained for DDG method with interface correction (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010) and symmetric DDG method (Vidden and Yan in J Comput Math 31(6):638–662, 2013). A series of numerical examples are carried out to illustrate the accuracy and capability of the schemes. Numerically we obtain optimal (k+1)th order convergence for DDG method with interface correction and symmetric DDG method on nonuniform and unstructured triangular meshes. An interface problem with discontinuous diffusion coefficients is investigated and optimal (k+1)th order accuracy is obtained. Peak solutions with sharp transitions are captured well. Highly oscillatory wave solutions of Helmholz equation are well resolved.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

User interface issues in supporting human-computer integrated scheduling

Explored here is the user interface problems encountered with the Operations Missions Planner (OMP) project at the Jet Propulsion Laboratory (JPL). OMP uses a unique iterative approach to planning that places additional requirements on the user interface, particularly to support system development and maintenance. These requirements are necessary to support the concepts of heuristically controlled search, in-progress assessment, and iterative refinement of the schedule. The techniques used to address the OMP interface needs are given.

Cooper, Lynne P.↗

Multi purpose display panel

The multi purpose panel (MPP) project was undertaken to demonstrate the feasibility of producing a control signal which could be time shared among several subsystems and which would permit rapid and inexpensive modification of control panel functions. It is intended to bridge the gap between Multifunction Display Systems, which offer excellent display flexibility but present man-machine interface problems, and dedicated control panels, which offer no flexibility. A control panel was developed with programmable displays located near enough to control and display components to provide an acceptable man-machine interface.

Source record↗

Tailoring MgZnO/CdSeTe Interfaces for Photovoltaics

Mg x Zn 1-x O (MZO) shows great promise to replace CdS as a buffer layer in CdTe-based solar cells. It is more transparent, and the MZO bandgap and electron density can be tuned, thus providing flexibility in controlling the conduction band offsets and recombination rates between transparent conductive oxide/MZO and MZO/CdSeTe interfaces. Integrating this material into solar cell devices has been frustrated by the common observation of abnormal current-voltage curves. Simulations indicate that this anomalous behavior can be attributed to front interface barrier effects. Experiments demonstrate that this common MZO interface problem can be resolved experimentally by surface preparation, preheat steps, and removing oxygen during absorber deposition and CdCl 2 treatment. Oxygen during the cell fabrication process is likely to alter MZO properties and MZO/CdSeTe band alignment. After addressing these interface issues and modest optimization, devices with high short-circuit density of 29 mA/cm 2 and efficiency above 16% are demonstrated.

14 SOLAR ENERGY↗

Hypertext-Based Design of a User Interface for Scheduling

Operations Mission Planner (OMP) is an ongoing research project at JPL that utilizes Artificial Intelligence techniques to create an intelligent, automated planning and scheduling system. The challenge with a user interface is to 1) present as much information as possible at a given moment and 2) allow the user to quickly navigate through the various types of displays. This paper describes a design which applies the hypertext model to solve user interface problems. The general paradigm is to provide maps and search queries to allow the user to quickly find an interesting conflict or problem. Then allow the user to navigate through the displays in a hypertext fashion.

hypertext↗

Materials Challenges and Opportunities for Energy Generation, Conversion, Delivery, and Storage (Applied Energy Tri-Laboratory Consortium Workshop Report)

This report documents the outcomes of the Tri-Laboratory Materials Workshop that was held July 31 and August 1, 2019 to begin addressing the needs, opportunities, and challenges associated with the development, fabrication, and testing of the needed materials and components for integrated hybrid energy systems (i.e., incorporating nuclear, fossil, and renewables for electric and thermal applications). This was accomplished by assembling the research program leads and principal investigators at Idaho National Laboratory (INL), National Energy Technology Laboratory (NETL), and National Renewable Energy Laboratory (NREL), who support the research and development of new technology and system integration. The team then identified and prioritized key materials development needs. This effort was intended to enhance communications and synergy among the Tri-Lab partners. Advanced functional and structural materials are central to transformative energy technologies for energy generation, conversion, delivery, and storage. With that in mind, the workshop focused on identifying and assessing the foundational materials research needs at both the basic and applied levels. Materials challenges include the ability to withstand harsh environments, such as high temperatures and pressures, corrosion, oxidation, or irradiation while maintaining flexible mission profiles and long service lifespans. Advanced energy system material challenges and needs range from materials for the capture, upgrading/concentration, storage, and delivery of low-grade heat to materials for high temperature environments that involve liquid metals, molten salt, and very high temperature gas heat delivery and storage systems. Material improvements are needed for hybrid energy systems due to accelerated corrosion and stress-fatigue failure of materials and equipment, which results from increased frequency and amplitude of thermal, mechanical, and electrical cycling of systems components. Multifunctional materials are needed for high temperature solid-oxide fuel cells, advanced electrochemical reactors, and in-process separation. Relative to materials manufacturing, application of advanced additive and subtractive methods need to be understood to develop both thin-layer homogenous materials and materials of graded composition. Materials modeling and machine learning will be critical to accelerate the design and production of power electronics, and nuclear reactor materials and fuel, as well as to gain an understanding of beneficial materials phenomena or deleterious microstructure evolution. There is also a need for standardized models, computational structures, data reporting protocols and modeling tools across the three laboratories. This would allow consistent results, analysis, and data sharing. Combining computational capabilities between the three laboratories (e.g., hardware, software) would greatly increase computational capabilities and throughput. The workshop identified the need for laboratories to anticipate and address problems that will occur during scale-up. Laboratory work must connect with industry to ensure that research focuses on processes that are scalable and marketable. Industry input and perspective are essential to guide laboratory research to meet these requirements and deploy new technology in industrial demonstrations. Another aspect of scale-up is the integration of multiple systems since new challenges often arise at the subsystem interfaces. Establishing a scale-up manufacturing demonstration/pilot plant, potentially as an industrial user facility, would be beneficial to the laboratories and industry. That modular scale-up manufacturing demonstration/pilot plant would allow researchers to find and resolve interface problems that cannot be identified by focusing only on individual parts. Communication exchanges among the organizers, attendees, and workshop survey responses indicate that the workshop was successful in achieving its goal to identify key technology gaps and research needs. Strong positive feedback was received on the sharing of ideas, capabilities, talent, and passion to move forward on the materials-related action items.

36 MATERIALS SCIENCE↗

Impact of space station appendage vibrations on the pointing performance of gimballed payloads

A study of the interface problems between the Space Station Structure (vibrations) and the Payload Pointing Control System was undertaken. A major goal of the study was to identify any bounding factors that might limit the achievement of required pointing accuracies. A major result is that the space station will have a disturbance-rich environment and the background levels will be large enough to impact the pointing of some of the payloads. The need for an interface vibration specification between the structure and the payloads was identified.

Hughes, Robert O.↗

Human Factor Challenges of Remotely Piloted Aircraft

The control stations of many unmanned systems have been characterized by inadequate human-system interfaces. Some of the interface problems may have been prevented had an existing regulation or cockpit design principle been applied. In other cases, the design problems may indicate a lack of suitable guidance material. The human factors of unmanned operations will be reviewed, and a NASA program to develop human-factor guidelines for control stations will be described. To be effective, guidelines must be relevant to a wide range of systems, must not be overly prescriptive, and must not impose premature standardization on evolving technologies. Several types of guidelines are described. These relate to required capabilities, information requirements, properties of the human machine interface, and general cognitive engineering principles.

Hobbs, Alan↗

Fluid mechanics in crystal growth - The 1982 Freeman scholar lecture

An attempt is made to unify the current state of knowledge in crystal growth techniques and fluid mechanics. After identifying important fluid dynamic problems for such representative crystal growth processes as closed tube vapor transport, open reactor vapor deposition, and the Czochralski and floating zone melt growth techniques, research results obtained to date are presented. It is noted that the major effort to date has been directed to the description of the nature and extent of bulk transport under realistic conditions, where bulk flow determines the heat and solute transport which strongly influence the temperature and concentration fields in the vicinity of the growth interface. Proper treatment of near field, or interface, problems cannot be given until the far field, or global flow, involved in a given crystal growth technique has been adequately described.

Ostrach, S.↗

Software handlers for process interfaces

The principles involved in the development of software handlers for custom interfacing problems are discussed. Handlers for the CAMAC standard are examined in detail. The types of transactions that must be supported have been established by standards groups, eliminating conflicting requirements arising out of different design philosophies and applications. Implementation of the standard handlers has been facilititated by standardization of hardware. The necessary local processors can be placed in the handler when it is written or at run time by means of input/output directives, or they can be built into a high-performance input/output processor. The full benefits of these process interfaces will only be realized when software requirements are incorporated uniformly into the hardware.

Bercaw, R. W.↗

Using Directional Diffusion Coefficients for Nonlinear Diffusion Acceleration of the First Order S{sub N} Equations in Near-Void Regions

The common definition of the diffusion coefficient as the inverse of three times the transport cross section is not compatible with voids. Morel introduced a non-local tensor diffusion coefficient that remains finite in voids. It can be obtained by solving an auxiliary transport problem without scattering or fission. Larsen and Trahan successfully applied this diffusion coefficient for enhancing the accuracy of diffusion solutions of very high temperature reactor (VHTR) problems that feature large, optically thin channels in the z-direction. It was demonstrated that a significant reduction of error can be achieved in particular in the optically thin region. Along the same line of thought, non-local diffusion tensors have been applied to modeling the TREAT reactor confirming the findings of Larsen and Trahan. Previous work of the authors have introduced a flexible Nonlinear-Diffusion Acceleration (NDA) method for the first order S{sub N} equations discretized with the discontinuous finite element method (DFEM). This NDA method uses a scalar diffusion coefficient in the low-order system that is obtained as the flux weighted average of the inverse transport cross section. Hence, it suffers from very large and potentially unbounded diffusion coefficients in the low order problem. However, it was noted that the choice of the diffusion coefficient does not influence consistency of the method at convergence and hence the diffusion coefficient is essentially a free parameter. The choice of the diffusion coefficient does, however, affect the convergence behavior of the nonlinear diffusion iterations. Within this work we use Morel's non-local diffusion coefficient in the aforementioned NDA formulation in lieu of the flux weighted inverse of three times the transport cross section. The goal of this paper is to demonstrate that significant enhancement of the spectral properties of NDA can be achieved in near void regions. For testing the spectral properties of the NDA with non-local diffusion coefficients, the periodical horizontal interface problem is used. This problem consists of alternating stripes of optically thin and thick materials both of which feature scattering ratios close to unity. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Using Directional Diffusion Coefficients for Nonlinear Diffusion Acceleration of the First Order SN Equations in Near-Void Regions

The common definition of the diffusion coeffcient as the inverse of three times the transport cross section is not compat- ible with voids. Morel introduced a non-local tensor diffusion coeffcient that remains finite in voids[1]. It can be obtained by solving an auxiliary transport problem without scattering or fission. Larsen and Trahan successfully applied this diffusion coeffcient for enhancing the accuracy of diffusion solutions of very high temperature reactor (VHTR) problems that feature large, optically thin channels in the z-direction [2]. It is demonstrated that a significant reduction of error can be achieved in particular in the optically thin region. Along the same line of thought, non-local diffusion tensors are applied modeling the TREAT reactor confirming the findings of Larsen and Trahan [3]. Previous work of the authors have introduced a flexible Nonlinear-Diffusion Acceleration (NDA) method for the first order S N equations discretized with the discontinuous finite element method (DFEM), [4], [5], [6]. This NDA method uses a scalar diffusion coeffcient in the low-order system that is obtained as the flux weighted average of the inverse transport cross section. Hence, it su?ers from very large and potentially unbounded diffusion coeffcients in the low order problem. However, it was noted that the choice of the diffusion coeffcient does not influence consistency of the method at convergence and hence the di?usion coeffcient is essentially a free parameter. The choice of the di?usion coeffcient does, however, affect the convergence behavior of the nonlinear di?usion iterations. Within this work we use Morel’s non-local di?usion coef- ficient in the aforementioned NDA formulation in lieu of the flux weighted inverse of three times the transport cross section. The goal of this paper is to demonstrate that significant en- hancement of the spectral properties of NDA can be achieved in near void regions. For testing the spectral properties of the NDA with non-local diffusion coeffcients, the periodical horizontal interface problem is used [7]. This problem consists of alternating stripes of optically thin and thick materials both of which feature scattering ratios close to unity.

97 MATHEMATICS AND COMPUTING↗

Efficient Operator-Coarsening Multigrid Schemes for Local Discontinuous Galerkin Methods

An efficient hp-multigrid scheme is presented for local discontinuous Galerkin (LDG) discretizations of elliptic problems, formulated around the idea of separately coarsening the underlying discrete gradient and divergence operators. We show that traditional multigrid coarsening of the primal formulation leads to poor and suboptimal multigrid performance, whereas coarsening of the flux formulation leads to essentially optimal convergence and is equivalent to a purely geometric multigrid method. The resulting operator-coarsening schemes do not require the entire mesh hierarchy to be explicitly built, thereby obviating the need to compute quadrature rules, lifting operators, and other mesh-related quantities on coarse meshes. We show that good multigrid convergence rates are achieved in a variety of numerical tests on two-dimensional and three-dimensional uniform and adaptive Cartesian grids, as well as for curved domains using implicitly defined meshes and for multiphase elliptic interface problems with complex geometry. Extensions, e.g., to non-LDG discretizations and fully unstructured meshes, are briefly discussed.

97 MATHEMATICS AND COMPUTING↗

A model and numerical method for compressible flows with capillary effects

A new model for interface problems with capillary effects in compressible fluids is presented together with a specific numerical method to treat capillary flows and pressure waves propagation. This new multiphase model is in agreement with physical principles of conservation and respects the second law of thermodynamics. A new numerical method is also proposed where the global system of equations is split into several submodels. Each submodel is hyperbolic or weakly hyperbolic and can be solved with an adequate numerical method. This method is tested and validated thanks to comparisons with analytical solutions (Laplace law) and with experimental results on droplet breakup induced by a shock wave.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Modeling curved interfaces without element‐partitioning in the extended finite element method

Summary In this paper, we model holes and material interfaces (weak discontinuities) in two‐dimensional linear elastic continua using the extended finite element method on higher‐order (spectral) finite element meshes. Arbitrary parametric curves such as rational Bézier curves and cubic Hermite curves are adopted in conjunction with the level set method to represent curved interfaces. Efficient computation of weak form integrals with polynomial integrands is realized via the homogeneous numerical integration scheme—a method that uses Euler's homogeneous function theorem and Stokes' theorem to reduce integration to the boundary of the domain. Numerical integration on cut elements requires the evaluation of a one‐dimensional integral over a parametric curve, and hence, the need to partition curved elements is eliminated. To improve stiffness matrix conditioning, ghost penalty stabilization and the Jacobi preconditioner are used. For material interface problems, we develop an enrichment function that captures weak discontinuities on spectral meshes. Taken together, we show through numerical experiments that these advances deliver optimal algebraic rates of convergence with h ‐refinement ( p =1,2,…,5) and exponential rates of convergence with p ‐refinement ( p =1,2,…,7) for elastostatic problems with holes and material inclusions on Cartesian p th‐order spectral finite element meshes.

Chin, Eric B.↗