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At least 469 records · Page 26

Computational methods for ideal compressible flow

Conservative dissipative difference schemes for computing one dimensional flow are introduced, and the recognition and representation of flow discontinuities are discussed. Multidimensional methods are outlined. Second order finite volume schemes are introduced. Conversion of difference schemes for a single linear convection equation into schemes for the hyperbolic system of the nonlinear conservation laws of ideal compressible flow is explained. Approximate Riemann solvers are presented. Monotone initial value interpolation; and limiters, switches, and artificial dissipation are considered.

Vanleer, B.↗

Optimization of Orifice Geometry for Cross-Flow Mixing in a Cylindrical Duct

Mixing of gaseous jets in a cross-flow has significant applications in engineering, one example of which is the dilution zone of a gas turbine combustor. Despite years of study, the design of jet injection in combustors is largely based on practical experience. A series of experiments was undertaken to delineate the optimal mixer orifice geometry. A cross-flow to core-flow momentum-flux ratio of 40 and a mass flow ratio of 2.5 were selected as representative of an advanced design. An experimental test matrix was designed around three variables: the number of orifices, the orifice aspect ratio (long-to-short dimension), and the orifice angle. A regression analysis was performed on the data to arrive at an interpolating equation that predicted the mixing performance of orifice geometry combinations within the range of the test matrix parameters. Results indicate that mixture uniformity is a non-linear function of the number of orifices, the orifice aspect ratio, and the orifice angle. Optimum mixing occurs when the asymptotic mean jet trajectories are in the range of 0.35 less than r/R less than 0.5 (where r = 0 is at the mixer wall) at z/R = 1.0. At the optimum number of orifices, the difference between shallow-angled slots with large aspect ratios and round holes is minimal and either approach will lead to good mixing performance. At the optimum number of orifices, it appears possible to have two local optimums where one corresponds to an aspect ratio of 1.0 and the other to a high aspect ratio.

Sowa, W. A.↗

Thickness Gauging of Single-Layer Conductive Materials with Two-Point Non Linear Calibration Algorithm

A thickness gauging instrument uses a flux focusing eddy current probe and two-point nonlinear calibration algorithm. The instrument is small and portable due to the simple interpretation and operational characteristics of the probe. A nonlinear interpolation scheme incorporated into the instrument enables a user to make highly accurate thickness measurements over a fairly wide calibration range from a single side of nonferromagnetic conductive metals. The instrument is very easy to use and can be calibrated quickly.

Fulton, James P.↗

Automated Approach to Very High-Order Aeroacoustic Computations

Computational aeroacoustics requires efficient, high-resolution simulation tools. For smooth problems, this is best accomplished with very high-order in space and time methods on small stencils. However, the complexity of highly accurate numerical methods can inhibit their practical application, especially in irregular geometries. This complexity is reduced by using a special form of Hermite divided-difference spatial interpolation on Cartesian grids, and a Cauchy-Kowalewski recursion procedure for time advancement. In addition, a stencil constraint tree reduces the complexity of interpolating grid points that am located near wall boundaries. These procedures are used to develop automatically and to implement very high-order methods (> 15) for solving the linearized Euler equations that can achieve less than one grid point per wavelength resolution away from boundaries by including spatial derivatives of the primitive variables at each grid point. The accuracy of stable surface treatments is currently limited to 11th order for grid aligned boundaries and to 2nd order for irregular boundaries.

Dyson, Rodger W.↗

Experimenting with the GMAO 4D Data Assimilation

The Global Modeling and Assimilation Office (GMAO) has been working to promote its prototype four-dimensional variational (4DVAR) system to a version that can be exercised at operationally desirable configurations. Beyond a general circulation model (GeM) and an analysis system, traditional 4DV AR requires availability of tangent linear (TL) and adjoint (AD) models of the corresponding GeM. The GMAO prototype 4DVAR uses the finite-volume-based GEOS GeM and the Grid-point Statistical Interpolation (GSI) system for the first two, and TL and AD models derived ITom an early version of the finite-volume hydrodynamics that is scientifically equivalent to the present GEOS nonlinear GeM but computationally rather outdated. Specifically, the TL and AD models hydrodynamics uses a simple (I-dimensional) latitudinal MPI domain decomposition, which has consequent low scalability and prevents the prototype 4DV AR ITom being used in realistic applications. In the near future, GMAO will be upgrading its operational GEOS GCM (and assimilation system) to use a cubed-sphere-based hydrodynamics. This versions of the dynamics scales to thousands of processes and has led to a decision to re-derive the TL and AD models for this more modern dynamics, thus taking advantage of a two-dimensional MPI decomposition and improved scalability properties. With the aid of the Transformation of Algorithms in FORTRAN (l'AF) automatic adjoint generation tool and some hand-coding, a version of the cubed-sphere-based TL and AD models, with a simplified vertical diffusion scheme, is now available, enabling multiple configurations of standard implementations of 4DV AR in GEOS. Concurrent to this development, collaboration with the National Centers for Environmental Prediction (NCEP) and the Earth System Research Laboratory (ESRL) has allowed GMAO to implement a hybrid-ensemble capability within the GEOS data assimilation system. Both 3Dand 4D-ensemble capabilities are presently available thus allowing GMAO to now evaluate the performance and benefit of various ensemble and variational assimilation strategies. This presentation will cover the most recent developments taking place at GMAO and show results from various comparisons from traditional techniques to more recent ensemble-based ones.

Todling, R.↗

Application of adaptive hierarchical sparse grid collocation to the uncertainty quantification of nuclear reactor simulators

Recent efforts in the application of uncertainty quantification to nuclear systems have utilized methods based on generalized perturbation theory and stochastic sampling. While these methods have proven to be effective they both have major drawbacks that may impede further progress. A relatively new approach based on spectral elements for uncertainty quantification is applied in this paper to several problems in reactor simulation. Spectral methods based on collocation attempt to couple the approximation free nature of stochastic sampling methods with the determinism of generalized perturbation theory. The specific spectral method used in this paper employs both the Smolyak algorithm and adaptivity by using Newton-Cotes collocation points along with linear hat basis functions. Using this approach, a surrogate model for the outputs of a computer code is constructed hierarchically by adaptively refining the collocation grid until the interpolant is converged to a user-defined threshold. The method inherently fits into the framework of parallel computing and allows for the extraction of meaningful statistics and data that are not within reach of stochastic sampling and generalized perturbation theory. This paper aims to demonstrate the advantages of spectral methods-especially when compared to current methods used in reactor physics for uncertainty quantification-and to illustrate their full potential. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Experimental and computing strategies in advanced material characterization problems

The mechanical characterization of materials relies more and more often on sophisticated experimental methods that permit to acquire a large amount of data and, contemporarily, to reduce the invasiveness of the tests. This evolution accompanies the growing demand of non-destructive diagnostic tools that assess the safety level of components in use in structures and infrastructures, for instance in the strategic energy sector. Advanced material systems and properties that are not amenable to traditional techniques, for instance thin layered structures and their adhesion on the relevant substrates, can be also characterized by means of combined experimental-numerical tools elaborating data acquired by full-field measurement techniques. In this context, parameter identification procedures involve the repeated simulation of the laboratory or in situ tests by sophisticated and usually expensive non-linear analyses while, in some situation, reliable and accurate results would be required in real time. The effectiveness and the filtering capabilities of reduced models based on decomposition and interpolation techniques can be profitably used to meet these conflicting requirements. This communication intends to summarize some results recently achieved in this field by the author and her co-workers. The aim is to foster further interaction between engineering and mathematical communities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

First-principles mode-by-mode analysis for electron-phonon scattering channels and mean free path spectra in GaAs

We present a first-principles framework to investigate the electron scattering channels and transport properties for polar materials by combining the exact solution of the linearized electron-phonon (e-ph) Boltzmann transport equation in its integral-differential form associated with the e-ph coupling matrices obtained from the polar Wannier interpolation scheme. No ad hoc parameter is required throughout this calculation, and GaAs, a well-studied polar material, is used as an example to demonstrate this method. In this work, the long-range and short-range contributions as well as the intravalley and intervalley transitions in the e-ph interactions (EPIs) have been quantitatively addressed. Promoted by such mode-by-mode analysis, we find that in GaAs, the piezoelectric scattering is comparable to deformation-potential scattering for electron scatterings by acoustic phonons in EPI even at room temperature, and it makes a significant contribution to mobility. Furthermore, we achieved good agreement with experimental data for the mobility, and we identified that electrons with mean free paths between 130 and 210 nm provide the dominant contribution to the electron transport at 300 K. As a result, such information provides a deeper understanding of the electron transport in GaAs, and the presented framework can be readily applied to other polar materials.

36 MATERIALS SCIENCE↗

An Evolve-Then-Correct Reduced Order Model for Hidden Fluid Dynamics

In this paper, we put forth an evolve-then-correct reduced order modeling approach that combines intrusive and nonintrusive models to take hidden physical processes into account. Specifically, we split the underlying dynamics into known and unknown components. In the known part, we first utilize an intrusive Galerkin method projected on a set of basis functions obtained by proper orthogonal decomposition. We then present two variants of correction formula based on the assumption that the observed data are a manifestation of all relevant processes. The first method uses a standard least-squares regression with a quadratic approximation and requires solving a rank-deficient linear system, while the second approach employs a recurrent neural network emulator to account for the correction term. We further enhance our approach by using an orthonormality conforming basis interpolation approach on a Grassmannian manifold to address off-design conditions. The proposed framework is illustrated here with the application of two-dimensional co-rotating vortex simulations under modeling uncertainty. The results demonstrate highly accurate predictions underlining the effectiveness of the evolve-then-correct approach toward real-time simulations, where the full process model is not known a priori.

long short-term memory↗

Interpolation using surface splines.

A surface spline is a mathematical tool for interpolating a function of two variables. It is based upon the small deflection equation of an infinite plate. The surface spline depends upon the solution of a system of linear equations, and thus, will ordinarily require the use of a digital computer. The closed form solution involves no functions more complicated than logarithms, and is easily coded. Several modifications which can be incorporated are discussed.

Harder, R. L.↗

Simplification of the Kalman filter for meteorological data assimilation

The paper proposes a new statistical method of data assimilation that is based on a simplification of the Kalman filter equations. The forecast error covariance evolution is approximated simply by advecting the mass-error covariance field, deriving the remaining covariances geostrophically, and accounting for external model-error forcing only at the end of each forecast cycle. This greatly reduces the cost of computation of the forecast error covariance. In simulations with a linear, one-dimensional shallow-water model and data generated artificially, the performance of the simplified filter is compared with that of the Kalman filter and the optimal interpolation (OI) method. The simplified filter produces analyses that are nearly optimal, and represents a significant improvement over OI.

Dee, Dick P.↗

Krylov subspace recycling for evolving structures

Krylov subspace recycling is a powerful tool when solving a long series of large, sparse linear systems that change only slowly over time. In PDE constrained shape optimization, these series appear naturally, as typically hundreds or thousands of optimization steps are needed with only small changes in the geometry. In this setting, however, applying Krylov subspace recycling can be a difficult task. As the geometry evolves, in general, so does the finite element mesh defined on or representing this geometry, including the numbers of nodes and elements and element connectivity. This is especially the case if re-meshing techniques are used. As a result, the number of algebraic degrees of freedom in the system changes, and in general the linear system matrices resulting from the finite element discretization change size from one optimization step to the next. Changes in the mesh connectivity also lead to structural changes in the matrices. In the case of re-meshing, even if the geometry changes only a little, the corresponding mesh might differ substantially from the previous one. Obviously, this prevents any straightforward mapping of the approximate invariant subspace of the linear system matrix (the focus of recycling in this work) from one optimization step to the next; similar problems arise for other selected subspaces. In this paper, we present an algorithm to map an approximate invariant subspace of the linear system matrix for the previous optimization step to an approximate invariant subspace of the linear system matrix for the current optimization step, for general meshes. This is achieved by exploiting the map from coefficient vectors to finite element functions on the mesh, combined with interpolation or approximation of functions on the finite element mesh. We demonstrate the effectiveness of our approach numerically with several proof of concept studies for a specific meshing technique.

42 ENGINEERING↗

A basis in an invariant subspace of analytic functions

The existence problem for a basis in a differentiation-invariant subspace of analytic functions defined in a bounded convex domain in the complex plane is investigated. Conditions are found for the solvability of a certain special interpolation problem in the space of entire functions of exponential type with conjugate diagrams lying in a fixed convex domain. These underlie sufficient conditions for the existence of a basis in the invariant subspace. This basis consists of linear combinations of eigenfunctions and associated functions of the differentiation operator, whose exponents are combined into relatively small clusters. Necessary conditions for the existence of a basis are also found. Under a natural constraint on the number of points in the groups, these coincide with the sufficient conditions. That is, a criterion is found under this constraint that a basis constructed from relatively small clusters exists in an invariant subspace of analytic functions in a bounded convex domain in the complex plane. Bibliography: 25 titles.

97 MATHEMATICS AND COMPUTING↗

ArborX 2.0

ArborX library tackles a problem of efficiently finding geometric objects that are close in space. Variations of this problem, such as finding the nearest neighbors of a point, or finding all objects within a certain distance, are inherent components of applications in many fields. The data may be large so that solving the problem efficiently may require significant computational resources, such as multiple processors or accelerators such as general purpose GPUs. ArborX' main advantage in its ability to solve large problems efficiently utilizing a combination of distributed and on-node parallelism. ArborX can be run efficiently on a wide variety of hardware, including GPUs from different vendors, which distinguishes it from other available libraries which typically choose only few of these. The other advantage is that it supports both types of user problems: spatial problems (useful for intersections and finding objects within certain distance), and nearest neighbor problems. ArborX also supports flexible interface in its interaction with a user. Particularly, it allows a user to call user's own function on a positive match, a functionality not rarely available in other libraries. ArborX implements construction and traversal algorithms using efficient tree structures, such as bounding volume hierarchy (BVH). At its core, ArborX uses linear BVH for its low construction cost and sufficient quality. ArborX implements both spatial and nearest-neighbor traversal algorithms. ArborX also provides several clustering algorithms (minimum spanning tree, DBSCAN, HDBSCAN*), interpolation using minimum least squares and ray tracing. ArborX is written using C++, and is parallelized using the message passing interface (MPI) for the distributed communication, and the Kokkos library for on-node parallelism. This approach allows ArborX to be run on a wide variety of hardware, from common laptops and desktops to supercomputers while using the same codebase.

Prokopenko, Andrey [Oak Ridge National Laboratory ↗

Temporal and spectral imaging with micro-CT

Purpose: Micro-CT is widely used for small animal imaging in preclinical studies of cardiopulmonary disease, but further development is needed to improve spatial resolution, temporal resolution, and material contrast. We present a technique for visualizing the changing distribution of iodine in the cardiac cycle with dual source micro-CT. Methods: The approach entails a retrospectively gated dual energy scan with optimized filters and voltages, and a series of computational operations to reconstruct the data. Projection interpolation and five-dimensional bilateral filtration (three spatial dimensions + time + energy) are used to reduce noise and artifacts associated with retrospective gating. We reconstruct separate volumes corresponding to different cardiac phases and apply a linear transformation to decompose these volumes into components representing concentrations of water and iodine. Since the resulting material images are still compromised by noise, we improve their quality in an iterative process that minimizes the discrepancy between the original acquired projections and the projections predicted by the reconstructed volumes. The values in the voxels of each of the reconstructed volumes represent the coefficients of linear combinations of basis functions over time and energy. We have implemented the reconstruction algorithm on a graphics processing unit (GPU) with CUDA. We tested the utility of the technique in simulations and applied the technique in an in vivo scan of a C57BL/6 mouse injected with blood pool contrast agent at a dose of 0.01 ml/g body weight. Postreconstruction, at each cardiac phase in the iodine images, we segmented the left ventricle and computed its volume. Using the maximum and minimum volumes in the left ventricle, we calculated the stroke volume, the ejection fraction, and the cardiac output. Results: Our proposed method produces five-dimensional volumetric images that distinguish different materials at different points in time, and can be used to segment regions containing iodinated blood and compute measures of cardiac function. Conclusions: We believe this combined spectral and temporal imaging technique will be useful for future studies of cardiopulmonary disease in small animals.

60 APPLIED LIFE SCIENCES↗

Adaptive AMG with Coarsening Based on Compatible Weighted Matching

We introduce a new composite adaptive Algebraic Multigrid (composite αAMG) method to solve systems of linear equations without a-priori knowledge or assumption on characteristics of near-null components of the AMG preconditioned problem referred to as algebraic smoothness. Our version of αAMG is a composite solver built through a bootstrap strategy aimed to obtain a desired convergence rate. The coarsening process employed to build each new solver component relies on a pairwise aggregation scheme based on maximum weighted matching in a graph and on principles of compatible relaxation. The latter replaces the commonly used characterization of strength of connection in both the coarse space selection and in the interpolation scheme. The goal is to design a method leading to scalable AMG for a wide class of problems that go beyond the standard elliptic Partial Differential Equations (PDEs). In the present work, we introduce the method and demonstrate its potential when applied to symmetric positive definite linear systems arising from finite element discretization of highly anisotropic elliptic PDEs on structured and unstructured meshes.

97 MATHEMATICS AND COMPUTING↗

Stability Assessment and Tuning of an Adaptively Augmented Classical Controller for Launch Vehicle Flight Control

Recently, a robust and practical adaptive control scheme for launch vehicles [ [1] has been introduced. It augments a classical controller with a real-time loop-gain adaptation, and it is therefore called Adaptive Augmentation Control (AAC). The loop-gain will be increased from the nominal design when the tracking error between the (filtered) output and the (filtered) command trajectory is large; whereas it will be decreased when excitation of flex or sloshing modes are detected. There is a need to determine the range and rate of the loop-gain adaptation in order to retain (exponential) stability, which is critical in vehicle operation, and to develop some theoretically based heuristic tuning methods for the adaptive law gain parameters. The classical launch vehicle flight controller design technics are based on gain-scheduling, whereby the launch vehicle dynamics model is linearized at selected operating points along the nominal tracking command trajectory, and Linear Time-Invariant (LTI) controller design techniques are employed to ensure asymptotic stability of the tracking error dynamics, typically by meeting some prescribed Gain Margin (GM) and Phase Margin (PM) specifications. The controller gains at the design points are then scheduled, tuned and sometimes interpolated to achieve good performance and stability robustness under external disturbances (e.g. winds) and structural perturbations (e.g. vehicle modeling errors). While the GM does give a bound for loop-gain variation without losing stability, it is for constant dispersions of the loop-gain because the GM is based on frequency-domain analysis, which is applicable only for LTI systems. The real-time adaptive loop-gain variation of the AAC effectively renders the closed-loop system a time-varying system, for which it is well-known that the LTI system stability criterion is neither necessary nor sufficient when applying to a Linear Time-Varying (LTV) system in a frozen-time fashion. Therefore, a generalized stability metric for time-varying loop=gain perturbations is needed for the AAC.

VanZwieten, Tannen↗

A scalable geometric multigrid solver for nonsymmetric elliptic systems with application to variable-density flows

A geometric multigrid algorithm is introduced for solving nonsymmetric linear systems resulting from the discretization of the variable density Navier–Stokes equations on nonuniform structured rectilinear grids and high-Reynolds number flows. The restriction operation is defined such that the resulting system on the coarser grids is symmetric, thereby allowing for the use of efficient smoother algorithms. To achieve an optimal rate of convergence, the sequence of interpolation and restriction operations are determined through a dynamic procedure. A parallel partitioning strategy is introduced to minimize communication while maintaining the load balance between all processors. To test the proposed algorithm, we consider two cases: 1) homogeneous isotropic turbulence discretized on uniform grids and 2) turbulent duct flow discretized on stretched grids. Testing the algorithm on systems with up to a billion unknowns shows that the cost varies linearly with the number of unknowns. This O (N) behavior confirms the robustness of the proposed multigrid method regarding ill-conditioning of large systems characteristic of multiscale high-Reynolds number turbulent flows. The robustness of our method to density variations is established by considering cases where density varies sharply in space by a factor of up to 104, showing its applicability to two-phase flow problems. Strong and weak scalability studies are carried out, employing up to 30,000 processors, to examine the parallel performance of our implementation. Excellent scalability of our solver is shown for a granularity as low as 104 to 105 unknowns per processor. At its tested peak throughput, it solves approximately 4 billion unknowns per second employing over 16,000 processors with a parallel efficiency higher than 50%.

Computer Science↗