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A structural design decomposition method utilizing substructuring

A new method of design decomposition for structural analysis and optimization is described. For this method, the structure is divided into substructures where each substructure has its structural response described by a structural-response subproblem, and its structural sizing determined from a structural-sizing subproblem. The structural responses of substructures that have rigid body modes when separated from the remainder of the structure are further decomposed into displacements that have no rigid body components, and a set of rigid body modes. The structural-response subproblems are linked together through forces determined within a structural-sizing coordination subproblem which also determines the magnitude of any rigid body displacements. Structural-sizing subproblems having constraints local to the substructures are linked together through penalty terms that are determined by a structural-sizing coordination subproblem. All the substructure structural-response subproblems are totally decoupled from each other, as are all the substructure structural-sizing subproblems, thus there is significant potential for use of parallel solution methods for these subproblems.

Scotti, Stephen J.↗

Root-Raised Cosine Filter Implementation That Uses Canonical Signed Digits for High-Speed Digital Filter Applications

NASA Lewis Research Center's Space Communications Division has been investigating high-speed digital filters that can operate at a higher speed than those in current use for a digital modulator and demodulator (modem). Using the Canonical Signed Digits (CSD) number representation for filter coefficients is a very effective way to increase the filter's speed while reducing complexity in the digital filter hardware design. This approach is a good alternative to using an expensive parallel-processing design technique or custom, application-specific integrated circuits. Such integrated circuits may not be suitable for applications that require filter speeds faster than what application-specific integrated circuits digital signal processors can offer for a dedicated channel. When a communication channel is a dedicated, multiplication process--a costly, time-consuming process--it can be greatly simplified by a replacement of the filter coefficients with CSD numbers. A computer code written with the MATLAB software package runs the program and generates CSD-represented filter coefficients that are based on minimizing minimum mean square errors. Also, the Alta Group of Cadence's Signal Processing Workstation is used to simulate and analyze the CSD filter responses. The impulse response of the root-raised cosine filter that is used as a base model is defined. From this filter, a set of coefficients is sampled and stored in a file. For the all coefficients, the optimal CSD number for each coefficient is searched on the basis of the minimum-mean-square-errors criterion. Because the distribution of CSD numbers is not uniform, quantization errors tend to be bigger for coefficients greater than 1/2. To offset errors that occur in a region of coefficients between 1/2 to 1 and to better represent fractions with CSD numbers, an extra nonzero digit is allowed for any coefficients exceeding 1/2. This will greatly improve frequency response as well as intersymbol interference at the receiver. The frequency response of a set of collected CSD-represented filter coefficients was compared with the same filter that was conventionally implemented. Analyses show CSD-implemented filters perform as well as conventional filters. Comparison of eye diagrams and bit-error-rate curves between CSD filters and traditionally implemented filters are almost indistinguishable. However, filter complexity was reduced from almost 3.5 to 1 for CSD filters. Complete computer simulation results are available. In the near future, work will focus on building actual working digital filter hardware in a field programmable gate array (FPGA).

Kim, Heechul↗

Early experiences on the OLCF Frontier system with AthenaPK and Parthenon–Hydro

The Oak Ridge Leadership Computing Facility (OLCF) has been preparing the nation's first exascale system, Frontier, for production and end users. Frontier is based on HPE Cray's new EX architecture and Slingshot interconnect and features 74 cabinets of optimized 3rd Gen AMD EPYC CPUs for HPC and AI and AMD Instinct 250X accelerators. As a part of this preparation, “real-world” user codes have been selected to help assess the functionality, performance, and usability of the system. This article describes early experiences using the system in collaboration with the Hamburg Observatory for two selected codes, which have since been adopted in the OLCF test harness. Experiences discussed include efforts to resolve performance variability and per-cycle slowdowns. Results are shown for a performance portable astrophysical magnetohydronamics code, AthenaPK, and a mini-application stressing the core functionality of a performance portable block-structured adaptive mesh refinement framework, Parthenon-Hydro. Here, these results show good scaling characteristics to the full system. At the largest scale, the Parthenon-Hydro miniapp reaches a total of $1.7$ $\times$ $10^{13}$ zone-cycles/s on 9216 nodes (73,728 logical GPUs) at ≈92% weak scaling parallel efficiency (starting from a single node using a second-order, finite-volume method).

97 MATHEMATICS AND COMPUTING↗

Study of the Alfven eigenmodes stability in CFQS plasma using a Landau closure model

The aim of this study is to analyze the stability of the Alfven eigenmodes (AE) in the Chinese First Quasi-axisymmetric Stellarator (CFQS). The AE stability is calculated using the code FAR3d that solves the reduced MHD equations to describe the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moment for the energetic particles (EP) species including the effect of the helical couplings and acoustic modes. The Landau damping and resonant destabilization effects are added in the model by a given closure relation. The simulation results indicate the destabilization of n = 1 to 4 AEs by EP during the slowing down process, particularly n = 1 and n = 2 toroidal AEs (TAE), n = 3 elliptical AE (EAE) and n = 4 non circular AE (NAE). If the resonance is caused by EPs with an energy above 17 keV (weakly thermalized EP), n = 2 EAEs and n = 3 NAEs are unstable. On the other hand, EPs with an energy below 17 keV (late thermalization stage) lead to the destabilization of n = 3 and n = 4 TAEs. The simulations for an off-axis NBI injection indicate the further destabilization of n = 2 to 4 AEs although the growth rate of the n = 1 AEs slightly decreases, so no clear optimization trend with respect to the NBI deposition region is identified. In addition, n = 2, 4 helical AE (HAE) are unstable above an EP β threshold. Also, if the thermal β of the simulation increases (higher thermal plasma density) the AE stability of the plasma improves. Overall, the simulations including the effect of the finite Larmor radius and electron-ion Landau damping show the stabilization of the n = 1 to 4 EAE/NAEs as well as a decrease of the growth rate and frequency of the n = 1 to 4 BAE/TAEs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Roles of Carburization and Oxidation on Transition-Metal Catalyzed Surface Reactions

Many industrial chemical transformation processes are based on reactions catalyzed by transition metals. In some cases the nano-size particles used as catalysts are synthesized simultaneously or right before the initiation of the main catalytic reaction. Synthesis treatments involve complex processes such as reductions followed by calcinations in oxygenated environments coupled to the presence of gases used for the main reaction. Synthesis details are crucial because they have important consequences on the catalyst shape, size, and chemical composition, and may also affect the structure and composition of the catalyst support. All these effects may alter the main catalyzed reaction in unexpected ways. This work focuses on the synthesis of the overall catalytic system that includes catalyst and support taking place in parallel with the initial stages of the main catalyzed reaction. Two important processes are characterized: carburization and oxidation of the transition metal catalyst during synthesis or initial stages of the main reaction. The objective is to understand how the coking mechanism coupled to surface oxidation and changes in the substrate influence the dry reforming of methane taken as a model reaction. The approach uses first principles computational methods to investigate the catalyst synthesis and characterization and catalytic reaction mechanisms. These studies are complemented with experimental characterization done by the group of Dr. Renu Sharma at the National Institute of Standards and Technology (unfunded collaborator) using high resolution transmission electron microscopy. Specific goals are to identify the role of the synthesis process on the initial nanocatalyst structure and composition, and to determine how that structure and composition may evolve after being exposed to the reactants atmosphere. These studies facilitate a systematic analysis of conditions where the nanoparticle composition can be optimized regarding activity and stability. Moreover, the fundamental study of catalyst/support interactions yields valuable insights for other catalytic processes and is a first step toward controlled nanocatalyst synthesis.

36 MATERIALS SCIENCE↗

Scalable Deep Learning-Based Microarchitecture Simulation on GPUs

Cycle-accurate microarchitecture simulators are essential tools for designers to architect, estimate, optimize, and manufacture new processors that meet specific design expectations. However, conventional simulators based on discrete-event methods often require an exceedingly long time-to-solution for the simulation of applications and architectures at full complexity and scale. Given the excitement around wielding the machine learning (ML) hammer to tackle various architecture problems, there have been attempts to employ ML to perform architecture simulations, such as Ithemal and SimNet. However, the direct application of existing ML approaches to architecture simulation may be even slower due to overwhelming memory traffic and stringent sequential computation logic. This work proposes the first graphics processing unit (GPU)-based microarchitecture simulator that fully unleashes the potential of GPUs to accelerate state-of-the-art ML-based simulators. First, considering the application traces are loaded from central processing unit (CPU) to GPU for simulation, we introduce various designs to reduce the data movement cost between CPUs and GPUs. Second, we propose a parallel simulation paradigm that partitions the application trace into sub-traces to simulate them in parallel with rigorous error analysis and effective error correction mechanisms. Combined, this scalable GPU-based simulator outperforms by orders of magnitude the traditional CPU-based simulators and the state-of-the-art ML-based simulators, i.e., SimNet and Ithemal.

97 MATHEMATICS AND COMPUTING↗

Ray Tracing Techniques for the Characterization of Lunar Communication Architectures

This paper provides an overview of the computational techniques used to characterize the viability of different lunar architectures and their ability to provide communication services to the lunar surface. This analysis was done with modern ray tracing techniques that allow for the computations to be done on Graphics Processing Unit (GPU) clusters for a high level of parallelism and severe reduction in computation time. The ray tracing computations were done with the GPU platform Compute Unified Device Architecture (CUDA) provided by NVIDIA which utilizes general-purpose computing on graphics processing units (GPGPU). This new method provides the advantage of being able to characterize a much larger portion of the lunar surface due to its computational efficiency as well as providing a more accurate representation of elevation angle limits instead of the typical and often inaccurate elevation angle mask. The Lunar surface can now be characterized with metrics such as contact time, outage time, and received data rate. With these metrics, different proposed Lunar architectures can be rapidly evaluated. This reduction in computation time not only leads to more accurate results but allows these results to be obtained in a time frame that allows for the complete characterization of the trade space. It is expected that these different architecture comparisons will lead to a conclusive determination of the optimal Lunar architecture and will allow for future Lunar missions to operate as close to real time as possible. In addition, this computation method can be used to recreate visibility figures generated by previous methods but with an increased level of accuracy.

Thomas Montano↗

MPACT Verification With Magnox Reactor Neutronics Progression Problems

MPACT is a state-of-the-art core simulator designed to perform high-fidelity analysis using whole-core, three-dimensional, pin-resolved neutron transport calculations on modern parallel computing hardware. MPACT was originally developed to model light water reactors, and its capabilities are being extended to simulate gas-cooled, graphite-moderated cores such as Magnox reactors. To verify MPACT’s performance in this new application, the code is being formally benchmarked using representative problems. Progression problems are a series of example models that increase in complexity designed to test a code’s performance. The progression problems include both beginning-of-cycle and depletion calculations. Reference solutions for each progression problem have been generated using Serpent 2, a continuous-energy Monte Carlo reactor physics burnup calculation code.Using the neutron multiplication eigenvalue ke as a metric, MPACT’s performance is assessed on each of the progression problems. Initial results showed that MPACT’s multi-group cross section libraries, originally developed for pressurized water reactor problems, were not sufficient to accurately solve Magnox problems. MPACT’s improved performance on the progression problems is demonstrated using this new optimized cross section library.

Luciano, Nicholas↗

Easy, Scalable Subsetting of GEDI Point Clouds

The GEDI Subsetter, a Python tool developed for NASA’s Multi-mission Algorithm and Analysis Platform (MAAP), optimizes the accessibility and visualization of GEDI point clouds by enabling users to efficiently subset data in a convenient, scalable manner. Complex science data often requires users to learn new software skills and handle many large files. Handling and cleaning large data sets is tedious and error-prone. These challenges significantly impede analysis. One of the goals of NASA's MAAP is to provide a platform that lowers the barrier to conducting research and analysis at scale. When a group of MAAP users wanted to conduct above-ground biomass estimation using GEDI data, we found that their existing workflow for leveraging GEDI data suffered from the barriers mentioned above. Furthermore, their workflow did not scale easily beyond a small number of granules. We found that existing tools related to GEDI data retrieval and subsetting were too limiting, so the GEDI Subsetter was written to support MAAP users’ needs. Being able to run many subsetting jobs simultaneously in the MAAP, and parallelizing the code itself, has led to significant speed improvements in obtaining relevant data, reducing subsetting time from hours to minutes. MAAP users can now more quickly and easily obtain only the data relevant to their research, by choosing which GEDI collection they want to work with (L1A, L2A, L2B, or L4A), and how they want to subset it, by specifying an area of interest, a temporal range, and relevant attributes. This has significantly reduced the feedback loop for users, allowing them to much more quickly subset GEDI data and begin their analysis. Although the GEDI Subsetter originally targeted users of the MAAP, it is generalized such that it can also be used outside of the MAAP and includes a command-line interface for convenience. Furthermore, with minor modifications, it should be possible to use it with non-GEDI data as the general pattern should be applicable to other sparse/track-based sensors.

Charles Daniels↗

Threat Agnostic Virulence Assessment of Pathogens

Virulence assessment of new, emerging, and engineered pathogens is critical to mounting an appropriate response to a biothreat agent. The capacity of the pathogen to colonize human and harm tissues must be characterized to understand pathogenicity pathways and optimize diagnosis and treatment of resulting disease. Respiratory pathogens are of interest because they can have high transmissibility rates, as observed with the SARS-CoV-2 virus, the causative agent of Covid-19. Current technologies are insufficient to assess threats due to their reliance on systems with only one cell type and on sequencing the pathogen. However, it is known that sequence is not an accurate predictor of function, and sequencing can be unreliable for newly emerged or engineered pathogens. An ideal system would consist of relevant epithelial cell types and an assay sensitive enough to detect changes in host responses that do not rely on DNA sequencing. We chose a system consisting of host lung epithelial cells that can be used to assess the virulence of unknown respiratory pathogens. We interrogated pathogens using this model and assess features of pathogenicity. Our objective is to leverage PNNLs strengths in tissue engineering and proteomics capabilities to build a multiple reaction monitoring (MRM) or parallel reaction monitoring (PRM) liquid chromatography-tandem mass spectrometry assay for human host cell proteins whose abundance is influenced by infection. These responses can were then assessed for relative virulence using pathogen agnostic signatures. When confronted with a pathogen, cells activate dedicated signaling pathways, typically through phosphorylation of regulatory proteins and downstream activation of host cell networks.

59 BASIC BIOLOGICAL SCIENCES↗

Predicting Selective Laser Printing Print Quality of Polymer Powders through Melt Flow Index

Selective Laser Sintering (SLS) uses a precisely controlled laser to fuse polymer powder to build complex 3D shapes. While SLS covers a wide application space, the processing knowledge of polymer powder is limited, restricting the number of commercial powders available. This study serves to expand the processing knowledge of polypropylene and polyethylene in parallel with a “mature” SLS feedstock, nylon, through melt flow index (MFI) characterization. Differential Scanning Calorimetry (DSC) was used to explore the sintering window of the polymers. Polyethylene and polypropylene exhibited a relatively narrow sintering window between 4 – 5 °C, whereas the sintering window of nylon was much wider, between 23 – 24 °C. This suggests that the print quality between polyethylene and polypropylene would be similar; however, X-ray computed tomography revealed a higher volume of print defects, voids, and de lamination in polyethylene than in polypropylene. MFI analysis provided additional insight into the difference in print quality, as the MFI of polyethylene was 7.16 g/10 min, 9.95 g/10 min for polypropylene, and 17.23 g/10 min for nylon. MFI is inversely correlated to melt viscosity, and a low melt viscosity is desired for proper coalescing between the layers and particles. These results suggest that MFI is a promising tool, in conjunction with traditional thermal analysis, for screening candidate powder feedstocks for SLS and optimization of print parameters for novel powders.

36 MATERIALS SCIENCE↗

Improved interpretation of satellite altimeter data using genetic algorithms

Genetic algorithms (GA) are optimization techniques that are based on the mechanics of evolution and natural selection. They take advantage of the power of cumulative selection, in which successive incremental improvements in a solution structure become the basis for continued development. A GA is an iterative procedure that maintains a 'population' of 'organisms' (candidate solutions). Through successive 'generations' (iterations) the population as a whole improves in simulation of Darwin's 'survival of the fittest'. GA's have been shown to be successful where noise significantly reduces the ability of other search techniques to work effectively. Satellite altimetry provides useful information about oceanographic phenomena. It provides rapid global coverage of the oceans and is not as severely hampered by cloud cover as infrared imagery. Despite these and other benefits, several factors lead to significant difficulty in interpretation. The GA approach to the improved interpretation of satellite data involves the representation of the ocean surface model as a string of parameters or coefficients from the model. The GA searches in parallel, a population of such representations (organisms) to obtain the individual that is best suited to 'survive', that is, the fittest as measured with respect to some 'fitness' function. The fittest organism is the one that best represents the ocean surface model with respect to the altimeter data.

Messa, Kenneth↗

SQUARE: Strategic Quantum Ancilla Reuse for Modular Quantum Programs via Cost-Effective Uncomputation

Compiling high-level quantum programs to machines that are size constrained (i.e. limited number of quantum bits) and time constrained (i.e. limited number of quantum operations) is challenging. In this paper, we present SQUARE (Strategic QUantum Ancilla REuse), a compilation infrastructure that tackles allocation and reclamation of scratch qubits (called ancilla) in modular quantum programs. At its core, SQUARE strategically performs uncomputation to create opportunities for qubit reuse. Current Noisy Intermediate-Scale Quantum (NISQ) computers and forward-looking Fault-Tolerant (FT) quantum computers have fundamentally different constraints such as data locality, instruction parallelism, and communication overhead. Our heuristic-based ancilla-reuse algorithm balances these considerations and fits computations into resource-constrained NISQ or FT quantum machines, throttling parallelism when necessary. To precisely capture the workload of a program, we propose an improved metric, the "active quantum volume," and use this metric to evaluate the effectiveness of our algorithm. Furthermore, our results show that SQUARE improves the average success rate of NISQ applications by 1.47X. Surprisingly, the additional gates for uncomputation create ancilla with better locality, and result in substantially fewer swap gates and less gate noise overall. SQUARE also achieves an average reduction of 1.5X (and up to 9.6X) in active quantum volume for FT machines.

compiler optimization↗

Combined Numerical/Analytical Perturbation Solutions of the Navier-Stokes Equations for Aerodynamic (Ejector Nozzle) Flows

In spite of the rapid advances in both scalar and parallel computational tools, the large number and breadth of variables involved in aerodynamic systems make the use of parabolized or even boundary layer fluid flow models impractical for both preliminary design and inverse design problems. Given this restriction, we have concluded that reduced or approximate models are an important family of tools for design purposes. This study of a combined perturbation/numerical modeling methodology with an application to ejector-mixer nozzles (shown schematically in the following figure) is nearing completion. The work is being funded by a grant from the NASA Lewis Research Center to Texas A&M University. These ejector-mixer nozzle models are designed to be of use to the High Speed Civil Transport Program and may be adopted by both NASA and industry. A computer code incorporating the ejector-mixer models is under development. This code, the Differential Reduced Ejector/Mixer Analysis (DREA), can be run fast enough to be used as a subroutine or to be called by a design optimization routine. Simplified conservation equations--x-momentum, energy, and mass conservation--are used to define the model. Unlike other preliminary design models, DREA requires minimal empirical input and includes vortical mixing and a fully compressible formulation among other features. DREA is being validated by comparing it with results obtained from open literature and proprietary industry data. Preliminary results for a subsonic ejector and a supersonic ejector are shown. In addition, dedicated experiments have been performed at Texas A&M. These experiments use a hydraulic/gas flow analog to provide information about the inviscid mixing interface structure. Final validation and documentation of this work is expected by May of 1997. However, preliminary versions of DREA can be expected in early 1997. In summary, DREA provides a sufficiently detailed and realistic ejector-mixer nozzle model at a computational cost compatible with preliminary design applications.

DeChant, Lawrence J.↗

An Antibody Cocktail-Based Immunoaffinity-LC-MS Method Enabled Ultra-Sensitive and Robust Quantification of Circulating Proinsulin Proteoforms and C-Peptide

Accurately measuring circulating proinsulin proteoforms is crucial for clinical investigation of diabetes, but was previously not feasible owing to limited assay specificity/sensitivity. Here, in this study, we devised a highly sensitive LC-MS-based strategy to quantify intact proinsulin, des-31,32 and des-64,65 proinsulin, and C-peptide in circulation. The method involves: (i) quantitative, robust affinity capture using an optimized antibody cocktail, eliminating the severe quantitative bias across multiple proteoforms typically introduced when using a single antibody; (ii) Lys-C digestion producing unique signature peptides for each proteoform, and (iii) trapping-nano-LC coupled with FAIMS/dCV-MS for an ultrasensitive analysis. The selective trapping/delivery ensured sensitive/selective analysis of the targets while achieving excellent analytical robustness that is critical for clinical assays, and the FAIMS/dCV substantially reduces baseline noise/interferences, further enhancing S/N. The assay achieved exceptional sensitivity, with serum LOQs of 1.7, 2.3, and 3.6 pg/mL respectively for intact-proinsulin, des-31,32 and des-64,65, representing the first assay capable of sensitively quantifying these major circulating proinsulin proteoforms. We applied this assay to 78 subjects, including autoantibody positive (n = 20) and new-onset type 1 diabetes (T1D, n = 19) with respective age/sex/BMI-matched controls, enabling the first accurate profiling of proinsulin proteoforms in clinical groups. The assay results demonstrated a clear separation of control and new-onset T1D groups that a parallel total-proinsulin ELISA assay fails to capture. Furthermore, distinct expression patterns in relative abundance ratios among proteoforms were observed across clinical groups. This assay may provide valuable insights into the β-cell functions and the onset/progression of diabetes and other associated conditions. Moreover, the strategy is broadly applicable to targeted measurement of other biomarker proteoforms.

Shen, Qingqing [University at Buffalo, NY (United ↗

ACCELERATOR CHALLENGES OF THE LHeC PROJECT

The LHeC project studies the design of a future electron-proton collider at CERN that will run in parallel to the standard LHC operation. For this purpose, the existing LHC storage ring will be combined with an Energy Recovery Linac (ERL), to accelerate electrons up to kinetic energy of 50 GeV. This concept - also applicable to the FCC-eh collider and studied at the PERLE project as prototype version - allows a peak luminosity of 10³⁴ cm⁻² s⁻¹. A sophisticated design of the RF structures, linacs, arcs, and interaction region is required. The electrons are accelerated and, after the interaction point, their energy is recovered through the same RF structures. While this energy recovery concept is a very promising approach, severe challenges are set by the layout of the interaction region, the beam separation concept and the design of the linac and arc lattice for the highest possible momentum acceptance. Emittance control and beam-beam effect of both, electron and proton beams, have been studied in front-to-end simulations and will be presented. We summarise the design principles of the ERL, the optimization of the arc lattice, and the main parameters of the project.

Holzer, B. J.↗

Automated Generation and Assessment of Autonomous Systems Test Cases

This slide presentation reviews some of the issues concerning verification and validation testing of autonomous spacecraft routinely culminates in the exploration of anomalous or faulted mission-like scenarios using the work involved during the Dawn mission's tests as examples. Prioritizing which scenarios to develop usually comes down to focusing on the most vulnerable areas and ensuring the best return on investment of test time. Rules-of-thumb strategies often come into play, such as injecting applicable anomalies prior to, during, and after system state changes; or, creating cases that ensure good safety-net algorithm coverage. Although experience and judgment in test selection can lead to high levels of confidence about the majority of a system's autonomy, it's likely that important test cases are overlooked. One method to fill in potential test coverage gaps is to automatically generate and execute test cases using algorithms that ensure desirable properties about the coverage. For example, generate cases for all possible fault monitors, and across all state change boundaries. Of course, the scope of coverage is determined by the test environment capabilities, where a faster-than-real-time, high-fidelity, software-only simulation would allow the broadest coverage. Even real-time systems that can be replicated and run in parallel, and that have reliable set-up and operations features provide an excellent resource for automated testing. Making detailed predictions for the outcome of such tests can be difficult, and when algorithmic means are employed to produce hundreds or even thousands of cases, generating predicts individually is impractical, and generating predicts with tools requires executable models of the design and environment that themselves require a complete test program. Therefore, evaluating the results of large number of mission scenario tests poses special challenges. A good approach to address this problem is to automatically score the results based on a range of metrics. Although the specific means of scoring depends highly on the application, the use of formal scoring - metrics has high value in identifying and prioritizing anomalies, and in presenting an overall picture of the state of the test program. In this paper we present a case study based on automatic generation and assessment of faulted test runs for the Dawn mission, and discuss its role in optimizing the allocation of resources for completing the test program.

Testing challenges↗

Optimal white-noise stochastic forcing for linear models of turbulent channel flow

In the present study an optimisation problem is formulated to determine the forcing of an eddy-viscosity-based linearised Navier–Stokes model in channel flow at $Re_\tau \approx 5200$ ( $Re_\tau$ is the friction Reynolds number), where the forcing is white-in-time and spatially decorrelated. The objective functional is prescribed such that the forcing drives a response to best match a set of velocity spectra from direct numerical simulation (DNS), as well as remaining sufficiently smooth. Strong quantitative agreement is obtained between the velocity spectra from the linear model with optimal forcing and from DNS, but only qualitative agreement between the Reynolds shear stress co-spectra from the model and DNS. The forcing spectra exhibit a level of self-similarity, associated with the primary peak in the velocity spectra, but they also reveal a non-negligible amount of energy spent in phenomenologically mimicking the non-self-similar part of the velocity spectra associated with energy cascade. By exploiting linearity, the effect of the individual forcing components is assessed and the contributions from the Orr mechanism and the lift-up effect are also identified. Finally, the effect of the strength of the eddy viscosity on the optimisation performance is investigated. The inclusion of the eddy viscosity diffusion operator is shown to be essential in modelling of the near-wall features, while still allowing the forcing of the self-similar primary peak. In particular, reducing the strength of the eddy viscosity results in a considerable increase in the near-wall forcing of wall-parallel components.

Mechanics↗