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At least 487 records · Page 27

Fluid Dynamics Effects on Microstructure Prediction in Single Laser Tracks for Additive Manufacturing

The Laser Powder Bed Fusion Additive Manufacturing (LPBFAM) is one of the most important processes for the production of lightweight, cost-effective, complex, and high-performance enduse parts. At present, the cost and time associated with LPBFAM process development is very high due to a lack of fundamental process understanding. In this project, a multi-physics model was developed on a highly parallel open-source code, Truchas, with the ultimate goal of providing experimentally validated process maps for tailoring microstructure to achieve desired performance for LPBFAM. As a critical step towards fully LPBFAM modeling, modeling of single-track laser fusion (STLF) were conducted. Multi-physics simulations were conducted using Truchas for STLF by considering heat transfer, phase-change, fluid dynamics, surface tension phenomena, and evaporation. In order to assess the effect of the fluid dynamics on the solidification and ensuing microstructure, a heat transfer-and-solidification-only (HTS) model and a fully coupled heat-transfer-solidification and fluid-dynamics (HTS-FD) model were considered. In the HTS_FD model, the fluid flow was considered to be laminar while the molten alloy surface is assumed to be flat and non-deformable. This study is one the first attempt to understand the effect of the fluid flow on microstructure in STLF and LPBFAM. The results show that the fluid flow affects the solidification and ensuing microstructure in STLF. In order to validate Truchas for STLF and LPBFAM modeling, experimental data, which was obtained at GE Global Research (GEGR) for liquid pool shape and microstructure, were compared with those from numerical simulation results. For the keyhole regime case, numerical simulation results indicate that the melt-pool shape was typical to that of the conduction case with very large deviations from the measured melt-pool depths. Two sensitivity studies were conducted by varying the evaporation flux and the surface tension coefficient at fixed laser absorptivities of 0.5 and 0.3, respectively. The minimum value for the overall combined error, between the calculated values with the HTS_FD model and measured values for both the width and height of the melt-pool, was attained for a surface tension coefficient of -0.75e-4 N/m. An analytical solidification model for the columnar-to-equiaxed transition (CET) in rapid solidification was used to assess the microstructure variation within the melt-pool. From numerical simulation results, thermal gradient, G, and solidification velocity, V, were obtained in order to predict the microstructure type (e.g., dendritic, cellular). For the fluid-flow HTS_FD model, G was found to exhibit a maximum at the extremity of the solidified pool (i.e., at the free surface). By contrast, for HTS simulations, G was found to exhibit a maximum around the entire edge of the solidified pool. For the HTS_FD simulations, the minimum values of the cooling rate, GV, were found to be approximately half than their corresponding values for HTS simulations. By contrast with the min GV values, the maximum values for GV were found to occur for the HTS_FD simulations. Thus, HTS_FD simulations were found to exhibit a wider range of cooling rates than the HTS simulations. Concerning the solidification maps, the variation of the solidification velocity, V, as function of the thermal gradient, G, was obtained. It was found that the fluid flow model results (HTS_FD) exhibited an increased spread in the V(G) variation within the melt pool with respect to the HTS model results (without the fluid flow). A preliminary correlation model for the primary dendrite arm spacing (PDAS) based on a power law dependence on thermal gradient and solidification velocity was used to estimate PDAS from HTS and HTS_FD simulations. For low laser powers and low laser speeds, the PDAS obtained 6 with the fluid dynamics model (HTS_FD) was larger by more than 30% with respect to the PDAS calculated with the simple HTS model. In the second part of the project, fifty-seven simulations were conducted in order to obtain data on microstructure variables that can be used for process map development. In order to cover the entire processing space, thirty-three cases were selected STLF process simulations at six power levels and six laser scanning speeds. The 57 STLF process simulations were conducted as follows: 33 simulations with the heat-transfer-only (HTS) model and 24 simulations with the fluid flow model (HTS_FD). The solidification map data shows that for all simulations, a columnar dendritic microstructure would be expected. It was found that the minimum, average, and maximum thermal gradient exhibit exponential variations with respect to a process variable defined as the ratio between the power and square root of scan speed.

36 MATERIALS SCIENCE↗

Modeling Variable Renewable Energy and Storage in the Power Sector

The emergence of variable renewable energy and battery storage technologies have fundamentally transformed the electric power sector and generated demand for analysis to understand their roles in future energy systems. Although unique characteristics of these resources are well-recognized and require more sophisticated methodologies to capture effectively, guidance is limited on best practices and research gaps. This paper selectively reviews recent literature and draws upon our collective modeling experience to offer recommendations to analysts and consumers of model outputs on approaches for modeling variable renewable energy and storage in long-term electric sector models. We focus on regional- and national-scale models with technological, temporal, and spatial detail given their prevalence in planning and policy analysis, though insights are applicable in other settings. The review highlights how the research frontier has advanced in representing renewables and energy storage over the past decade; however, given the many considerations involved with appropriately capturing salient economic and operational characteristics of renewables, there is a gap between commonly used models and state-of-the-art methods. Model simplifications can materially impact policy analysis associated with power sector decarbonization and high renewables deployment, and improving model representations of variable renewables can enhance insights for policymakers and other stakeholders. This review can point the way for improved methods for established models and designs for emerging ones.

energy and environmental policy↗

A multi-dimensional parametric study of variability in multi-phase flow dynamics during geologic CO 2 sequestration accelerated with machine learning

Successful geologic CO 2 storage projects depend on numerical simulations to predict reservoir performance during site selection, injection verification, and post-injection monitoring phases of the project. These numerical simulations solve non-linear sets of coupled partial differential equations, while accounting for multi-phase fluid dynamics on the basis of constitutive equations that are embedded into the solution scheme. As a consequence, individual simulations often require tens to hundreds of hours to complete on high-performance computing clusters. Moreover, laboratory experiments reveal that parametric functions for capillary pressure and relative permeability exhibit substantial variability, even within the same rock type. This combination of computational expense and wide-ranging parametric variability means that there remains substantial uncertainty in the behavior of multi-phase CO 2 -water systems, particularly in the context of feedbacks between relative permeability and capillary pressure. To bridge this knowledge gap, here we develop a novel workflow that utilizes physics-based numerical simulation to train an artificial neural network (ANN) emulator for interrogating the multivariate parameter space that governs both capillary pressure and relative permeability. With this approach, the ANN is trained to emulate both fluid pressure distribution and CO 2 saturation, which are then interrogated quantitatively to generate parametric response surface mappings with high-fidelity resolution. Results from this study initially show that capillary entry pressure is the dominant control on both CO 2 plume geometry and fluid pressure propagation when considering the combined effects of capillary pressure and relative permeability, particularly when phase interference is low and residual CO 2 saturation is high. Moreover, the ANN emulator provides tremendous computational speed-up by computing 2691 individual simulations in several minutes; whereas, the same simulation ensemble would have required ~3 years of simulation time using only physics-based simulation methods (25,000 times speed up).

58 GEOSCIENCES↗

Substitution Models of Protein Evolution with Selection on Enzymatic Activity

Abstract Substitution models of evolution are necessary for diverse evolutionary analyses including phylogenetic tree and ancestral sequence reconstructions. At the protein level, empirical substitution models are traditionally used due to their simplicity, but they ignore the variability of substitution patterns among protein sites. Next, in order to improve the realism of the modeling of protein evolution, a series of structurally constrained substitution models were presented, but still they usually ignore constraints on the protein activity. Here, we present a substitution model of protein evolution with selection on both protein structure and enzymatic activity, and that can be applied to phylogenetics. In particular, the model considers the binding affinity of the enzyme–substrate complex as well as structural constraints that include the flexibility of structural flaps, hydrogen bonds, amino acids backbone radius of gyration, and solvent-accessible surface area that are quantified through molecular dynamics simulations. We applied the model to the HIV-1 protease and evaluated it by phylogenetic likelihood in comparison with the best-fitting empirical substitution model and a structurally constrained substitution model that ignores the enzymatic activity. We found that accounting for selection on the protein activity improves the fitting of the modeled functional regions with the real observations, especially in data with high molecular identity, which recommends considering constraints on the protein activity in the development of substitution models of evolution.

Ferreiro, David↗

Probabilistic Context Neighborhood model for lattices

Here we present the Probabilistic Context Neighborhood model designed for two-dimensional lattices as a variation of a Markov random field assuming discrete values. In this model, the neighborhood structure has a fixed geometry but a variable order, depending on the neighbors’ values. Our model extends the Probabilistic Context Tree model, originally applicable to one-dimensional space. It retains advantageous properties, such as representing the dependence neighborhood structure as a graph in a tree format, facilitating an understanding of model complexity. Furthermore, we adapt the algorithm used to estimate the Probabilistic Context Tree to estimate the parameters of the proposed model. We illustrate the accuracy of our estimation methodology through simulation studies. Additionally, we apply the Probabilistic Context Neighborhood model to spatial real-world data, showcasing its practical utility.

97 MATHEMATICS AND COMPUTING↗

Fldgen v1.0: an emulator with internal variability and space–time correlation for Earth system models

Earth system models (ESMs) are the gold standard for producing future projections of climate change, but running them is difficult and costly, and thus researchers are generally limited to a small selection of scenarios. This paper presents a technique for detailed emulation of the Earth system model (ESM) temperature output, based on the construction of a deterministic model for the mean response to global temperature. The residuals between the mean response and the ESM output temperature fields are used to construct variability fields that are added to the mean response to produce the final product. The method produces grid-level output with spatially and temporally coherent variability. Output fields include random components, so the system may be run as many times as necessary to produce large ensembles of fields for applications that require them. We introduce the method, show example outputs, and present statistical verification that it reproduces the ESM properties it is intended to capture. This method, available as an open-source R package, should be useful in the study of climate variability and its contribution to uncertainties in the interactions between human and Earth systems.

58 GEOSCIENCES↗

Optimization of well design and CO 2 injection strategy for risk reduction in Class VI geological carbon sequestration wells

The safety and durability of Class VI wells are critical for geological carbon sequestration (GCS). However, current GCS operations face unique challenges: unlike traditional Class II wells, Class VI CO 2 injection wells operate at rates up to 100 times higher, dramatically increasing the risk of wellbore leakage and structural compromise due to severe temperature drops and associated mechanical stresses. Despite existing guidelines on material selection, there remains a substantial gap in understanding how rapid CO 2 injection rates, low surface temperatures, and variable reservoir conditions interact to threaten long-term well integrity. This study presents a comprehensive, original workflow integrating advanced analytical and numerical models for both well flow and well integrity analysis. By systematically simulating a wide range of field-relevant scenarios—including variations in injection rate, CO 2 temperature, and reservoir pressure—this work provides the first cross-validated assessment of cooling effects on wellbore. The results reveal that extreme temperature drops, up to 60 °C, can occur under high injection rates, particularly in depleted reservoirs, significantly increasing the risk of cement failure. Building on these insights, the study proposes innovative, practical well design and operational strategies, including ductile cement formulations, pre-stressing techniques, advanced insulation coatings, and proactive management of injection rates. The safety of Class VI well extends beyond simply using CO 2 resistant materials. Cement materials should possess optimal thermo-hydraulic-mechanical-chemical properties for effective performance. This work provides a scientific basis for optimizing Class VI well designs, with direct benefits for minimizing environmental risk, lowering operational costs, and enhancing the long-term reliability of GCS.

25 ENERGY STORAGE↗

MODE: A Web Application for Interactive Visualization and Exploration of Omics Data

Studies generating transcriptomics, proteomics, lipidomics, and metabolomics (colloquially referred to as “omics”) data allow researchers to find biomarkers or molecular targets, or understand complex biological structures and functions by identifying changes in biomolecule abundance and expression between experimental conditions. Omics data is multi-dimensional and oftentimes summarization techniques such as principal component analysis (PCA) are used to identify high-level patterns in data. Though useful, these summaries don’t allow exploration of detailed patterns in omics data that may have biological relevance. The use of interactive HTML displays with plots allows researchers to interact with omics data at a detailed level, but building these displays requires significant coding expertise. To overcome this barrier, the software MODE was built to empower users to build their own interactive HTML displays to support scientific discovery. These displays are easily shareable, do not depend on a specific operating system, and allow users to effortlessly sort and filter plots by categorical or numerical variables. MODE allows users to build and share these displays with several options for plot design and meta selection. In conclusion, the MODE web application and its capabilities are presented and then demonstrated on lipidomics data from a leaf wounding study.

lipidomics↗

Towards non-contact pollution monitoring in sewers with hyperspectral imaging

Monitoring water quality in sewers is challenging, particularly because state-of-the-art technologies require contact with the raw wastewater. The presence of fat, oil, grease, and solids makes automated grab sampling difficult and causes sensor fouling. To overcome these limitations, non-contact methods based on light reflectance, such as hyperspectral imaging (HSI), are gaining attention. However, HSI has never been tested for raw wastewater. To assess its accuracy for measuring pollution, we developed a laboratory setup and performed targeted experiments with a combination of raw and diluted wastewater, as well as synthetic turbidity stock solutions. We measured seven pollution variables: chemical oxygen demand, turbidity, dissolved organic compounds, ammonium, total nitrogen, phosphate, and sulphates. We used automated pixel selection and partial least squares regression to retrieve pollution information from the hyperspectral images. Our results, based on 144 samples, suggest that HSI can estimate pollution levels with a precision in the range of state-of-the-art absorbance spectrophotometric methods. Additionally, we found that the combination of pixel and wavelength selection, enabled by the hyperspectral data structure, significantly influences the performance of partial least square modelling. Overall, our findings indicate that HSI is a promising technology for non-contact monitoring of water quality in raw wastewater.

54 ENVIRONMENTAL SCIENCES↗

CFD and systems engineering to minimize membrane-based carbon capture costs

In this study, we propose a superstructure for membrane-based carbon capture, addressing these challenges through the formulation of an optimization problem. The case study considers a flue gas with a flowrate of 1000 mol/s and a 30 % CO2 (molar basis), which is representative of steel plants. Reduced models, derived from rigorous CFD simulations of membrane modules, are utilized to enhance the efficiency of the optimization process. The reduced model includes specific input variables such as inlet flow rate, retentate and permeate pressures, and inlet CO2 concentration; while the CO2 recovery and purity in the permeate side are considered as output variables. In this way, we exploit the information from the CFD simulations in the superstructure, aiding in the selection of the optimal configuration for the multi-stage membrane process. The results underscore the efficiency of a multi-stage membrane design, showing capture costs around 45 $/t-CO2.

Pedrozo, Hector A.↗

Optimizing Alabama’s CO 2 Storage in Shelby County (Project OASIS): Task 4.0 Deliverable – Geologic Analysis Report

Project OASIS (Optimizing Alabama’s CO 2 Storage in Shelby County) is a geologic and reservoir characterization study designed to evaluate deep saline formations for potential long-term carbon dioxide (CO 2 ) storage in central Alabama near the National Carbon Capture Center (NCCC) and Alabama Power’s Plant Gaston. The project centers on the Cambro-Ordovician Knox Group and underlying strata such as the Conasauga and Rome Formations, which were investigated through the drilling of two stratigraphic test wells to obtain electronic well logs, core, and sidewall core plugs. These data provide direct measurements of porosity, permeability, and lithologic variability critical for reservoir characterization. Complementing the well program, a limited 2D seismic survey was acquired to help select the site for Westover #2, and a more regional Seismic Exchange (SEI) seismic survey was licensed and interpreted to define structural and stratigraphic frameworks in a new Static Earth Model (SEM), map reservoir continuity, and identify potential sealing intervals. Integrated with geologic and reservoir modeling, these datasets form the basis for evaluating storage capacity, injectivity, and containment.

20 FOSSIL-FUELED POWER PLANTS↗

Optimizing Alabama’s CO 2 Storage in Shelby County (Project OASIS): Task 6.0 Deliverable – CarbonSAFE Phase III Readiness

The OASIS CarbonSAFE Phase II Project OASIS (Optimizing Alabama’s CO 2 Storage in Shelby County) is a geologic and reservoir characterization study designed to evaluate deep saline formations for potential long-term carbon dioxide (CO 2 ) storage in central Alabama near the National Carbon Capture Center (NCCC) and Alabama Power’s Plant Gaston. The project centers on understanding the potential of the Cambro-Ordovician Knox Group and underlying strata such as the Conasauga and Rome Formations for geologic storage of CO 2 . These formations were investigated as part of SECARB-USA (DE-FE0031830) and Project OASIS through the drilling of two stratigraphic test wells to obtain electronic well logs, core, and sidewall core plugs. These data provide direct measurements of porosity, permeability, and lithologic variability critical for reservoir characterization. Complementing the well program, a limited 2D seismic survey was conducted to help select the site for Westover #2 as part of SECARB-USA (DE-FE0031830), and a more regional Seismic Exchange (SEI) seismic survey was licensed and interpreted to define structural and stratigraphic frameworks in a new Static Earth Model (SEM), map reservoir continuity, and to identify potential sealing intervals. Integrated with geologic and reservoir modeling, these datasets form the basis for evaluating storage capacity, injectivity, and containment. While this document endeavors to provide readers with a high-level overview of Project OASIS activities and its suitability for subsequent CarbonSAFE Phases, such as a Phase III effort. Other project deliverables and milestones will provide more details on individual subjects.

20 FOSSIL-FUELED POWER PLANTS↗

Kinetic Monte Carlo Simulations of Chemical Reactions on Surfaces

Lattice based kinetic Monte Carlo (kMC) simulations are a powerful tool for micro-kinetic modeling. The kinetic Monte Carlo technique stochastically simulates chemical reaction processes (e.g. adsorption, desorption, diffusion), where the probability of a given reaction process being selected is weighted by its rate constant. The open source software package, KMOS1, allows fast construction of kMC simulations by automatically implementing a computationally efficient kMC framework, thus allowing the researcher to focus on accurate parameterization and formulation of the kinetic model. From this, the spatiotemporal evolution (e.g. concentration, surface configuration, turnover frequencies) of crystal surfaces or bulk crystalline structures is obtained. KMOS uses the variable step-size method implementation of kMC. At each step, the VSSM updates available events, calculates the corresponding transition rates and simulation time, and selects one of the available events. The lattice based kMC technique has many potential applications within SRNL where chemical kinetics are of interest. By transitioning through time along a trajectory of configuration space, fundamental insights to a system's dominant reactions and parameters can be gained, leading to improved materials and process design. In this work, we have established capabilities for fast implementation of kMC simulations through the installation and testing of the KMOS software on SRNL high performance computing resources. The parameterization of kMC simulations is often performed from first-principles energetic calculations. For the purposes of this work, the test cases use arbitrary species and thus, have arbitrary parameterization. In order to demonstrate the use of KMOS, two primary test cases are shown. Case 1 involves simple adsorption and desorption. Case 2 involves a slightly more complex mechanism. The evolution of the surface concentration and the final surface configuration for simulation Case 2 is shown. Rate-limiting processes and rate-limiting configurations are not always known or understood, but kMC provides information pertaining to both. The capability to implement efficient micro-kinetic models using the kinetic Monte Carlo technique has been established through the testing and installation of KMOS on SRNL HPC resources.

97 MATHEMATICS AND COMPUTING↗

Multiple-wavelength Variability and Quasi-periodic Oscillation of PMN J0948+0022

We present a comprehensive analysis of multiple-wavelength observational data of the first GeV-selected narrow-line Seyfert 1 galaxy PMN J0948+0022. We derive its light curves in the γ -ray and X-ray bands from the data observed with Fermi /LAT and Swift /XRT, and generate the optical and radio light curves by collecting the data from the literature. These light curves show significant flux variations. With the LAT data we show that this source is analogous to typical flat spectrum radio quasars in the L {sub γ} –Γ {sub γ} plane, where L {sub γ} and Γ {sub γ} are the luminosity and spectral index in the LAT energy band. The γ -ray flux is correlated with the V-band flux with a lag of ∼44 days, and a moderate quasi-periodic oscillation (QPO) with a periodicity of ∼490 days observed in the LAT light curve. A similar QPO signature is also found in the V-band light curve. The γ -ray flux is not correlated with the radio flux in 15 GHz, and no similar QPO signature is found at a confidence level of 95%. Possible mechanisms of the QPO are discussed. We propose that gravitational-wave observations in the future may clarify the current plausible models for the QPO.

79 ASTRONOMY AND ASTROPHYSICS↗

First Measurement of Differential Charged Current Quasielastic-like $\nu_\mu$–Argon Scattering Cross Sections in Kinematic Imbalance Variables with the MicroBooNE Detector

We report the first measurement of flux-integrated multi-differential cross sections for charged-current events with muon neutrinos scattering on argon with solely a muon and a single proton in the final state as a function of kinematic imbalance variables. The measurement was carried out using the Booster Neutrino Beam at Fermi National Accelerator Laboratory within the MicroBooNE Liquid Argon Time Projection Chamber detector with an exposure of 6.79 × 10 20 protons on target. Events were selected to enhance the contribution of charged-current mesonless interactions with one proton detected in the final state. The data discussed here are reported in terms of multi-differential cross sections in kinematic imbalance variables, which are generally sensitive to nuclear effects. The double-differential results in these variables can provide an excellent handle to disentagle specific nuclear aspects not easily isolated via single differential cross sections. Our results pave a path towards identifying regions of the phase-space where future interaction modeling development and Monte Carlo neutrino generator tuning efforts should concentrate.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Nickel Enhances InPd-Catalyzed Nitrate Reduction Activity and N 2 Selectivity

Palladium–indium (PdIn) is a well-established bimetallic composition for reductively degrading nitrate anions, one of the most ubiquitous contaminants in the groundwater. However, the scarcity and the variable price of these rare-earth and platinum group critical metals may hinder their use for water treatment. Nickel (Ni), a nonprecious metal in the same element group as Pd, could partially replace and lower Pd usage if the resulting trimetallic composition is sufficiently catalytically active. Herein, we report the synthesis and nitrate reduction catalysis of activated carbon-supported “In-on-Pd-on-Ni” catalysts (InPdNi/AC). While bimetallic InPd/AC (0.05 wt % In, 1.3 wt % Pd) was expectedly active, trimetallic InPdNi/AC containing the same In amount, much less Pd (0.1 wt %), and 1 wt % Ni was >17 more active (k cat ≈ 20 vs 349 L min –1 g surface metal –1 ). X-ray photoelectron spectroscopy (XPS) and density functional theory (DFT) calculations showed that Pd gained electron density from Ni, correlating to the increased nitrate reduction activity. Ammonium byproduct selectivity for InPdNi/AC (18% at 50% nitrate conversion) was lower compared to that of InPd/AC (48%), suggestive of the higher surface coverage of NO or its greater reactivity with NO 2 – , which led to more N 2 . Accounting for the catalyst precursor, manufacturing costs, and spent metal recovery, we calculated that Ni incorporation lowered the net catalyst cost significantly (from $\$$1028/kg to $\$$170/kg). The trimetallic composition lowered, by ∼26 times, the catalyst cost of a stirred tank reactor sized to the same treatment capacity as that for the bimetallic case. In conclusion, the results demonstrate that the partial replacement of the precious metal with an earth-abundant one leads to a higher efficiency and lower cost denitrification catalyst, via a material strategy that should be beneficial for other clean-water catalytic systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The LSST AGN Data Challenge: Selection Methods

Abstract Development of the Rubin Observatory Legacy Survey of Space and Time (LSST) includes a series of Data Challenges (DCs) arranged by various LSST Scientific Collaborations that are taking place during the project's preoperational phase. The AGN Science Collaboration Data Challenge (AGNSC-DC) is a partial prototype of the expected LSST data on active galactic nuclei (AGNs), aimed at validating machine learning approaches for AGN selection and characterization in large surveys like LSST. The AGNSC-DC took place in 2021, focusing on accuracy, robustness, and scalability. The training and the blinded data sets were constructed to mimic the future LSST release catalogs using the data from the Sloan Digital Sky Survey Stripe 82 region and the XMM-Newton Large Scale Structure Survey region. Data features were divided into astrometry, photometry, color, morphology, redshift, and class label with the addition of variability features and images. We present the results of four submitted solutions to DCs using both classical and machine learning methods. We systematically test the performance of supervised models (support vector machine, random forest, extreme gradient boosting, artificial neural network, convolutional neural network) and unsupervised ones (deep embedding clustering) when applied to the problem of classifying/clustering sources as stars, galaxies, or AGNs. We obtained classification accuracy of 97.5% for supervised models and clustering accuracy of 96.0% for unsupervised ones and 95.0% with a classic approach for a blinded data set. We find that variability features significantly improve the accuracy of the trained models, and correlation analysis among different bands enables a fast and inexpensive first-order selection of quasar candidates.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

A variable high-order shock-capturing finite difference method with GP-WENO

Here, we present a new finite difference shock-capturing scheme for hyperbolic equations on static uniform grids. The method provides selectable high-order accuracy by employing a kernel-based Gaussian Process (GP) data prediction method which is an extension of the GP high-order method originally introduced in a finite volume framework by the same authors. The method interpolates Riemann states to high order, replacing the conventional polynomial interpolations with polynomial-free GP-based interpolations. For shocks and discontinuities, this GP interpolation scheme uses a nonlinear shock handling strategy similar to Weighted Essentially Non-Oscillatory (WENO), with a novelty consisting in the fact that nonlinear smoothness indicators are formulated in terms of the Gaussian likelihood of the local stencil data, replacing the conventional L 2 -type smoothness indicators of the original WENO method. We demonstrate that these GP-based smoothness indicators play a key role in the new algorithm, providing significant improvements in delivering high – and selectable – order accuracy in smooth flows, while successfully delivering non-oscillatory solution behavior in discontinuous flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗