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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Automated and efficient local adaptive regression for principal component-based reduced-order modeling of turbulent reacting flows

Principal Component Analysis can be used to reduce the cost of Computational Fluid Dynamics simulations of turbulent reacting flows by reducing the dimensionality of the transported variables through projection of the thermochemical state onto a lower-dimensional manifold. However, because of the nonlinearity of the principal component source terms, nonlinear regression techniques must be utilized for the source terms in terms of the principal components. Unfortunately, widely available and utilized nonlinear regression techniques can have prohibitive computational requirements and/or accuracy that is highly dependent on user experience in ad hoc tuning of model architecture and hyperparameters. Here, in this work, a new nonlinear regression approach is proposed that is both computationally efficient and automated so does not require any user input. The approach is evaluated through a priori prediction of principal component source terms using data from a Direct Numerical Simulation of a turbulent nonpremixed n-heptane/air jet flame. In particular, the proposed framework consists of local regressions whose complexity is adapted according to the local nonlinearity of the data: local linear regression when accurate enough and local Artificial Neural Networks when nonlinear regression is required. The number of local clusters for local regression is determined automatically using the Davies-Bouldin index. In addition, Bayesian optimization is utilized for model training (i.e., to select the best architectures and hyperparameters of the nonlinear regressions in an unsupervised fashion), eliminating ad hoc hand-tuning and/or expensive grid searches. Overall, compared to a single, global neural network, the new local adaptive regression approach is shown to have comparable accuracy but 69% less training time due to the utilization of local linear regression and faster training of local neural networks.

42 ENGINEERING↗
DOE OSTI2020

A crisis for the verification and validation of turbulence simulations

Three algorithms have been proposed for solution of the Rayleigh–Taylor turbulent mixing problem. They are based upon three different physical principles governing the Euler equations for fluid flow. The principles serve to select the physically relevant solution from among many nonunique solutions. The admissibility principle is in dispute. The three different algorithms, expressing the three physical admissibility principles can be formulated in terms of the three energy dissipation rates or the entropy production rates, as selected by the size of the sub grid scale coefficients. These have maximal values or less than maximal values. The resulting solutions are markedly different. We find strong validation evidence that supports the maximum rate principle, based on a review of prior results and on new results presented here. We review experimental data used for validation and sufficient to discriminate among the three. We present a new analysis of this data. We show that the hypothesized long wave length perturbations in the initial conditions are not significant, so that validation can be based on this data in a straight forward manner. One of the algorithms is labeled direct numerical simulation, but is not, and as a consequence, the two algorithms with less than maximal SGS coefficients are variants of one another. Finally recommendations for the numerical modeling of the deflagration to detonation transition in type Ia supernova are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Effects of thermophoresis on high-pressure binary-species boundary layers with uniform and non-uniform compositions

Direct numerical simulations of high-pressure binary-species temporal boundary layers are performed to investigate the flow physics for three situations: (1) uniform and equal composition, (2) uniform but unequal compositions and (3) non-uniform composition. Both colder- and hotter-wall situations compared with the free stream are simulated. The working fluid is a nitrogen/methane mixture. The analysis is performed at a case-specific self-similar state. Even when the initial composition is uniform, the methane mean mass fraction decreases near the colder wall, whereas it increases near the hotter wall and the mass fraction fluctuates in the entire boundary layer. Analysis of the species-mass diffusion balance and flow structures reveal that both mass-fraction variation and fluctuations are induced by the Soret effect. When the initial composition is non-uniform and the wall is colder, the methane mean mass fraction monotonically increases from the wall akin to its initial profile. However, when the wall is hotter the mean mass fraction decreases near the wall in contrast to its initial profile, a fact traced through the species-mass diffusion balance to the Soret effect being large and enriching methane near the wall. In contrast, the direction of the Soret flux is opposite for the colder wall, thus keeping the methane concentration small. Although the initial magnitude of the difference between the wall and free-stream temperature is the same in all cases, the situation is not symmetric between colder- and hotter-wall cases; the flow structure exhibits much smaller scales when the wall is hotter than when the wall is colder.

Mechanics↗
DOE OSTI2025

Beehive haloscope for high-mass axion dark matter

We propose a new haloscope geometry that can arbitrarily increase the resonator volume for a given target axion mass. This geometry consists of closely packed, overlapping coaxial cavities operating as a single resonator. While the resonant frequency is still determined by the dimensions of the individual “cells,” the strong interactions between the cells encourage the entire “beehive” to oscillate in phase, a phenomenon expected of tightly coupled harmonic oscillators. This synchronization behavior allows the construction of a singly connected large volume resonator at high frequency by simply increasing the number of the cells. Using direct numerical simulations, we verify the existence of a global eigenmode that has a high (40%) form factor in a 169-element beehive resonator. The resonant frequency of the eigenmode is tunable by moving the center rods laterally in unison. The form factor is very tolerant to dimensional deviations and misalignment as a result of mode hybridization due to strong coupling. The beehive haloscope inherits many appealing properties from the conventional coaxial cavity: a high quality factor, compatibility with a solenoid magnet, and ease of fabrication, tuning, and coupling. We argue that this geometry is an excellent candidate for high-mass axion searches covering the post-inflationary parameter space (>5 GHz).

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Microstructural and infiltration properties of woven preforms during chemical vapor infiltration

Interface-resolved direct numerical simulations (DNSs) of chemical vapor infiltration (CVI) have been performed over a range of furnace-operating conditions (Thiele moduli) and for practical woven preform geometries. A level-set method is used to resolve the geometry of the initial preform at tow scale. The interface between the vapor and solid phase is then evolved in time through the entire CVI densification cycle, fully resolving the time-varying topology between the two phases. In contrast to previous level-set methods for CVI simulation, the physical reaction and diffusion processes govern the level-set movement in the current approach. The surface deposition kinetics is described by the usual one-step model. In this paper, the DNS data are used to study the evolving porosity, surface-to-volume ratio, and flow infiltration properties (permeability and effective diffusivities). Additionally, comparisons are made to popularly-assumed structure functions and the standard, Kozeny–Carmen porous media model commonly employed in modeled CFD simulations of CVI. The virtual DNS experiments reveal a Thiele modulus and preform geometry (fabric layup) dependence which the existing microstructural and infiltration models are not able to describe throughout the entire densification process. The DNS-based, woven geometry-specific correlations can be applied directly to mean-field, furnace-scale CFD simulations.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Machine-Learned Manifold-Based Models for Large Eddy Simulation of Turbulent Combustion

Reduced-order manifold combustion models are commonly used to lower the cost of reacting Large Eddy Simulations (LES) and may be derived either from physical principles as in flamelet models or from data-driven methods like Principal Component Analysis (PCA). In either case, neural networks are increasingly used as part of these models to provide a nonlinear mapping between a small set of pre-defined variables that parameterize the manifold and outputs of interest, such as reaction rates. In this work, we propose a new manifold-based modeling approach that combines the definition of the manifold-parameterizing variables (linear combinations of species), the nonlinear mapping to the outputs, and closure of filtered quantities for LES into the structure of a single neural network. This allows the process used to train the neural network to simultaneously optimize both the functional form of the model and the identities of the inputs to the model. The new approach can flexibly incorporate thermochemical data from any combustion system; if trained on data from 1D flames it can be interpreted as an optimized flamelet model, but it can also be used to learn models from data from more complex configurations. This work presents a priori evaluations of the new approach in both contexts. Evaluation using data from 1D premixed flames demonstrates the physical interpretability of the manifold variables generated by the new approach. Evaluation using data from direct numerical simulations of turbulent flames shows improved predictions relative to either flamelet or PCA-based models in a more complex configuration.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

Taking control of compressible modes: bulk viscosity and the turbulent dynamo

Many polyatomic astrophysical plasmas are compressible and out of chemical and thermal equilibrium, introducing a bulk viscosity into the plasma via the internal degrees of freedom of the molecular composition, directly impacting the decay of compressible modes, $\mathrm{{\boldsymbol {\mathit {v}}}}_{\parallel }(\boldsymbol {k})$. This is especially important for small-scale, turbulent dynamo processes in the interstellar medium (ISM), which are known to be sensitive to the effects of compression. To control the viscous properties of $\mathrm{{\boldsymbol {\mathit {v}}}}_{\parallel }(\boldsymbol {k})$, we perform trans-sonic, visco-resistive dynamo simulations with additional bulk viscosity $\nu _{\text{bulk}}$, deriving a new $\nu _{\text{bulk}}$ Reynolds number $\text{Re}_{\text{bulk}}$, and viscous Prandtl number $\text{P}\nu \equiv \text{Re}_{\text{bulk}}/ \text{Re}_{\text{shear}}$, where $\text{Re}_{\text{shear}}$ is the shear viscosity Reynolds number. We derive a framework for decomposing $E_{\rm mag}$ growth rates into incompressible and compressible terms via orthogonal tensor decompositions of $\boldsymbol {\nabla }\otimes \mathrm{{\boldsymbol {\mathit {v}}}}$, where $\mathrm{{\boldsymbol {\mathit {v}}}}$ is the fluid velocity. We find that $\mathrm{{\boldsymbol {\mathit {v}}}}_{\parallel }(\boldsymbol {k})$ play a dual role, growing and decaying $E_{\rm mag}$, and that field-line stretching is the main driver of growth, even in compressible dynamos. In the absence of $\nu _{\text{bulk}}$ ($\text{P}\nu \rightarrow \infty$), $\mathrm{{\boldsymbol {\mathit {v}}}}_{\parallel }(\boldsymbol {k})$ pile up on small-scales, creating a spectral bottleneck, which disappears for $\text{P}\nu \approx 1$. As $\text{P}\nu$ decreases, $\mathrm{{\boldsymbol {\mathit {v}}}}_{\parallel }(\boldsymbol {k})$ are dissipated at increasingly larger scales, in turn suppressing incompressible modes through a coupling between high-k modes. We emphasize the importance of further understanding the role of $\nu _{\text{bulk}}$ in compressible astrophysical plasmas, which we estimate could be as strong as the shear viscosity in the cold ISM, and highlight that compressible direct numerical simulations without bulk viscosity have unresolved compressible mode dissipation scales.

MHD↗
DOE OSTI2022

Co-optimized machine-learned manifold models for large eddy simulation of turbulent combustion

Many modeling approaches in large eddy simulation (LES) of turbulent combustion employ a projection of the thermochemical state onto a low-dimensional manifold within state space to reduce the number of transported variables and hence computational cost. Flamelet-generated manifolds (FGM) is an example of a well-established, physics-based approach, but increasingly, principal component analysis (PCA) is being used as a data-driven method for generating manifold models. For both approaches, the nonlinear relationship between the location on the predefined manifold and the outputs of interest, such as reaction rates, can be tabulated or encoded in a neural network. This work proposes a new approach for manifold modeling that extends these existing approaches. A modified neural network structure simultaneously encodes the definition of the manifold variables, the nonlinear mapping, and the subfilter closure for LES. This allows all three of these aspects of the model to be co-optimized, generating a model from any source of combustion thermochemical state data. The manifold parameterizing variables are constrained to be linear combinations of species, as in FGM and PCA-based models, to aid in interpretability and implementation. For LES, subfilter variances of the manifold variables are also included as inputs. Two types of a priori analysis are performed to evaluate the new approach. In the first, the model is trained on data from one-dimensional premixed flames. In this case, the approach recovers the behavior of flamelet-based manifold approaches, and in fact slightly improves performance by identifying an optimized progress variable. The approach is also applied to data from direct numerical simulations of spherical ignition kernels in isotropic turbulence. For any specified manifold dimensionality, the new approach provides substantially lower prediction errors than a PCA-based model developed from the same data set. Additionally, the LES formulation of the new approach can provide accurate predictions for filtered reaction rates across a variety of filter widths.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Numerical and boundary condition effects on the prediction of detonation engine behavior using detailed numerical simulations

High-fidelity numerical simulations of an experimental rotating detonation engine with discrete fuel/air injection were conducted. A series of configurations with different feed-plenum pressures but with constant equivalence ratio were studied. Detailed chemical kinetics for the hydrogen/air system is used. A resolution study for the full rotating detonation engine (RDE) system simulation is also conducted. Two kinds of boundary conditions, a total pressure boundary and a constant mass flow rate boundary, are used to assess the effects of the inlet boundary. As mass flow rate is increased, the total pressure boundary causes more error in the axial pressure distribution while the constant mass flow rate gives a better solution for all cases ran. The simulations confirm experimental findings, and reproduce qualitative as well as some of the quantitative trends. These results demonstrate that a) fuel-air mixing is highly non-uniform within the detonation chamber, leading to variations in local equivalence ratio, b) the fuel and oxidizer injectors experience significant backflow as the detonation wave passes over, but recover at different rates which further augments the inefficiencies in mixing, and c) parasitic combustion in the mixing region makes the detonation wave weak by extending the reaction zone across the wave.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2025

A discontinuous Galerkin spectral element method for compressible reacting flows

High-order methods have recently been shown to be an effective tool for high-fidelity flow computations like direct numerical simulations and large-eddy simulations because of their strong balance between accuracy and computational cost. In this work, a high-order discontinuous Galerkin spectral element method (DGSEM) is developed to solve the chemically reacting Navier-Stokes equations. To handle the disparate length and time scales associated with these equations, we develop a novel method which combines the spectral accuracy of the SEM with the flexibility of the DG approach. The framework, implemented in the spectral element code Nek5000, is well suited to capture turbulence in smooth regions of the flow, while maintaining numerical stability in the presence of shocks. An entropy-residual based artificial viscosity is added to smooth shocked regions of flow, and a positivity-preserving limiter is implemented to suppress non-physical oscillations. These enhancements support the numerical stability of the hydrodynamic sub-step, which is decoupled from the chemistry integration through a second-order operator splitting method. Here, a series of smooth and discontinuous validation cases are presented in increasing physical and computational complexity for both inviscid and viscous flows. In particular, simulations of canonical one-dimensional and two-dimensional detonations are performed, and the high-order numerical results are validated against available literature data. Additional validation studies are carried out for classical three-dimensional numerical simulations of incompressible and compressible turbulent flows.

Compressible reacting flows↗
DOE OSTI2025

Turbulent burning velocity of lean premixed hydrogen/air flames at engine conditions: Effects of turbulence intensity and length scale

For turbulent lean premixed hydrogen flames with strong thermodiffusively instabilities, most previous studies have focused on the influence of turbulence intensity, whereas the role of turbulence length scale is less well understood. Here, this study addresses this gap by conducting direct numerical simulations (DNS) of statistically planar turbulent premixed flames for a lean (ϕ=0.35) hydrogen/air mixture under independently varied turbulence intensity (u') and length scale (l T ) at engine-relevant thermodynamics conditions. Results show that as u' increases, the flame front becomes increasingly wrinkled, forming smaller cellular structures. In contrast, l T variations do not significantly alter the size of these structures. For the turbulent burning velocity (S T ), the normalized S T (i.e., S T /S L , where S L is the laminar flame speed) increases linearly with u', driven by both enhanced flame surface wrinkling (i.e., increased A T /A L ) and enhanced local burning rate (i.e., increased I 0 ). However, increasing l T reduces I 0 , despite a continued increase in A T /A L , resulting in only a marginal increase in S T /S L . To reveal the underlying mechanisms, especially the decreasing trend of I 0 with l T , local flame dynamics analyses are performed. It is found that as l T increases, the interaction between thermodiffusive effects and turbulence weakens due to the reduced tangential strain rate, while the flame curvature remains largely unchanged. This suppresses local reactivity enhancement and thus decreases I 0 , In contrast, an increase in u' enhances the interaction by amplifying both curvature fluctuation and tangential strain rate, leading to increased local reactivity (increased I 0 ). Finally, based on the DNS data, several new scaling models are proposed for the three global properties, S T /S L , A T /A L , and I 0 , and showed improvements compared to existing models. These findings provide new insights into the flame-turbulence interactions in thermodiffusively unstable hydrogen flames. The DNS dataset is also useful for the development of turbulent combustion models applicable to practical engine simulations.

Engine-relevant condition↗
DOE OSTI2020

HTR solver: An open-source exascale-oriented task-based multi-GPU high-order code for hypersonic aerothermodynamics

In this study, the open-source Hypersonics Task-based Research (HTR) solver for hypersonic aerothermodynamics is described. The physical formulation of the code includes thermochemical effects induced by high temperatures (vibrational excitation and chemical dissociation). The HTR solver uses high-order TENO-based spatial discretization on structured grids and efficient time integrators for stiff systems, is highly scalable in GPU-based supercomputers as a result of its implementation in the Regent/Legion stack, and is designed for direct numerical simulations of canonical hypersonic flows at high Reynolds numbers. Additionally, the performance of the HTR solver is tested with benchmark cases including inviscid vortex advection, low- and high-speed laminar boundary layers, inviscid one-dimensional compressible flows in shock tubes, supersonic turbulent channel flows, and hypersonic transitional boundary layers of both calorically perfect gases and dissociating air.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

HTR-1.3 solver: Predicting electrified combustion using the hypersonic task-based research solver

Here this manuscript presents an updated open-source version of the Hypersonics Task-based Research (HTR) solver. The solver, whose main features are presented in Di Renzo et al. (2020) and Di Renzo & Pirozzoli (2021), is designed for direct numerical simulation of reacting flows at high Reynolds numbers. This new version extends the applications of the HTR solver to turbulent combustion in the presence of external electric fields. In particular, a new distributed Poisson solver compatible with heterogeneous architectures has been incorporated in the algorithm to compute the electric potential distribution in bi-periodic configurations. The drift fluxes of the electrically charged species are now included in the transport equations using a targeted essentially non-oscillatory scheme. A verification of these new features of the solver is provided using one-dimensional burner stabilized flames, whereas a three dimensional turbulent flame is utilized to discuss the scalability of the proposed numerical tool.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Effective kinetics driven by dynamic concentration gradients under coupled transport and reaction

Biogeochemical reaction kinetics are generally established from batch reactors where concentrations are uniform. In natural systems, many biogeochemical processes are characterized by spatially and temporally variable concentration gradients that often occur at scales which are not resolved by field measurements or biogeochemical and reactive transport models. Yet, it is not clear how these sub-scale chemical gradients affect reaction kinetics compared to batch kinetics. Here we investigate this question by studying the paradigmatic case of localized pulses of solute reacting with a solid or a dissolved species in excess. Additionally, we consider non-linear biogeochemical reactions, representative of mineral dissolution, adsorption and redox reactions, which we quantify using simplified power-law kinetics. The combined effect of diffusion and reaction leads to effective kinetics that differ quantitatively and qualitatively from the batch kinetics. Depending on the nonlinearity (reaction order) of the local kinetics, these effects lead to either enhancement or decrease of the overall reaction rate, and result in a rich variety of reaction dynamics. We derive analytical results for the effective kinetics, which are validated by comparison to direct numerical simulations for a broad range of Damköhler numbers and reaction order. Our findings provide new insights into the interpretation of imperfectly mixed lab experiments, the effective kinetics of field systems characterized by intermittent reactant release and the integration of sub-scale concentration gradients in reactive transport models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

CFD-DEM and PR-DNS studies of low-temperature densely packed beds

Over the past few decades, granular media is gaining attention as a viable option for heat transfer fluids (HTFs). Several research efforts are studying the use of particle-based heat transfer fluids in a wide variety of applications. With this motivation, the current work focusses on analyzing the different heat transfer mechanisms in low-temperature mono-sized densely packed granular media. To study the heat transfer behavior of granular media at different scales, the current work employs a two-way coupled computational strategy. The motion of particles is solved using the Discrete Element Method (DEM) and the interstitial air is solved using a Finite-Volume (CFD) approach. The Open-Source library CFDEM Coupling® is used in the current study to join the Finite Volume PISO solver of OpenFOAM® and the DEM solver of LIGGGHTS®. Typically, particle-particle contact conduction and particle-air convection are the most popular closure models. But recent research identified a different heat transfer phenomenon in packed beds that cannot be identified by conduction or convection models. While closure models were developed to implement this on a CFD-DEM framework, they did not capture the effect of intra-particulate thermal gradients on this phenomenon. Hence the current work also employs Particle-Resolved Direct Numerical Simulations (PR-DNS) to gain valuable insights allowing for the modification of existing models. A new closure model is then proposed here and is implemented in the CFD-DEM framework. This model provides key insights into the different heat transfer mechanism of packed beds.

42 ENGINEERING↗
DOE OSTI2020

Multiscale formulation of frictional contact mechanics at the pore scale

Direct numerical simulation (DNS) yields the highest fidelity predictions of mechanical deformation at the pore scale, but is prohibitively expensive for analyzing large or many samples. Discrete element methods (DEM) are an efficient alternative, but are limited to granular media and incapable of estimating or controlling prediction errors. We present a pore-level multiscale method (PLMM) that approximates DNS efficiently and with controllable accuracy. We focus on the linear elastic response of a consolidated geologic porous medium with arbitrary microstructure, heterogeneous mineralogy, containing cracks or defects. PLMM decomposes the solid phase into non-overlapping subdomains, on which local basis functions are constructed. The bases are then coupled with a global interface problem that accounts for slip or stick contact conditions between the subdomains. PLMM produces an initial, but accurate, approximation to DNS that can be iteratively improved. It is amenable to parallelism and allows for different mesh, models, and physics in each subdomain. An algebraic interpretation of PLMM as a preconditioner is also presented to allow non-intrusive implementation into existing solvers. Lastly, this work extends previous developments of PLMM in fluid dynamics to solid mechanics and enables future extensions towards modeling coupled flow and mechanics problems.

42 ENGINEERING↗
DOE OSTI2021

Explicit physics-informed neural networks for nonlinear closure: The case of transport in tissues

In upscaling methods, closures for nonlinear problems present a well-known challenge. While a number of theoretical methods have been proposed for handling such closures, nonlinearities still remain a significant obstacle for many problems. In this work, we use a combination of formal upscaling and data-driven machine learning for explicitly closing a nonlinear transport and reaction process in multiscale tissues. The classical effectiveness factor model is used to formulate the macroscale reaction kinetics. We train a multilayer perceptron network using training data generated by direct numerical simulations over microscale examples. Once trained, the network is used in an algorithm for numerically solving the upscaled (coarse-grained) differential equation describing mass transport and reaction in two example tissues. The network is described as being explicit in the sense that the network is trained using macroscale concentrations and gradients of concentration as components of the feature space rather than incorporating them as part of a constraint in the optimization process. Network training and solutions to the macroscale transport equations were computed for two different tissues. The two tissue types (brain and liver) exhibit markedly different geometrical complexity and spatial scale (cell size and sample size). The upscaled solutions for the average concentration are compared with numerical solutions derived from the microscale concentration fields by a posteriori averaging. There are three outcomes of this work of particular note. 1) Our overall approach results in an upscaled nonlinear PDE. The PDE is closed using a neural network, and our approach results in the definition of the classical effectiveness factor for effecting closure. 2) We identify particular source terms for the closure problem that are important for representing the structure of the closure. These source terms involve macroscale concentrations and their gradients. We adopt these source terms to use as explicit features in the learning algorithm. We find the trained networks that include the macroscale source terms generate models that are able to predict the correction factor with increased fidelity over those that do not. 3) We find that the trained network exhibits good generalizability, and it is able to predict the effectiveness factor with high fidelity for realistically-structured tissues despite the significantly different scale and geometrical complexity of the two example tissue types. This latter result emphasizes our purposeful connection between conventional averaging methods with the use of machine learning for closure; this contrasts with some machine learning methods for upscaling where the exact form of the macroscale equation remains unknown.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Dynamic calibration of differential equations using machine learning, with application to turbulence models

We present a methodology for calibration of parametric ordinary and partial differential equation models, using off-the-shelf software for back-propagation in Neural Networks (NN). As a prototypical example, we consider calibration of a Reynolds-averaged Navier-Stokes (RANS) turbulence closure model, against ground truth data from direct numerical simulations (DNS) of two different turbulent flows. Numerical time integration is represented as a custom NN, where only the RANS model parameters are trainable. A loss function is defined to quantify the mismatch between the NN prediction and the ground truth over a predefined, finite time integration window. This loss function is then minimized using a gradient descent method utilizing the back-propagation algorithm. Furthermore, this dynamic approach to training is to be contrasted with a static approach, wherein a least square regression estimate for parameters is obtained in the limit of an infinitesimal time integration window. In a first test of static and dynamic approaches against ground truth data generated by the model, the former proves to be significantly faster and more accurate than the latter at recovering the parameters. When both calibration approaches are tested against DNS data, for which it is known that the model cannot achieve a perfect fit, the static approach yields a good prediction only for short times, while the dynamic approach results in physical and stable predictions over the entire integration window. After optimization of the dynamic approach for time step, spatial resolution, stability, and physics-based constraints, we obtain a 50% improvement of outcomes over those obtained from the existing, manually calibrated set of parameters, demonstrating the merits of this systematic and automated procedure.

97 MATHEMATICS AND COMPUTING↗