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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Numerical algorithms for water waves with background flow over obstacles and topography

Abstract We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiply connected fluid domain that includes stationary obstacles and variable bottom topography. One approach is formulated in terms of the surface velocity potential while the other evolves the vortex sheet strength. Both methods employ layer potentials in the form of periodized Cauchy integrals to compute the normal velocity of the free surface, are compatible with arbitrary parameterizations of the free surface and boundaries, and allow for circulation around each obstacle, which leads to multiple-valued velocity potentials but single-valued stream functions. We prove that the resulting second-kind Fredholm integral equations are invertible, possibly after a physically motivated finite-rank correction. In an angle-arclength setting, we show how to avoid curve reconstruction errors that are incompatible with spatial periodicity. We use the proposed methods to study gravity-capillary waves generated by flow around several elliptical obstacles above a flat or variable bottom boundary. In each case, the free surface eventually self-intersects in a splash singularity or collides with a boundary. We also show how to evaluate the velocity and pressure with spectral accuracy throughout the fluid, including near the free surface and solid boundaries. To assess the accuracy of the time evolution, we monitor energy conservation and the decay of Fourier modes and compare the numerical results of the two methods to each other. We implement several solvers for the discretized linear systems and compare their performance. The fastest approach employs a graphics processing unit (GPU) to construct the matrices and carry out iterations of the generalized minimal residual method (GMRES).

Ambrose, David M.↗
DOE OSTI2024

Numerical analysis of a time discretized method for nonlinear filtering problem with Lévy process observations

Abstract In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is an unnormalized probability density function of the filter solution. Then, we apply a splitting-up technique to decompose the Zakai equation into three stochastic differential equations, based on which we construct a splitting-up approximate solution and prove its half-order convergence. Furthermore, we apply a finite difference method to construct a time semi-discrete approximate solution to the splitting-up system and prove its half-order convergence to the exact solution of the Zakai equation. Finally, we present some numerical experiments to demonstrate the theoretical analysis.

Mathematics↗
DOE OSTI2020

An Efficient Numerical Algorithm for Solving Data Driven Feedback Control Problems

The goal of this paper is to solve a class of stochastic optimal control problems numerically, in which the state process is governed by an Itô type stochastic differential equation with control process entering both in the drift and the diffusion, and is observed partially. The optimal control of feedback form is determined based on the available observational data. In this work, we call this type of control problems the data driven feedback control. The computational framework that we introduce to solve such type of problems aims to find the best estimate for the optimal control as a conditional expectation given the observational information. To make our method feasible in providing timely feedback to the controlled system from data, we develop an efficient stochastic optimization algorithm to implement our computational framework.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Numerical Simulation and Experimental Investigation of Nitrogen Transfer Mechanism from Gas to Liquid Steel During Pressurized Electroslag Remelting Process

Since the gas–slag–metal three-phase transfer mechanism of nitrogen is not suitable to account for the nitrogen pickup during pressurized electroslag remelting process, the laboratory experiments have been carried out to study the transfer mechanism of nitrogen using different nitrogen partial pressures and electrode immersion depths. Then, two possible transfer mechanisms of nitrogen have been proposed, and a 2D transient numerical model has been developed to investigate the behavior of nitrogen based on the new proposed mechanisms. The simulated results are compared with the experiment to validate the feasibility of new proposed mechanism. The results show that the nitrogen content in ingot increases with the increasing nitrogen partial pressure and decreasing electrode immersion depth. At the current experimental condition, the electrode immersion depth seems to play a more important role in the nitrogen pickup than the nitrogen partial pressure. Due to the limits of thermodynamic and kinetic conditions, the nitrogen pickup is negligible via the transfer from gas to liquid metal through molten slag whether nitrogen chemically or physically dissolves into slag. The mechanism that nitrogen directly reacts with the partially exposed liquid metal film under the electrode tip due to the fluctuation of gas/slag interface could reasonably account for the experimental results. Furthermore, based on the mechanism, the predicted variation tendency of nitrogen content in ingot is in agreement with the experiment.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Numerical and experimental investigation of the geometry dependent layer-wise evolution of temperature during laser powder bed fusion of Ti–6Al–4V

Abstract Laser powder bed fusion (L-PBF) is currently the additive manufacturing process with the widest industrial use for metal parts. Yet some hurdles persist on the way to a widespread industrial serial production, with reproducibility of the process and the resulting part properties being a major concern. As the geometry changes, so do the local boundary conditions for heat dissipation. Consequently, the use of global, geometry-independent processing parameters, which are today’s state of the art, may result in varying part properties or even defects. This paper presents a numerical simulation as a method to predict the geometry-dependent temperature evolution during the build. For demonstration, an overhang structure with varying angles towards the build platform was manufactured using Ti–6Al–4V. A calibrated infrared camera was integrated into a commercial L-PBF system to measure the temperature evolution over time for a total build height of 10 mm, and the results are used for validation of the simulation. It is shown that the simulation is capable of predicting the temperature between layers. The deviations between simulation and measurement remain in single digit range for smaller overhang structures (90°, 60° and 45°). For large overhang structures (30°), the simulation tends to over-predict the temperatures up to 15 °C. Experiments with varying process parameters showed the feasibility of energy reduction as compensation of the heat accumulation produced by overhang structures.

Li, Gefei (ORCID:0000000174837952)↗
DOE OSTI2022

Sensitivity Analysis for Solutions to Heterogeneous Nonlocal Systems. Theoretical and Numerical Studies

The paper presents a collection of results on continuous dependence for solutions to nonlocal problems under perturbations of data and system parameters. The integral operators appearing in the systems capture interactions via heterogeneous kernels that exhibit different types of weak singularities, space dependence, even regions of zero-interaction. Here, the stability results showcase explicit bounds involving the measure of the domain and of the interaction collar size, nonlocal Poincaré constant, and other parameters. In the nonlinear setting, the bounds quantify in different L p norms the sensitivity of solutions under different nonlinearity profiles. The results are validated by numerical simulations showcasing discontinuous solutions, varying horizons of interactions, and symmetric and heterogeneous kernels.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Theory and numerics of subspace approximation of eigenvalue problems

Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to mitigate the computational burden associated with high-fidelity systems. Furthermore, we provide general error estimates under non-simple eigenvalue conditions, establishing some theoretical foundations for understanding the convergence behavior of subspace approximations. Numerical examples, including problems with one-dimensional to three-dimensional spatial domain and one-dimensional to two-dimensional parameter domain, are presented to demonstrate the efficacy of reduced basis method in handling parametric variations in boundary conditions and coefficient fields to achieve significant computational savings while maintaining high accuracy, making them promising tools for practical applications in large-scale eigenvalue computations.

Eigenvalue problems↗
DOE OSTI2024

Numerical investigation of equivalence ratio effects on Flex-Fuel mixing controlled combustion enabled by prechamber ignition

There is interest in adapting renewable and low-carbon intensity fuels to heavy-duty engines to help displace criteria and greenhouse gas emissions associated with diesel combustion. Low-carbon fuels have inherently low cetane numbers and thus pose a significant challenge when considering direct substitution in diesel combustion systems. Use of an actively fueled prechamber as an ignition source to initiate mixing-controlled combustion (PC-MCC) of low-cetane fuels is becoming an attractive combustion mode to alleviate the identified reactivity deficit. This work focuses on the utilization of an active prechamber to facilitate diesel-like combustion of bioethanol-gasoline fuel blends in a heavy-duty engine. Recent results in this emerging technology suggest that ignition quality is uniquely coupled to prechamber equivalence ratio. In this numerical study, the fundamental implications of prechamber equivalence ratio on the ignition performance of direct injected fuels ranging from E10 to E100 are investigated using CONVERGE. Parametric studies of the prechamber operating strategy were assessed at diesel-like conditions to characterize the performance trends relative to a diesel baseline at the same boundary conditions. Simulation results indicate that PC-MCC is flex-fuel capable and achieves diesel-like ignition qualities and combustion processes for all fuels considered under stoichiometric and rich prechamber conditions. To characterize the equivalence ratio trends observed, a novel inflow boundary modeling technique was utilized to prescribe turbulent jets in place of the prechamber where selective speciation of the jet composition was conducted to isolate the ignition contributions of radical and reacting species in lean, stoichiometric, and rich jets. The inflow boundary modeling suggests that excess fuel and combustion intermediates present in jets produced from stratified and fuel-rich prechamber operation promotes higher jet temperatures and as such are superior ignition sources. Relative to a lean prechamber jet, the peak temperature of a reacting jet from a rich prechamber was up to 600 K hotter at fixed distances from the orifice exit. Furthermore, radicals also demonstrated an influence on the ignition process, but the combustion mode was identified to be thermally dominant.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2022

ARPIST: Provably accurate and stable numerical integration over spherical triangles

Numerical integration on spherical triangles, including the computation of their areas, is a core computation in geomathematics. The commonly used techniques sometimes suffer from instabilities and significant loss of accuracy. We describe a new algorithm, called ARPIST, for accurate and stable integration of functions on spherical triangles. ARPIST is based on an easy-to-implement transformation to the spherical triangle from its corresponding linear triangle via radial projection to achieve high accuracy and efficiency. More importantly, ARPIST overcomes potential instabilities in computing the Jacobian of the transformation, even for poorly shaped triangles that may occur at poles in regular longitude-latitude meshes, by avoiding potential catastrophic rounding errors. We compare our proposed technique with L’Huilier’s Theorem for computing the area of spherical triangles, and also compare it with the recently developed LSQST method (Beckmann et al., 2014) and a radial-basis-function-based technique (Reeger and Fornberg, 2016) for integration of smooth functions on spherical triangulations. In conclusion, our results show that ARPIST enables better or comparable accuracy over previous methods while being easier to implement, significantly faster, and more tolerant of poor element shapes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Numerical investigation of thermomechanical response of multiscale porous Ultra-High Temperature Ceramics

Recent advances in Ultra-High Temperature Ceramics (UHTC) manufacturing have permitted the development of multiscale porous UHTC microstructures. Within the target application of hypersonic vehicles, dense UHTCs are suitable for thermal protection on leading edges, whereas porous UHTCs may find a role in providing thermally insulated interfaces for temperature-sensitive interior components. Designing vehicles incorporating porous UHTCs requires a characterization of their thermomechanical properties across the full range of expected operating temperatures spanning –20 °C–2500 °C. This research represents a preliminary study in performing this characterization. Several numerical experiments are performed using a coupled thermomechanical implementation of the Material Point Method to determine the temperature dependence of effective material properties both with and without damage. Furthermore, complex time-dependent boundary conditions derived from known hypersonic flight profiles are simulated in order to probe the various couplings between deformation, damage and heat transfer. It is shown that the model reveals the importance of micro-buckling in determining effective material stiffness and thermal conductivity.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Scaled boundary cubature scheme for numerical integration over planar regions with affine and curved boundaries

This paper introduces the scaled boundary cubature (SBC) scheme for accurate and efficient integration of functions over polygons and two-dimensional regions bounded by parametric curves. Over two-dimensional domains, the SBC method reduces integration over a region bounded by m curves to integration over m regions (referred to as curved triangular regions), where each region is bounded by two line segments and a curve. With proper (counterclockwise) orientation of the boundary curves, the scheme is applicable to convex and nonconvex domains. Additionally, for star-convex domains, a tensor-product cubature rule with positive weights and integration points in the interior of the domain is obtained. If the integrand is homogeneous, we show that this new method reduces to the homogeneous numerical integration scheme; however, the SBC scheme is more versatile since it is equally applicable to both homogeneous and non-homogeneous functions. This paper also introduces several methods for smoothing integrands with point singularities and near-singularities. When these methods are used, highly efficient integration of weakly singular functions is realized. Finally, the SBC method is applied to a number of benchmark problems, which reveal its broad applicability and superior performance (in terms of time to generate a rule and accuracy per cubature point) when compared to existing methods for integration.

42 ENGINEERING↗
DOE OSTI2025

A comparative study of calibration techniques for finite strain elastoplasticity: Numerically-exact sensitivities for FEMU and VFM

Accurate identification of material parameters is crucial for predictive modeling in computational mechanics. Here, the two primary approaches in the experimental mechanics community for calibration from full-field digital image correlation data are known as finite element model updating (FEMU) and the virtual fields method (VFM). In VFM, the objective function is a squared mismatch between internal and external virtual work or power. In FEMU, the objective function quantifies the weighted mismatch between model predictions and corresponding experimentally measured quantities of interest. It is minimized by iteratively updating the parameters of an FE model. While FEMU is seen as more flexible, VFM is commonly used instead of FEMU due to its considerably greater computational expense. However, comparisons between the two methods usually involve approximations of gradients or sensitivities with finite difference schemes, thereby making direct assessments difficult. Hence, in this study, we compare VFM and FEMU in the context of numerically-exact sensitivities obtained through local sensitivity analyses and the application of automatic differentiation software. To this end, we conduct a series of test cases to assess both methods under practical challenges using a finite strain elastoplasticity model.

Automatic differentiation↗
DOE OSTI2020

A direct numerical simulation of Jet A flame kernel quenching

The safe operation of aeronautical engines requires an understanding of flame ignition, propagation and extinction. In this study, direct numerical simulations are performed using a 29 species reduced chemical mechanism for jet fuel surrogate Jet A to understand the flame quenching process. Here, initially laminar spherical flames of varying sizes and equivalence ratios are subject to an identical periodic domain of decaying and isotropic high intensity turbulence with a turbulent Reynolds number of 2400. All cases become quenched, except for the larger kernel with lower Karlovitz number. An analysis of the flame structure shows broadened preheat zone, flame shortening on the product side, differential species diffusion and partial fuel pyrolysis in the fresh mixture. Two extinction mechanisms are identified arising from flame shortening and high flame stretch. Flame shortening occurs due to turbulence-chemistry interactions that resemble the flame–flame interaction in a laminar counterflow reactant-to-reactant configuration, which contorts and breaks up the ignition kernel. Flame stretch is a local effect that attenuates the heat release rate and causes the flame to retreat towards the product mixtures, similar to what has been observed for reactant-to-product laminar counterflow flames. Chemical explosive mode analysis was also performed to quantify the flame structure and local combustion mode. The diffusion–reaction balance in pinched-off flame islands favors extinction of these smaller structures, while auto-ignition modes are observed within the flame kernel after fresh mixture is engulfed and preheated in the product kernel. Statistics of the density-weighted displacement speed conditional on local combustion mode indicates strong correlation between the local extinction mode and negative displacement speed. The local balance between diffusion and reaction ultimately determines the propensity for local extinction in both laminar and turbulent flames, the extent of which has an impact on global flame propagation.

42 ENGINEERING↗
DOE OSTI2022

A direct numerical simulation study of the dilution tolerance of propane combustion under spark-ignition engine conditions

Modern spark ignition internal combustion (IC) engines rely on highly diluted fuel-air mixtures to achieve high brake thermal efficiencies. To support this, new engine designs have introduced high stroke-to-bore ratios and cylinder head designs that promote high tumble flow and turbulence intensities. However, mixture dilution through exhaust gas recirculation (EGR) is limited by combustion instabilities manifested in the form of cycle-to-cycle variability. Propane has been observed to have superior EGR dilution tolerance than gasoline, which makes it a very competitive low-carbon fuel for the new IC engines without sacrificing efficiency. Two-dimensional direct numerical simulations (DNS) are performed with detailed chemistry to study and contrast the effect of turbulence intensity and dilution on propane and iso-octane premixed flames at high pressure conditions similar to those in-cylinder. A new reduced mechanism for propane consisting of 53 transported species and 17 quasi-steady state species is developed based on a previously published mechanism and used in these simulations. Three levels of turbulence intensity and two levels of exhaust gas dilution are chosen based on conditions relevant to IC engine operation. The DNS results are analyzed based on the evolution of the flame surface area and the statistics of its driving terms, which are found to be similar for both fuels when there is no dilution but considerably different under high dilution. The analysis of the DNS data provides fundamental insights into the underlying mechanisms for improved stability under dilution.

42 ENGINEERING↗
DOE OSTI2023

Direct numerical simulation of a turbulent methane/air flame impinged by a sub-breakdown electric field

Here, the effects of an external electric field on a turbulent methane/air diffusion flame are analyzed in this work using direct numerical simulations. The analyzed configuration consists of a temporally evolving mixing layer of air and a mixture of methane and nitrogen at 1 atm that is impinged by an electric field in the direction normal to the mean mixing plane. The combustion and chemi-ionization reactions involved in the flow are modeled using finite-rate chemistry and a reduced reaction scheme consisting of 26 species and 134 reactions. The mass diffusion and ion-wind effects are modeled using a detailed description of the diffusion coefficients and electric mobilities based on kinetic theory. The presented calculations show that the turbulence generated within the mixing layer is mostly unaffected by the applied electric field for the configuration under exam. In fact, the electric body force is developed away from the mixing region where the flow is uniform. Conversely, the turbulence is able to introduce very high intermittency in the electrically charged species concentration and, consequently, in the electric body force. Such intermittency will constitute a challenge in the future formulation of combustion models that take into account ion-wind effects.

09 BIOMASS FUELS↗
DOE OSTI2024

Direct numerical simulations of turbulent premixed cool flames: Global and local flame dynamics analysis

The cool flame dynamics, especially in turbulent flows, is of great interest for both practical application and fundamental research. Here, in this study, a series of direct numerical simulations of turbulent premixed n-C 7 H 16 /O 2 /O 3 /N 2 cool flames are performed, with the focus on the influence of turbulence intensity (u'/S L , where S L is the laminar flame speed) on the flame structure as well as the global and local cool flame dynamics. It is found that the cool flame front is considerably wrinkled by turbulence at high u'/S L , leading to significantly thickened turbulent cool flame brush and largely altered local reactivity compared with the reference laminar flame. However, the turbulent flame structure in the temperature space is found to be insensitive to u'/S L . Besides, with increasing u'/S L , the normalized turbulent cool flame speed (S L /S L ) is monotonically increased, attributed to substantial augmentation on the flame surface area (A T /A L ), while the stretching factor (I 0 ) remains almost constant and is smaller than 1. The underlying mechanisms for such variations are revealed through local flame dynamics analysis. Specifically, the local flame displacement speed S d is found to be strongly negatively correlated with flame curvature; meanwhile, such negative correlation and the probability distribution function (PDF) of flame curvature are barely influenced by u'/S L , leading to a weak dependence of I 0 on u'/S L . In contrast, the PDF of the tangential strain rate is found to span a much wider range and shift to the positive side as u'/S L increases, suggesting that the enhanced tangential strain rate is the main cause for the increase in surface area of the turbulent premixed cool flame. Finally, the influence of equivalence ratio on above findings is found to be insignificant, indicating that although the local reactivity of turbulent premixed cool flames is altered due to the differential diffusion, the resultant flame- stretch interaction is insensitive to the equivalence ratio. This study presents some unique cool flame dynamics that are distinct from hot flames, which can help improve the understanding and modeling of turbulent cool flames.

Cool flames↗
DOE OSTI2025

Numerical framework for integrated additive manufacturing-compression molding (AM-CM) of thermoplastic composites

Additive manufacturing-compression molding (AM-CM) has emerged as a transformative technology in advanced composite manufacturing. Additive manufacturing (AM) offers high design flexibility and the ability to produce complex geometries with precisely aligned fibers in the preferred orientation. Compression molding (CM) enhances composite materials by providing excellent dimensional stability, reduced porosity, high production rates, and a smooth surface finish. Despite these advantages, extensive integrated analysis is required to optimize processing conditions for improved fiber orientation distribution (FOD) and porosity control. Here, this study develops a comprehensive numerical model to simulate the AM-CM manufacturing process. The model isolates the effects of both the AM and CM phases while also capturing their integration. Additionally, it accounts for heat transfer, temperature-dependent viscosity, and fiber orientation in the extruded fiber-filled polymer, accurately representing material behavior during processing. This approach enables the analysis of interactions between deposited beads of complex strand shapes and their interface regions after full compression. Moreover, the model predicts key parameters such as polymer flowability, fiber orientation, and temperature evolution in AM-CM parts. By optimizing processing conditions, it facilitates a controlled and predictable microstructure.

36 MATERIALS SCIENCE↗
DOE OSTI2022

An efficient high-order numerical solver for diffusion equations with strong anisotropy

In this paper, we present an interior penalty discontinuous Galerkin finite element scheme for solving diffusion problems with strong anisotropy arising in magnetized plasmas for fusion applications. Additionally, we demonstrate the accuracy produced by the high-order scheme and develop an efficient preconditioning technique to solve the corresponding linear system, which is robust to the mesh size and anisotropy of the problem. Several numerical tests are provided to validate the accuracy and efficiency of the proposed algorithm.

97 MATHEMATICS AND COMPUTING↗