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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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NASA NTRS1988

Thermoviscoplastic model with application to copper

A viscoplastic model is developed which is applicable to anisothermal, cyclic, and multiaxial loading conditions. Three internal state variables are used in the model; one to account for kinematic effects, and the other two to account for isotropic effects. One of the isotropic variables is a measure of yield strength, while the other is a measure of limit strength. Each internal state variable evolves through a process of competition between strain hardening and recovery. There is no explicit coupling between dynamic and thermal recovery in any evolutionary equation, which is a useful simplification in the development of the model. The thermodynamic condition of intrinsic dissipation constrains the thermal recovery function of the model. Application of the model is made to copper, and cyclic experiments under isothermal, thermomechanical, and nonproportional loading conditions are considered. Correlations and predictions of the model are representative of observed material behavior.

Freed, Alan D.↗

DOE OSTI2026

Dispersive and nondispersive 𝐾-matrix formalisms

The modeling of coupled-channel effects has become increasingly important due to the availability of highly precise data for a large variety of hadronic (re)scattering processes. The 𝐾-matrix is a powerful, yet comparatively simple, method to describe scattering amplitudes, including coupled-channel effects, with the aim of interpreting experimental data. Throughout the literature, a range of dispersive and nondispersive 𝐾-matrix methods are employed. Here, we compare the dispersive and nondispersive formulations in the context of the N/D method. It is shown that the methods are equivalent in the physical region under 𝐾-matrix reparametrization. Differences away from the physical region are examined. Applications to synthetic data are used to illustrate the effects of model choices concerning form factors and the application of dispersion relations, with the goal of clarifying best practices. We find no clear preference with regard to dispersive modeling. In contrast, we find that interpretational ambiguity of the bare model parameters—and even of the form of the bare model—is endemic, and recommend a thorough sampling of data and model spaces to assess conclusion robustness.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

Development of Critical Experiments to Benchmark Moderator Temperature Reactivity Worth

The simulation of nuclear reactors requires being able to accurately model several different interrelated physical processes including neutronics, heat production, fluid/thermal physics, structural mechanics, fuel behavior, chemistry, and balance-of-plant. In order to design and use new types of nuclear reactors, modern codes have been developed which couple together the behavior of these different physical models to accurately consider the feedback effects between different physical effects. The SHARP toolset, part of the Nuclear Energy Advanced Modeling and Simulation (NEAMS) project, is an example of an effort to combine models of neutronics, thermal-hydraulics, and structural mechanics in a coupled simulation to model any type of nuclear reactor as accurately as possible. The validation of multi-physics coupling techniques requires new experimental benchmark experiments specifically designed for that purpose. As a preliminary step towards design of these experiments, a series of measurements have been performed to demonstrate the temperature-dependent neutronic behavior of a well-characterized reactor assembly for comparison with the available codes. The facility adopted for these experiments is Walthousen Reactor Critical Facility (RCF) at Rensselaer Polytechnic Institute (RPI). The RCF is unique in several aspects and provides several advantages to this type of experiment. Built in 1954 by the American Locomotive Company (ALCO), the RCF has been used to design small compact reactors. RPI acquired the facility in 1963, and the highly-enriched uranium fuel was later swapped for low-enriched fuel pins that were excess from the SPERT facility experiments. Nowadays, The RCF is regarded as a teaching and research facility, permitting the training of licensed Senior Reactor Operators, and offering a critical experiments laboratory course to students. The reactor core standard configuration consists of 332 or 333 UO{sub 2} fuel pins, containing a total of 35.2 grams of U- 235 each (4.81 % enriched). The pins are arranged in a regular lattice with a pitch of 1.6256 cm. The number and configuration of these pins are flexible, and the reactor's overall thermal power is limited to no more than 15 W. As the low thermal output of the reactor does not induce any measurable temperature changes, the effect of temperature in the reactor is observed by applying two 18- kW electric heaters to the water moderator, with mechanical agitators to maintain uniformity in moderator temperature. Before beginning experiments, each fuel pin inside the core was surveyed for mechanical defects (bending or warping) that may contribute to uncertainty in core behavior. Every fuel pin has been individually removed from the core and checked for any irregularities on its surface (caused by shocks or usage). About 12 % of the 333 pins were found to have a small degree of warping and were replaced with excess pins available in the facility. In doing this, we made sure all the pins are identical, thereby increasing the accuracy of future models. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2019

Close-contact melting on an isothermal surface with the inclusion of non-Newtonian effects

The present study deals with a theoretical investigation of a close-contact melting (CCM) process involving a vertical cylinder on a horizontal isothermal surface, where the liquid phase is a non-Newtonian viscoplastic fluid that behaves according to the Bingham model. Accordingly, a new approach is formulated based on the thin layer approximation and different quasi-steady process assumptions. By analytical derivation, an algebraic equation that relates the molten layer thickness and the solid bulk height is developed. The problem is then solved numerically, coupled with another equation for the melting rate. The new model shows that as the yield stress increases the melting rate decreases and the molten layer thickness increases. It is found that under certain conditions, the model can be reduced to a form that allows an analytical solution. The approximate model predicts an exponential dependence of both the melt fraction and the molten layer thickness. Comparison between the numerical and analytical solutions shows that the analytical approximation provides an excellent estimation for sufficiently large values of the yield stress. Dimensional analysis, which is supported by the analytical model results, reveals the dimensionless groups that govern the problem. For the general case, the melt fraction is a function of two dimensionless groups. For the analytical approximation, it is shown that the melt fraction is governed by a single dimensionless group and that the molten layer thickness is governed by two dimensionless groups.

Mechanics↗

NASA NTRS1992

Computational simulation of coupled material degradation processes for probabilistic lifetime strength of aerospace materials

The research included ongoing development of methodology that provides probabilistic lifetime strength of aerospace materials via computational simulation. A probabilistic material strength degradation model, in the form of a randomized multifactor interaction equation, is postulated for strength degradation of structural components of aerospace propulsion systems subjected to a number of effects or primative variables. These primative variable may include high temperature, fatigue or creep. In most cases, strength is reduced as a result of the action of a variable. This multifactor interaction strength degradation equation has been randomized and is included in the computer program, PROMISS. Also included in the research is the development of methodology to calibrate the above described constitutive equation using actual experimental materials data together with linear regression of that data, thereby predicting values for the empirical material constraints for each effect or primative variable. This regression methodology is included in the computer program, PROMISC. Actual experimental materials data were obtained from the open literature for materials typically of interest to those studying aerospace propulsion system components. Material data for Inconel 718 was analyzed using the developed methodology.

Boyce, Lola↗

NASA NTRSDate not supplied

Pushing the Limits of Aquatic Remote Sensing: Synthetic Data and Deep Learning for Fast Inverse Emulation of A Coupled Ocean-Atmosphere Radiative Transfer Model

The inversion of electromagnetic information to physical and biological properties of the water column is a notoriously difficult problem, yet fundamental to our ability of understanding aquatic processes on large time and space scales. There is now a growing necessity to develop pragmatic approaches that allow timely and effective extrapolation of local processes, to spatially resolved global products, and to promote operational and sustainable resource policy management. This presentation will discuss research integrating advanced biological and radiative modeling, high-end computation, and machine learning to develop a portable global processor for simultaneous retrieval of atmosphere and water optics for diverse aquatic systems from the open and coastal ocean to optically extreme inland waters and harmful algal blooms. We will discuss some of the basic concepts behind the forward modeling approach including DEAP, the novel Distributed Equivalent Algal Populations model, for developing large spectral libraries of aquatic particle optics to aid in our ability to distinguish phytoplankton functional types (PFTs) and inorganic material, as well as other factors which enable comprehensive modeling from the benthos to top-of-atmosphere (TOA). This information is being used to understand how we can leverage next-generation deep learning methods for maximum information retrieval and rapid image processing, while also providing capabilities to identify minimum sensor spectral requirements necessary for certain aquatic applications. Further, I will touch on how we envision this research to enable the aquatic community for science discovery and how we are moving closer towards the capability for high-fidelity global analysis of aquatic ecosystems.

Jeremy Alan Kravitz↗

DOE OSTI2014

New production mechanism for keV sterile neutrino Dark Matter by decays of frozen-in scalars

We propose a new production mechanism for keV sterile neutrino Dark Matter. In our setting, we assume the existence of a scalar singlet particle which never entered thermal equilibrium in the early Universe, since it only couples to the Standard Model fields by a really small Higgs portal interaction. For suitable values of this coupling, the scalar can undergo the so-called freeze-in process, and in this way be efficiently produced in the early Universe. These scalars can then decay into keV sterile neutrinos and produce the correct Dark Matter abundance. While similar settings in which the scalar does enter thermal equilibrium and then freezes out have been studied previously, the mechanism proposed here is new and represents a versatile extension of the known case. We perform a detailed numerical calculation of the DM production using a set of coupled Boltzmann equations, and we illustrate the successful regions in the parameter space. Our production mechanism notably can even work in models where active-sterile mixing is completely absent.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

A mechanistic model for creep and thermal aging in Alloy 709

This report describes a physics-based model for creep and thermal aging in Alloy 709. Alloy 709 is an advanced austenitic alloy, targeted for use in future Sodium Fast Reactors (SFRs) and other advanced reactors. The material has superior high temperature properties compared to currently qualified 316 and 304 stainless steels. However, the available creep and thermal aging test database for Alloy 709 is significantly more limited compared to the historical materials. The physics-based model developed here is one way to accelerate the qualification of the material by providing more accurate long-term predictions for creep properties and thermal aging, compared to current empirical time-extrapolate techniques. The crystal plasticity finite element model is used to predict the deformation and failure of alloy 709. The same setup for the CPFE model is used in both the baseline model calibration process and the simulation campaigns for parameter inference. Specific constitutive choices are made for Alloy 709 to capture the primary deformation mechanisms. The dislocation creep formulation developed by Hu and Cocks is extended to account for coupled precipitation formation and the grain boundary cavitation model developed by Sham, Needleman, et al. is used to model grain boundary cavitation-induced failure. A novel update algorithm is proposed to render the semi-discrete constitutive update for the Sham-Needleman model unconditionally stable. A progressive calibration approach is adopted based on the observations that several types of material responses can be effectively decoupled. A surrogate model is trained based on full-fledged CPFE simulations to accelerate the forward model evaluations, and stochastic variational inference (SVI) is used to calibrate the unknown microstructural model parameters. The calibrated mechanistic model is used to predict the long-term creep life of Alloy 709, and the predictions are compared against classical empirical approaches.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Model-independent tuning for maximizing free electron laser pulse energy

The output power of a free electron laser (FEL) has extremely high variance even when all FEL parameter set points are held constant because of the stochastic nature of the self-amplified spontaneous emission (SASE) FEL process, drift of thousands of coupled parameters, such as thermal drifts, and uncertainty and time variation of the electron distribution coming off of the photo cathode and entering the accelerator. In this work, we demonstrate the application of automatic, model-independent feedback for the maximization of average pulse energy of the light produced by free electron lasers. We present experimental results from both the European x-ray free electron laser at DESY and from the Linac Coherent Light Source at SLAC. We demonstrate application of the technique on rf systems for automatically adjusting the longitudinal phase space of the beam, for adjusting the phase shifter gaps between the undulators, and for adjusting steering magnets between undulator sections to maximize the FEL output power. We show that we can tune up to 105 components simultaneously based only on noisy average bunch energy measurements.

47 OTHER INSTRUMENTATION↗

DOE OSTI2015

WE-AB-303-09: Rapid Projection Computations for On-Board Digital Tomosynthesis in Radiation Therapy

Purpose: To facilitate fast and accurate iterative volumetric image reconstruction from limited-angle on-board projections. Methods: Intrafraction motion hinders the clinical applicability of modern radiotherapy techniques, such as lung stereotactic body radiation therapy (SBRT). The LIVE system may impact clinical practice by recovering volumetric information via Digital Tomosynthesis (DTS), thus entailing low time and radiation dose for image acquisition during treatment. The DTS is estimated as a deformation of prior CT via iterative registration with on-board images; this shifts the challenge to the computational domain, owing largely to repeated projection computations across iterations. We address this issue by composing efficient digital projection operators from their constituent parts. This allows us to separate the static (projection geometry) and dynamic (volume/image data) parts of projection operations by means of pre-computations, enabling fast on-board processing, while also relaxing constraints on underlying numerical models (e.g. regridding interpolation kernels). Further decoupling the projectors into simpler ones ensures the incurred memory overhead remains low, within the capacity of a single GPU. These operators depend only on the treatment plan and may be reused across iterations and patients. The dynamic processing load is kept to a minimum and maps well to the GPU computational model. Results: We have integrated efficient, pre-computable modules for volumetric ray-casting and FDK-based back-projection with the LIVE processing pipeline. Our results show a 60x acceleration of the DTS computations, compared to the previous version, using a single GPU; presently, reconstruction is attained within a couple of minutes. The present implementation allows for significant flexibility in terms of the numerical and operational projection model; we are investigating the benefit of further optimizations and accurate digital projection sub-kernels. Conclusion: Composable projection operators constitute a versatile research tool which can greatly accelerate iterative registration algorithms and may be conducive to the clinical applicability of LIVE. National Institutes of Health Grant No. R01-CA184173; GPU donation by NVIDIA Corporation.

60 APPLIED LIFE SCIENCES↗

NASA NTRS2023

Modulation of the Seasonal Cycle of the Antarctic Sea Ice Extent By Sea Ice Processes and Feedbacks With the Ocean and the Atmosphere

The seasonal cycle of the Antarctic sea ice extent is strongly asymmetric, with a relatively slow increase after the summer minimum followed by a more rapid decrease after the winter maximum. This cycle is intimately linked to the seasonal cycle of the insolation received at the top of the atmosphere, but sea ice processes as well as the exchanges with the atmosphere and ocean may also play a role. To quantify these contributions, a series of idealized sensitivity experiments have been performed with an eddy-permitting (∘) NEMO-LIM3 (Nucleus for European Modelling of the Ocean–Louvain-la-Neuve sea ice model version 3) Southern Ocean configuration, including a representation of ice shelf cavities, in which the model was either driven by an atmospheric reanalysis or coupled to the COSMO-CLM2 regional atmospheric model. In those experiments, sea ice thermodynamics and dynamics as well as the exchanges with the ocean and atmosphere are strongly perturbed. This perturbation is achieved by modifying snow and ice thermal conductivities, the vertical mixing in the ocean top layers, the effect of freshwater uptake and release upon sea ice growth and melt, ice dynamics, and surface albedo. We find that the evolution of sea ice extent during the ice advance season is largely independent of the direct effect of the perturbation and appears thus mainly controlled by initial state in summer and subsequent insolation changes. In contrast, the melting rate varies strongly between the experiments during the retreat, in particular if the surface albedo or sea ice transport are modified, demonstrating a strong contribution of those elements to the evolution of ice coverage through spring and summer. As with the advance phase, the retreat is also influenced by conditions at the beginning of the melt season in September. Atmospheric feedbacks enhance the model winter ice extent response to any of the perturbed processes, and the enhancement is strongest when the albedo is modified. The response of sea ice volume and extent to changes in entrainment of subsurface warm waters to the ocean surface is also greatly amplified by the coupling with the atmosphere.

regional atmosphere ocean sea ice model↗

DOE OSTI2023

Measurement of the properties of Higgs boson production at $\sqrt{s}$ = 13 TeV in the H → γγ channel using 139 fb -1 of pp collision data with the ATLAS experiment

Measurements of Higgs boson production cross-sections are carried out in the diphoton decay channel using 139 fb -1 of pp collision data at $\sqrt{s}$ = 13 TeV collected by the ATLAS experiment at the LHC. The analysis is based on the definition of 101 distinct signal regions using machine-learning techniques. The inclusive Higgs boson signal strength in the diphoton channel is measured to be $1.04^{+0.10}_{-0.09}$. Cross-sections for gluon-gluon fusion, vector-boson fusion, associated production with a W or Z boson, and top associated production processes are reported. An upper limit of 10 times the Standard Model prediction is set for the associated production process of a Higgs boson with a single top quark, which has a unique sensitivity to the sign of the top quark Yukawa coupling. Higgs boson production is further characterized through measurements of Simplified Template Cross-Sections (STXS). In total, cross-sections of 28 STXS regions are measured. The measured STXS cross-sections are compatible with their Standard Model predictions, with a p-value of 93%. The measurements are also used to set constraints on Higgs boson coupling strengths, as well as on new interactions beyond the Standard Model in an effective field theory approach. No significant deviations from the Standard Model predictions are observed in these measurements, which provide significant sensitivity improvements compared to the previous ATLAS results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

A Large Eddy Simulation Study of Flow Turbulence, Alumina Transport, and Bath Temperature Evolution in Conventional Aluminum-Smelting Cell Using OpenFOAM

In this study, a Large Eddy Simulation (LES) of the aluminum-smelting process is performed using OpenFOAM. To understand the coupled behavior of heat transfer, mass transfer, and flow of the smelting process, a multi-physics computational fluid dynamics (CFD) model based on the Eulerian–Eulerian multi-fluid approach is adopted. The model accounts for CO 2 bubble and magnetohydrodynamics (MHD)-driven flow, along with alumina dissolution, transport, and bath temperature evolution. The simulation predictions show small-scale turbulent vortical structures in the anode–cathode space caused by combined effect of MHD and CO 2 bubble-bath interactions and relatively large-scale asymmetric vortices in the inter-anode space caused by the CO 2 bubble-bath interactions. The vortex formation at the edges of the anodes evidently aids in transporting alumina from the central channel to the bottom of the anodes and prevents accumulation of gas bubbles in the periphery of the anode bottom. Symmetric bath cold spots are observed in the vicinity of the feeder. Cold spots are also observed in the anode–cathode distance space below the anode bottom due to the transport of undissolved solid to this region by the flow. The findings from the work are useful in developing and designing alumina-feeding strategy leading to reduced anode effects and smooth operation of the cell. The work also highlights the important flow structures in conventional aluminum-smelting cell.

36 MATERIALS SCIENCE↗

DOE OSTI2013

Stochastic joint inversion of hydrogeophysical data for salt tracer test monitoring and hydraulic conductivity imaging

The assessment of hydraulic conductivity of heterogeneous aquifers is a difficult task using traditional hydrogeological methods (e.g., steady state or transient pumping tests) due to their low spatial resolution. Geophysical measurements performed at the ground surface and in boreholes provide additional information for increasing the resolution and accuracy of the inverted hydraulic conductivity field. We used a stochastic joint inversion of Direct Current (DC) resistivity and Self-Potential (SP) data plus in situ measurement of the salinity in a downstream well during a synthetic salt tracer experiment to reconstruct the hydraulic conductivity field between two wells. The pilot point parameterization was used to avoid over-parameterization of the inverse problem. Bounds on the model parameters were used to promote a consistent Markov chain Monte Carlo sampling of the model parameters. To evaluate the effectiveness of the joint inversion process, we compared 8 cases in which the geophysical data are coupled or not to the in situ sampling of the salinity to map the hydraulic conductivity. We first tested the effectiveness of the inversion of each type of data alone (concentration sampling, self-potential, and DC resistivity), and then we combined the data two by two. We finally combined all the data together to show the value of each type of geophysical data in the joint inversion process because of their different sensitivity map. We also investigated a case in which the data were contaminated with noise and the variogram unknown and inverted stochastically. The results of the inversion revealed that incorporating the self-potential data improves the estimate of hydraulic conductivity field especially when the self-potential data were combined to the salt concentration measurement in the second well or to the time-lapse cross-well electrical resistivity data. Various tests were also performed to quantify the uncertainty in the inverted hydraulic conductivity field.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2019

Approaches to multi-scale analyses of mechanically and thermally-driven migration of fluid inclusions in salt rocks

Fluid inclusions are found within mineral crystals or along grain boundaries in many sedimentary rocks, notably in evaporite formations, and can migrate along a thermal or hydro-mechanical gradient. Shale and salt rocks have been considered potential host rocks for radioactive waste disposal, due to their low permeability. Previously stagnant inclusions may become mobilised by a perturbation of the in situ state by a geotechnical installation or the emplacement of heat-generating waste. Here, the migration of fluid inclusions can thus have important impacts on the long-term performance of a geologic repository for high-level radioactive waste disposal. As a part of the international research project DECOVALEX-2019, two aspects of fluid inclusion migration in rock salt are currently investigated under different boundary conditions: a) altered hydro-mechanical conditions as a consequence of tunnel excavation or borehole drilling and b) coupled thermo-hydro-mechanical-chemical conditions during the heating period of the post-closure phase of a repository.

58 GEOSCIENCES↗

DOE OSTI2025

Modeling Framework to Predict Melting Dynamics at Microstructural Defects in TNT-HMX High Explosive Composites

Many high explosive (HE) formulations are composite materials whose microstructure is understood to impact functional characteristics. Interfaces are known to mediate the formation of hot spots that control their safety and initiation. Here, to study such processes at molecular scales, we developed all-atom force fields (FFs) for Octol, a prototypical HE formulation comprised of TNT (2,4,6-trinitrotoluene) and HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine). We extended a FF for TNT and recasted it in a form that can be readily combined with a well-established FF for HMX. The resulting FF was extensively validated against experimental results and density functional theory calculations. We applied the new combined TNT-HMX FF to predict and rank surface and interface energies, which indicate that there is an energetic driver for coarsening of microstructural grains in TNT-HMX composites. Finally, we assess the impact of several microstructural environments on the dynamic melting of TNT crystal under ultrafast thermal loading. We find that both free surfaces and planar material interfaces are effective nucleation points for TNT melting. However, MD simulations show that TNT crystal is prone to superheating by at least 50 K on subnanosecond time scales and that the degree of superheating is inversely correlated with surface and interface energy. The modeling framework presented here will enable future studies on hot spot formation processes in accident scenarios that are governed by strong coupling between microstructural interfaces, material mechanics, momentum and energy transport, phase transitions, and chemistry.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Evaluation of Flow Routing on the Unstructured Voronoi Meshes in Earth System Modeling

Flow routing is a fundamental process of Earth System Models' (ESMs) river component. Traditional flow routing models rely on Cartesian rectangular meshes, which exhibit limitations, particularly when coupled with unstructured mesh-based ocean components. They also lack the support for regionally refined models. While previous studies have highlighted the potential benefits of unstructured meshes for flow routing, their widespread application and comprehensive evaluation within ESMs remain limited. This study extends the river component of the Energy Exascale Earth System Model to unstructured Voronoi meshes. We evaluated the model's performance in simulating river discharge and water depth across three watersheds spanning the Arctic, temperate, and tropical regions. The results show that while providing several benefits, unstructured mesh-based flow routing can achieve comparable performance to structured mesh-based routing, and their difference is often less than 10%. Although the unstructured mesh-based method could address several existing limitations, this research also shows that additional improvements in the numerical method are needed to fully exploit the advantages of unstructured mesh for hydrologic and ESMs.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

A new approach for simulating inhomogeneous chemical kinetics

Abstract In this paper, inhomogeneous chemical kinetics are simulated by describing the concentrations of interacting chemical species by a linear expansion of basis functions in such a manner that the coupled reaction and diffusion processes are propagated through time efficiently by tailor-made numerical methods. The approach is illustrated through modelling $$\alpha$$ α - and $$\gamma$$ γ -radiolysis in thin layers of water and at their solid interfaces from the start of the chemical phase until equilibrium was established. The method’s efficiency is such that hundreds of such systems can be modelled in a few hours using a single core of a typical laptop, allowing the investigation of the effects of the underlying parameter space. Illustrative calculations showing the effects of changing dose-rate and water-layer thickness are presented. Other simulations are presented which show the approach’s capability to solve problems with spherical symmetry (an approximation to an isolated radiolytic spur), where the hollowing out of an initial Gaussian distribution is observed, in line with previous calculations. These illustrative simulations show the generality and the computational efficiency of this approach to solving reaction-diffusion problems. Furthermore, these example simulations illustrate the method’s suitability for simulating solid-fluid interfaces, which have received a lot of experimental attention in contrast to the lack of computational studies.

97 MATHEMATICS AND COMPUTING↗