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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

The impact of capillary heterogeneity on CO 2 flow and trapping across scales

Capillary heterogeneity has been identified over the last decade as a key control on subsurface CO 2 flow behavior during geological CO 2 sequestration. These heterogeneities can be formed in all sedimentary rocks, ranging from slight variations in the sand grain sizes to extensive sequences of interbedded sands, shales, and limestones. Capillary heterogeneity has been largely, although not entirely, overlooked in subsurface flow modeling because it is assumed to only directly influence fluid redistribution over scales of centimeters to meters. However, even small-scale fluid movements can result in dramatic impacts on the mobility and trapping of the CO 2 over kilometers. Therefore, neglecting capillary heterogeneity at multiple scales could potentially lead to errors in modeling and predicting field-scale plume migration. In this review paper, we aim to provide a consistent overview to (1) establish that capillary heterogeneity can have a major impact on CO 2 plume migration, (2) establish the respective length scales at which capillary heterogeneity matters, and (3) provide guidance for numerical modeling. This review covers pertinent literature and extracts key observations from the core to the field scales. Experimental studies have shown that millimeter-decimeter scale capillary heterogeneity can cause the so-called capillary heterogeneity trapping in addition to pore-scale residual trapping. Even at such a small scale, capillary heterogeneity can already lead to complex upscaled constitutive relationships, such as flow-rate dependent and anisotropic relative permeability, which affects field-scale CO 2 migration even when field-scale heterogeneities are present. Under gravity-dominated flow regimes, centimeter-meter scale capillary heterogeneity can entrap a significant amount of CO 2 at field scale, not just after imbibition but also during drainage. In certain cases, the presence of capillary heterogeneity can even completely stop the vertical movement of the CO 2 plume, hence greatly reducing leakage risks. At meter-kilometer scale, the influence of capillary heterogeneity is more pronounced and can hinder or redirect CO 2 migration in both lateral and vertical directions. The impact of capillary heterogeneity across multiple spatial scales poses a great challenge in modeling CO 2 migration at field scale, because it is practically impossible to build a field-scale earth model with grid blocks at millimeter scale. We recommend a hierarchical modeling approach to address this challenge. At field scale, earth models are built to capture geological features and heterogeneities in high but still practical grid resolutions. For each facies or rock type of the field-scale model, high- resolution meter-scale “conceptual” models are built with millimeter-scale grid blocks to capture representative fine-scale bedding geometries and heterogeneities in various environments of deposition, bridging the gap from subcore scale to the size of a field-scale simulation grid block. Upscaling is then used to preserve the smaller-scale flow dynamics of various rock types in field-scale simulations. Here, future work is needed to (1) refine, improve, and validate the hierarchical modeling approach; (2) build libraries of fine-scale bedding models for facies in various environments of deposition; (3) quantify multiscale capillary heterogeneity effects under subsurface uncertainties; (4) gain learning from different storage formations; and (5) establish best practices that balance accuracy and computational speed.

Capillary heterogeneity↗

DOE OSTI2025

Numerical simulation of flow and mixing in fracture intersections

Fluid transport through fractured geological formations is strongly influenced by the redistribution of solutes at fracture intersections. In this study, we perform detailed numerical simulations of flow and scalar transport within the intersection of two smooth, planar fractures. The analysis focuses on the mixing ratio, the proportion of solute flux exiting along the outlet branch aligned with the primary inlet flow direction, relative to the total solute flux at the outlets. We systematically investigate how the mixing ratio varies with four key parameters: Peclet number, Reynolds number, flow rate ratio between outlet branches, and fracture intersection angle. Results show that the mixing ratio decreases with increasing Peclet number and outlet flow rate ratio, consistent with reduced diffusive spreading and enhanced streamline routing. While low Reynolds numbers have minimal impact, inertial effects at higher Reynolds numbers significantly increase the mixing ratio. Additionally, acute and obtuse intersection angles alter flow partitioning and modify the solute distribution at the outlets. These findings provide a quantitative basis for incorporating physically realistic mixing behavior—intermediate between complete mixing and streamline-following assumptions—into network-scale transport models. The results have direct relevance to subsurface energy systems, including geothermal energy production, carbon sequestration, and contaminant remediation.

58 GEOSCIENCES↗

DOE OSTI2021

Heat transfer and pseudo phase transition for low-Reynolds, mixed-convection channel flow in the supercritical thermodynamic regime

Fluids at supercritical thermodynamic conditions are inherently complex due to the large variations in thermodynamic and transport properties. Multiple recent numerical and experimental investigations indicate ongoing interest for these fluids, especially supercritical CO and supercritical water, for a variety of applications. The potential heat transfer benefits in this regime are directly influenced by the extreme variations in thermodynamic and transport properties, which occur at, and above, the critical point. Limited studies have been conducted for low-Reynolds/intermediate-Rayleigh numbers mixed-convection channel flow of supercritical water, which is the focus of this study. To investigate the thermally driven hydrodynamic instabilities in this regime, we use a high-order fully-implicit numerical method. As expected, in this channel configuration and flow regime, a competition arises between the forced and the natural convection. Buoyancy, driven by the thermal gradient at the wall, pushes the fluid upwards in the channel, while inertial forces drive the fluid from inlet to outlet. We observe significant differences in the heat transfer coefficient between the top and bottom walls of the channel flow, due to natural convection, and unstable plumes. We further quantify the buoyancy forces along the channel flow through evaluation of the Richardson number. Simulations show that with a higher negative Richardson number, there are more unstable structures along the channel, resulting in enhanced mixing. Furthermore, we demonstrate the existence of gas-like, liquid-like, and the possibility of pseudo-two-phase regimes in the supercritical fluid. The pseudo-two-phase regime occurs when the range of fluid temperatures is crossing the pseudo-critical line, also known as the Widom line. The density of the fluid varies significantly near the Widom line, and further influences the natural convection and heat transfer in the flow.

42 ENGINEERING↗

DOE OSTI2023

Development of experimental and computational frameworks to predict subcooled flow boiling in the LANL Isotope Production Facility

Cooling is crucial to maintain the integrity of target systems in isotope production facilities. At Los Alamos National Laboratory (LANL)’s Isotope Production Facility (IPF), multiple encapsulated targets are stacked and irradiated in tandem with a 100 MeV, ~250μA proton beam. To facilitate effective heat removal, these stacked targets are separated and cooled via a series of water channels. At these beam currents, this high-energy proton beam heats the target system, likely initiating subcooled flow boiling in the cooling channels. However, in-beam monitoring of the IPF target system is not possible due to the extreme radiation environment, and the necessarily significant shielding. To better understand high-power target performance, we developed ex-situ experimental and computational frameworks to predict the behavior of subcooled flow boiling at IPF. Subcooled flow boiling experiments on Inconel 625 samples under IPF conditions (2 bar pressure, 10 GPM flow rate (i.e., 2249 kg/m 2 /s), 85 K subcooling) revealed that IPF's average operating power is at the early stage of boiling with a heat transfer coefficient of 48,000 W/m 2 /s. The proposed modeling framework enables us to predict a complete boiling curve, i.e., single-phase heat transfer, onset of nucleate boiling, two-phase heat transfer, and critical heat flux (CHF), with specification of input boiling parameters up to intermediate heat flux levels. The estimated CHF under IPF conditions is 5.2 MW/m 2 . Experimental data under reduced conditions (2 bar pressure, 1.5 GPM flow rate (i.e., 337 kg/m 2 /s), 45 K subcooling) served as validation cases for the computational modeling. This computational model can be further extended to more complicated systems replicating the real IPF configuration, for instance, to study void distribution as a function of the incident proton beam profile and coolant velocity profile of multiple cooling channels. Finally, the proposed experimental and computational frameworks provide a means to better understand cooling systems in the isotope production facilities at different accelerators, where in-beam monitoring of the cooling process is not available.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2022

A gradient-based deep neural network model for simulating multiphase flow in porous media

We report simulation of multiphase flow in porous media is crucial for the effective management of subsurface energy and environment-related activities. The numerical simulators used for modeling such processes rely on spatial and temporal discretization of the governing mass and energy balance partial-differential equations (PDEs) into algebraic systems via finite-difference/volume/element methods. These simulators usually require dedicated software development and maintenance, and suffer low efficiency from a runtime and memory standpoint for problems with multi-scale heterogeneity, coupled-physics processes or fluids with complex phase behavior. Therefore, developing cost-effective, data-driven models can become a practical choice, and in this work, we choose deep learning approaches as they can handle high dimensional data and accurately predict state variables with strong nonlinearity. In this paper, we describe a gradient-based deep neural network (GDNN) constrained by the physics related to multiphase flow in porous media. We tackle the nonlinearity of flow in porous media induced by rock heterogeneity, fluid properties, and fluid-rock interactions by decomposing the nonlinear PDEs into a dictionary of elementary differential operators. We use a combination of operators to handle rock spatial heterogeneity and fluid flow by advection. Since the augmented differential operators are inherently related to the physics of fluid flow, we treat them as first principles prior knowledge to regularize the GDNN training. We use the example of pressure management at geologic CO 2 storage sites, where CO 2 is injected in saline aquifers and brine is produced, and apply GDNN to construct a predictive model that is trained with physics-based simulation data and emulates the physics process. We demonstrate that GDNN can effectively predict the nonlinear patterns of subsurface responses, including the temporal and spatial evolution of the pressure and saturation plumes. We also successfully extend the GDNN to convolutional neural network (CNN), namely gradient-based CNN (GCNN), and validate its capability to improve the prediction accuracy. GDNN has great potential to tackle challenging problems that are governed by highly nonlinear physics and enable the development of data-driven models with higher fidelity.

42 ENGINEERING↗

DOE OSTI2021

Analytical modeling for redox flow battery design

Deeper market penetration of redox flow batteries requires optimization of the cell performance. Though important for optimization, detailed analytical solutions have not been developed for electrolyte flow, mass and charge transport, and reaction kinetics within redox flow batteries. To this end, here we present analytical solutions to active species concentration and over-potential based on advection-diffusion transport for ions and Bulter-Volmer model for interface reaction kinetics. The solutions were validated with results from a finite element model. These solutions were then applied to investigate the relationship between over-potential and state of charge, current density, reaction rate constant, flow velocity, diffusivity, total active species concentration, and electrode structure. Explicit formulas were identified for minimum activation over-potential and limiting current density as well as their dependence on electrolyte properties, operation conditions, and electrode structure. With our new mathematical formulas, this work provides a theoretical framework for flow battery design.

25 ENERGY STORAGE↗

DOE OSTI2023

Data-driven acoustic measurement of moisture content in flowing biomass

Measuring the moisture content in flowing biomass is critical to processes such as liquid biofuel conversion, such as biogasoline, biodiesel, bio jet kerosene, etc. However, biomass tends to flow in aggregates, which results in significant inhomogeneities in the amount of biomass flowing in front of a sensor at a given time, and there can be significant overlap in the material properties of dry vs wet biomass, leading to poor signal-to-noise ratio. We present a technique for identifying biomass moisture content using a series of acoustic pitch-catch measurements to quantify the sound speed and acoustic amplitude through the biomass, in conjunction with classical machine learning techniques, including Naive Bayes, Random Forest, and K-Nearest Neighbors classification. We amplify the differences between the acoustic measurements in different moisture levels by collecting a series of pulse-echo measurements, which we sort in order of ascending sound speed. We test the accuracy of the technique on experimentally-prepared batches of corn stover biomass with specified moisture levels and measure the average error in the estimated moisture level as a function of the number of pitch-catch measurements used. We observe average estimation errors as low as 6.7% by increasing the number of measurements and optimizing the hyperparameters. This work presents a novel method determining moisture content in flowing biomass with inhomogeneous flow. Additionally, this technique has application in optimizing biomass conversion processes, as well as other fields including, paper production, natural fiber processing, and mineral extraction.

09 BIOMASS FUELS↗

DOE OSTI2021

Experimental and computational investigation of interactive flow induced oscillations of two tandem rough cylinders at 3×10 4 ≤Re≤1.2×10 5

The interactive flow induced oscillations (FIO) of two adjacent, elastically mounted, rigid, tandem, locally-rough cylinders in transverse flow direction are analyzed utilizing two-dimensional Unsteady Reynolds-Averaged Navier-Stokes (2-D URANS) equations and verified experimentally in the proximity-wake region. Three sets of experiments and simulations (K = 600N/m, ζ = 0.14; K = 600N/m, ζ = 0.26; K = 1,200N/m, ζ = 0.26; K is spring stiffness, ζ is damping ratio) of two tandem cylinders with turbulence stimulation are tested and simulated for Reynolds number in the range of 30,000 = Re ≤ 120,000. The reduced velocity range is U* = 2.48–14.22, the mass ratio is m* = 1.343, and the center-to-center in-flow spacing to diameter ratio is d/D = 2.57. The characteristics of amplitude response, frequency response, lift force, and interactive wake patterns are presented and discussed. The trends of the amplitude and frequency responses from numerical simulations are in good agreement with experimental results. The main conclusions of Reynolds number effect on interactive flow induced oscillations are: (1) Five significant flow patterns between two tandem locally-rough cylinders for different Reynolds numbers are observed through analyzing the complex but stable interactions between vortices and cylinders. (2) In the initial and upper VIV branches, the downstream cylinder's FIO is seriously interfered by the wake of the upstream cylinder. (3) The downstream cylinder is strongly impinged by the vortices shed from the upstream cylinder resulting in nearly 180O out-of-phase oscillations in transition from VIV to galloping and in-phase oscillations in galloping.

42 ENGINEERING↗

DOE OSTI2022

Experimental characterization of extreme temperature granular flows for solar thermal energy transport and storage

High-temperature, dense granular flows along an inclined plane were considered for solar thermal energy transport and storage with sintered bauxite particles. A series of experiments was performed for particle inlet temperatures of ~ 200, 400, 600, and 800 °C to understand the mechanisms of granular flows at extreme temperatures. Mass flow rates were measured using a load cell and free-surface velocities were measured and computed using particle image velocimetry. Surface temperatures were measured using infrared cameras. A significant decrease in steady-state particle mass flow rate was observed with increasing temperature due to changing flow properties. A decrease in bulk particle free-surface velocities was observed at higher temperatures. Free-surface velocity measurement error between experiments were within 20% of the average. The particle surface temperatures decreased from inlet to outlet with larger gradients at higher temperatures observed due to increasing convection and radiative heat losses. Here, a decrease in temperature was observed along the side walls due to a decrease in particle velocities.

14 SOLAR ENERGY↗

DOE OSTI2023

The influence of temperature history and flow mixing on the vapor-phase speciation of uranium oxide nanoparticles

The transport of radioactive material following a nuclear event depends heavily on fallout characteristics (e.g., composition, shape, and size), which in turn are controlled by the conditions under which the fallout forms. To this end, we use a novel plasma flow reactor (PFR) to explore how conditions including temperature history and gas mixing influence the chemical speciation and physical characteristics of uranium oxide nanoparticles. The PFR consists of a glass tube attached to an inductively coupled plasma (ICP) torch via an adaptor piece (ring flow injector) located downstream of the plasma-generating RF coil. We increase the gas flow rates from normal ICP operating conditions to higher values both upstream at the RF coil and downstream at the ring flow injector to create four distinct temperature profiles and two distinct gas flow mixing conditions (normal and higher Ar atomic ratios). Ex situ transmission electron microscopy (TEM) analysis is used to determine the crystal structure, morphology, and size distribution of the synthesized particles as a function of temperature and mixing. The particles display a striking dependence on these conditions in terms of the resulting speciation of uranium oxide: lower temperature (higher upstream) and slower cooling (normal downstream with normal Ar atomic ratio mixing) favor the formation of α-UO 3 particles, while faster cooling (higher downstream with higher Ar atomic ratio mixing) and higher temperature (normal upstream) favor the formation of UO 2 particles. The extent of gas mixing dictates particle aggregation: better mixing encourages the particles to aggregate more extensively. Here these results demonstrate the sensitivity of uranium to initial local conditions and can be used to improve our understanding of the kinetics that drive uranium speciation and ultimately inform fallout transport models.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

The role of gas flow distributions on CO 2 mineralization within monolithic cemented composites: coupled CFD-factorial design approach

The carbonation kinetics of monolithic cementing composites are strongly affected by gas transport which is, in turn, influenced by microstructural resistances and the presence of liquid water within pore networks. The non-uniform gas flow distribution within the CO 2 mineralization reactor can impart mass transfer resistance in the monolith microstructure, which affects the uptake of CO 2 (“carbonation”) of the cementing composites. This paper demonstrates how the gas spatial distribution (velocity and flow rate; quantified by CFD analysis) and processing conditions (temperature, relative humidity, and flow rate; quantified by factorial design) affect drying and carbonation, and in turn, the engineering properties of a representative ‘monolithic’ carbonate-cemented concrete component (i.e., herein concrete masonry unit: CMUs, also known as concrete block). It is shown that the gas flow distribution affects drying front penetration and results in moisture and carbonation gradients within the monolith. Particularly, variations in drying kinetics caused by non-uniformity of the contacting gas velocity impose gradients in moisture saturation, which results in increasing microstructural resistance to CO 2 transport. The resultant non-uniform carbonate-mineral formation (i.e., carbonate cementation), if not controlled, can produce gradients in mechanical properties and may alter failure patterns upon loading. Finally, these insights inform the optimal design of gas flow distribution systems and processing conditions within CO 2 mineralization reactors for the manufacturing of low-CO 2 concrete components using CO 2 -dilute industrial flue gas streams.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Analytical model for quasi-linear flow response to resonant magnetic perturbation in resistive-inertial and viscous-resistive regimes

In this work, a quasi-linear model for plasma flow response to the resonant magnetic perturbation (RMP) in a tokamak has been rigorously developed in the resistive-inertial (RI) and viscousresistive (VR) regimes purely from the two-field reduced MHD model. Models for plasma response to RMP are commonly composed of equations for the resonant magnetic field response (i.e. the magnetic island) and the torque balance of plasma flow. However, in previous plasma response models, the magnetic island and the torque balance equations are often derived separately from reduced MHD and full MHD equations, respectively. By contrast, in this work we derive both the magnetic island response and the torque balance equations in a quasi-linear model for plasma flow response entirely from a set of two-field reduced MHD equations. Such a quasi-linear model can recover previous plasma flow response models within certain limits and approximations. Furthermore, the physical origins of quasi-linear forces and moments in the flow response equation are also accurately calculated and clarified self-consistently.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Comparison of local and global gyrokinetic calculations of collisionless zonal flow damping in quasi-symmetric stellarators

The linear collisionless damping of zonal flows is calculated for quasi-symmetric stellarator equilibria in flux-tube, flux-surface, and full-volume geometry. Equilibria are studied from the quasi-helical symmetry configuration of the Helically Symmetric eXperiment (HSX), a broken symmetry configuration of HSX, and the quasi-axial symmetry geometry of the National Compact Stellarator eXperiment (NCSX). Zonal flow oscillations and long-time damping affect the zonal flow evolution, and the zonal flow residual goes to zero for small radial wavenumber. The oscillation frequency and damping rate depend on the bounce-averaged radial particle drift in accordance with theory. While each flux tube on a flux surface is unique, several different flux tubes in HSX or NCSX can reproduce the zonal flow damping from a flux-surface calculation given an adequate parallel extent. The flux-surface or flux-tube calculations can accurately reproduce the full-volume long-time residual for moderate kx, but the oscillation and damping time scales are longer in local representations, particularly for small kx approaching the system size.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Scaling of the mean transverse flow and Reynolds shear stress in turbulent plane jet

Here, proper scaling for the mean transverse flow and Reynolds shear stress in a turbulent plane jet is determined using a scaling patch approach. By seeking an admissible scaling, a key concept in the scaling patch approach, for the mean continuity equation, a proper scale for the mean transverse flow in a turbulent plane jet is found as V ref = –δdU ctr /dx, where δ is the jet half width and dU ctr /dx is the decay rate of the mean axial velocity at the jet centerline. By seeking an admissible scaling for the mean axial momentum equation, a proper scale for the kinematic Reynolds shear stress is found as R uv,ref =U ctr V ref , which is a mix of the velocity scales in the axial and transverse directions. Approximation functions for the scaled mean transverse flow and Reynolds shear stress are developed and found to agree well with experimental and numerical data. Similarities and differences between the scales of the mean transverse flow and Reynolds shear stress in turbulent plane jets and zero-pressure-gradient turbulent boundary layer flows are clarified.

42 ENGINEERING↗

DOE OSTI2023

Ensemble flow reconstruction in the atmospheric boundary layer from spatially limited measurements through latent diffusion models

Due to costs and practical constraints, field campaigns in the atmospheric boundary layer typically only measure a fraction of the atmospheric volume of interest. Machine learning techniques have previously successfully reconstructed unobserved regions of flow in canonical fluid mechanics problems and two-dimensional geophysical flows, but these techniques have not yet been demonstrated in the three-dimensional atmospheric boundary layer. Here, we conduct a numerical analogue of a field campaign with spatially limited measurements using large-eddy simulation. We pose flow reconstruction as an inpainting problem, and reconstruct realistic samples of turbulent, three-dimensional flow with the use of a latent diffusion model. The diffusion model generates physically plausible turbulent structures on larger spatial scales, even when input observations cover less than 1% of the volume. Through a combination of qualitative visualization and quantitative assessment, we demonstrate that the diffusion model generates meaningfully diverse samples when conditioned on just one observation. These samples successfully serve as initial conditions for a large-eddy simulation code. We find that diffusion models show promise and potential for other applications for other turbulent flow reconstruction problems.

17 WIND ENERGY↗

DOE OSTI2024

When do waves drive plasma flows?

Flows and rotation, particularly E×B rotation, are critical to improving plasma performance, and waves are a primary tool of plasma control. Thus, it is paramount to understand under what conditions waves can drive E×B flows in plasmas. In this didactic review, an invited paper accompanying the 2023 Marshall N. Rosenbluth Doctoral Thesis Award, this question is answered in the context of momentum-conserving quasilinear theory. There are two primary frameworks for momentum-conserving quasilinear theories that can handle both resonant and nonresonant particles: Eulerian averaging theories and oscillation-center Hamiltonian theories. There are also two different paradigmatic wave problems: plane-wave initial value problems, and steady-state boundary value problems. Here, it is shown that each of these frameworks “naturally” works better with a different problem type. By using these theories, one finds a great difference in the behavior of time- vs space-dependent waves. A time-evolving plane wave can only drive flow if the electromagnetic momentum of the wave, given by the Poynting flux, changes. This result precludes flow drive by any planar electrostatic wave. In contrast, a steady-state spatially evolving wave can drive flow whenever there is divergence in the flux of Minkowski momentum, a completely different physical quantity. This review aims to provide a high-level, intuitive understanding of the very different behaviors observed for these two types of problem.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Solving the Hele–Shaw flow using the Harrow–Hassidim–Lloyd algorithm on superconducting devices: A study of efficiency and challenges

The development of quantum processors for practical fluid flow problems is a promising yet distant goal. Recent advances in quantum linear solvers have highlighted their potential for classical fluid dynamics. In this study, we evaluate the Harrow–Hassidim–Lloyd (HHL) quantum linear systems algorithm (QLSA) for solving the idealized Hele–Shaw flow. Our focus is on the accuracy and computational cost of the HHL solver, which we find to be sensitive to the condition number, scaling exponentially with problem size. This emphasizes the need for preconditioning to enhance the practical use of QLSAs in fluid flow applications. Moreover, we perform shots-based simulations on quantum simulators and test the HHL solver on superconducting quantum devices, where noise, large circuit depths, and gate errors limit performance. Error suppression and mitigation techniques improve accuracy, suggesting that such fluid flow problems can benchmark noise mitigation efforts. Finally, our findings provide a foundation for future, more complex application of QLSAs in fluid flow simulations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗