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Turbulence Simulations of Transonic Flows over NACA-0012 and OAT15A Airfoils

Three different simulation approaches, namely unsteady Reynolds-averaged Navier-Stokes (URANS), delayed detached-eddy simulation (DDES), and wall-modeled large-eddy simulation (WMLES) are employed to simulate transonic flow over an NACA-0012, OAT15A airfoils at different angles of attack covering pre- and post-buffet-onset regimes. The freestream Mach number is 0.75, and the Reynolds number based on the chord length is 10 and 3million, respectively. The NASA FUN3D solver is used for the simulations, which is an unstructured, compressible flow solver. The URANS simulations are performed using the Spalart-Allmaras (SA) model with the compressibility correction, the DDES predictions are based on the SA model, and the WMLES are performed using an equilibrium wall-model. The unsteady RANS simulations, only with the compressibility correction, predict the pre- and post- buffet characteristics, which compare well with the experimental results. DDES results predicted a lower buffet onset angle compared to experiment. The predicted shock locations are upstream of the locations predicted by URANS. Using a fine grid in the spanwise direction, WMLES predictions show buffeting consistent with the experiment.

Computational Fluid Dynamics↗

NASA NTRS2024

Expansion of Check-Cases for 6DOF Simulation

This effort expands upon a previous NASA activity that developed flight simulation benchmark check-cases to include new check-cases for the Cislunar domain, comparing multiple NASA simulation tools. The results of this effort describe the benefits of standardizing inputs, simulation comparisons and describe an interactive website that enables comparison of externally provided simulation data. Participating simulations improved their software and identified implementation errors. This activity elevated simulation credibility and provided a measure of validation for the simulations actively in use for NASA’s Human Landing Systems (HLS).

Modeling↗

DOE OSTI2024

Regional-scale fault-to-structure earthquake simulations with the EQSIM framework: Workflow maturation and computational performance on GPU-accelerated exascale platforms

Continuous advancements in scientific and engineering understanding of earthquake phenomena, combined with the associated development of representative physics-based models, is providing a foundation for high-performance, fault-to-structure earthquake simulations. However, regional-scale applications of high-performance models have been challenged by the computational requirements at the resolutions required for engineering risk assessments. The EarthQuake SIMulation (EQSIM) framework, a software application development under the US Department of Energy (DOE) Exascale Computing Project, is focused on overcoming the existing computational barriers and enabling routine regional-scale simulations at resolutions relevant to a breadth of engineered systems. This multidisciplinary software development—drawing upon expertise in geophysics, engineering, applied math and computer science—is preparing the advanced computational workflow necessary to fully exploit the DOE’s exaflop computer platforms coming online in the 2023 to 2024 timeframe. Achievement of the computational performance required for high-resolution regional models containing upward of hundreds of billions to trillions of model grid points requires numerical efficiency in every phase of a regional simulation. This includes run time start-up and regional model generation, effective distribution of the computational workload across thousands of computer nodes, efficient coupling of regional geophysics and local engineering models, and application-tailored highly efficient transfer, storage, and interrogation of very large volumes of simulation data. This article summarizes the most recent advancements and refinements incorporated in the workflow design for the EQSIM integrated fault-to-structure framework, which are based on extensive numerical testing across multiple graphics processing unit (GPU)-accelerated platforms, and demonstrates the computational performance achieved on the world’s first exaflop computer platform through representative regional-scale earthquake simulations for the San Francisco Bay Area in California, USA.

58 GEOSCIENCES↗

DOE OSTI2025

Efficient Simulation of Open Quantum Systems on NISQ Trapped‐Ion Hardware

Abstract Simulating open quantum systems, which interact with external environments, presents significant challenges on noisy intermediate‐scale quantum (NISQ) devices due to limited qubit resources and noise. In this study, an efficient framework is proposed for simulating open quantum systems on NISQ hardware by leveraging a time‐perturbative Kraus operator representation of the system's dynamics. This approach avoids the computationally expensive Trotterization method and exploits the Lindblad master equation to represent time evolution in a compact form, particularly for systems satisfying specific commutation relations. The efficiency of this method is demonstrated by simulating quantum channels, such as the continuous‐time Pauli channel and damped harmonic oscillators, on NISQ trapped‐ion hardware, including IonQ Harmony and Quantinuum H1‐1. Additionally, hardware‐agnostic error mitigation techniques are introduced, including Pauli channel fitting and quantum depolarizing channel inversion, to enhance the fidelity of quantum simulations. These results show strong agreement between the simulations on real quantum hardware and exact solutions, highlighting the potential of Kraus‐based methods for scalable and accurate simulation of open quantum systems on NISQ devices. This framework opens pathways for simulating more complex systems under realistic conditions in the near term.

Burdine, Colin [Department of Electrical and Compu↗

DOE OSTI2024

Numerical simulation of involute-plate research reactor flow behavior using RANS, LES and DNS

This paper investigates the flow behavior of involute-plate research reactors by performing Reynolds-Averaged Navier Stokes simulation (RANS), Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) of the channel flow between fuel plates. By modeling turbulence with different numerical approaches, this study provides data with three levels of fidelity. For the RANS simulation, three widely used turbulence models, i.e., k-ε, k-ω, Reynolds Stress Turbulence model (RST) are applied by using the commercial CFD code STAR-CCM +. For LES and DNS, the open-source CFD code, Nek5000, is used given its outstanding scalability on High Performance Computer (HPC) and high-order technique. The results from RANS simulations are compared with that from LES and DNS for benchmarking. Both macroscale parameters and turbulence statistics, such as velocity magnitude, lateral velocity and turbulence kinetic energy, are presented and analyzed. The results from RANS simulation achieve good agreement with LES and DNS on velocity and turbulence kinetic energy prediction. The RST turbulence model predicts the most similar flow pattern of lateral velocity as compared to LES and DNS. The Lambda-2 (λ2) criterion with a reasonable threshold is used to demonstrate the instantaneous vortices distribution in the involute channel from both LES and DNS calculation. The DNS simulation captures more detailed turbulence especially near the corner, which explains the discrepancy between LES and DNS results near the corner. The normalized RMS error are defined and calculated to assess the performance of those turbulence models. The RST model captures the anisotropic feature of turbulence, which enable it to outperform other turbulence models for predicting the flow behavior in an involute channel. Although some discrepancies are found between LES and DNS results in the corner, the overall deviations between LES and DNS are found to be small. In conclusion, given that the computational cost of DNS calculation is an order of magnitude higher, using LES data for benchmarking RANS model is a cost-effective approach.

DNS↗

DOE OSTI2025

Dynamics and lipid membrane coupling of the RAS-RAF complex revealed via multiscale simulations

To gain molecular and mechanistic insights into initiation of the RAS-RAF signaling cascade, we developed and used a combination of multiscale simulation and experimental approaches. The influence and impact of the membrane on RAS and RAF proteins is a factor we are just beginning to understand and appreciate in more detail. Molecular simulation is an ideal methodology to further study this complicated relationship between the membrane and associated proteins. Our previous work using Multiscale Machine-learned Modeling Infrastructure investigated different lipid compositions solely around the KRAS4b protein and the interplay between protein behavior and these membrane environments. Multiscale Machine-learned Modeling Infrastructure uses machine learning to couple adjacent simulation scales and has been efficiently scaled across some of the world’s largest high-performance computers. Recently, we have expanded this multiresolution framework to include the all-atom simulation scale and to incorporate the RAF RBDCRD domains. Here, we present the overall analysis results from this new simulation campaign comprising a mixture of RAS and RAF RBDCRD proteins. Approximately 35,000 coarse-grained and 10,000 all-atom molecular dynamics simulations were completed, sampled from a variety of protein/lipid composition configurations that were generated from a micron-scale continuum simulation containing hundreds of copies of the proteins. Our studies suggest that orientations of the RAS-RBDCRD complex on the membrane occupy distinct configurational states, and the spatial patterns of lipid arrangements around these different protein states are unique to each state. The extent and size of lipid “fingerprints” imposed on the membrane by the RAS-RBDCRD protein complex are significantly larger than observed for just the RAS protein on its own. These protein complexes strongly associate, but we do not observe statistically significant preferred protein-protein orientations. These observations indicate that spatial colocalization of RAS-RBDCRD proteins in the same vicinity may be assisted by specific membrane environments, acting to increase the probability of signaling complex formation.

Carpenter, Timothy S. [Lawrence Livermore National↗

DOE OSTI2026

From models to reality: a systematic review on simulated and measured residential heat pump energy savings

High-performance HVAC solutions are central to residential energy management. A substantial share of these are electric, reversible-cycle systems, with heat pumps representing the largest portion of current and near-term adoption. This review synthesizes peer-reviewed and grey literature on residential space heating and cooling heat pumps. The academic literature is dominated by modeling (73.8%), with limited field measurement (13.1%). Grey literature from United States serve as a supplemental resource providing measured savings. Conversions from electric-resistance heating consistently show the largest site energy reductions, while oil/propane baselines yield moderate savings, and gas baseline scenario often deliver small and region-dependent savings. This study cross-checks the grey literature measured data with simulation data filtered from the ResStock dataset. The comparison indicates a discrepancy between simulations and measured data: simulated site EUIs are typically lower than measured EUIs, but percentage energy savings fall in similar ranges, implying simulations capture directional effects while underestimating energy use. Factors associated with variability and model–measurement differences include system characterization and control representation (e.g., backup heat engagement, thermostat/setpoint strategies, commissioning/installation quality), occupant behavior, weather normalization, metering scope, and envelope characterization. This paper also outlines the proposed methodology for comparing simulation and measured data for heat pumps. It emphasizes the metrics used for comparison and units harmonization, building characteristics matching, and compact metadata are needed for simulations to match measured data. The proposed methodology is expected to improve the credibility of simulated savings as measured evidence grows.

Yu, Lili↗

DOE OSTI2024

Automation and optimization of stopping and range of ions in matter simulation runtime

Prior to every ion implantation experiment a simulation of the ion range and other relevant parameters is performed using Monte-Carlo based codes. Although increasing computing power has improved the speed of these calculations, the demands on Monte-Carlo codes are also increasing, requiring evaluation of the optimal number of simulations while ensuring accuracy within threshold bounds. We evaluate the “Stopping and Range of Ions in Matter” (SRIM) code due to its widespread usage. We show how dividing simulations into multiple parallel simulations with different random seeds can lead to calculation speedup and find lower bounds for the required number of ion traces simulated based on an exemplar system of a Ga focused ion beam and a high energy C beam as used in high linear energy transfer testing. Here our results indicate simulations can yield results within the underlying data accuracy of SRIM at 10X and 100X shorter simulation time than the SRIM default values.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

Comparison of volatiles evolving from selected highland and mare lunar regolith simulants during vacuum sintering

Volatiles evolving from JSC-1A, NU-LHT-4M and CSM-LHT-1G lunar regolith simulants during in vacuo thermal processing were analyzed using mass spectrometry as a function of temperature. Two high-fidelity simulants, JSC-1A (mare) and NU-LHT-4M (highland), were compared to a newly developed CSM-LHT-1G highland simulant, modified to closely match lunar geochemistry. Large autogenous gas loads were observed for all investigated materials. Mineralogical knowledge was used to identify and attribute individual volatile species to reacting, transforming, or decomposing constituents (hydrates, carbonates, sulfates, sulfides, clays, etc.) of the respective regolith simulant in the self-generated gas environment. Cumulative mass losses for individual simulant components as a function of temperature were quantified using mass spectrometry in conjunction with thermogravimetric analysis. Investigation of the four components of CSM-LHT-1G – anorthosite, basalt, augite, and glass – aided the attribution of volatile species to specific compounds and their respective sources. The results showed significant decomposition of non-lunar phases present in the man-made regolith simulants below the typical glass crystallization temperatures, which paves the way to devising methods for enhancing the fidelity of the simulants. Finally, high gas loads and corrosive gases (HF and HCl) were recognized as potential hazards, pertaining to the development of large testbed facilities.

42 ENGINEERING↗

DOE OSTI2025

Combining Reactive Quantum-Mechanical Molecular-Dynamics Simulations with Mutagenesis, Crystallography, and Enzyme Kinetics to Reveal Plausible Steps of Isocyanide Hydratase Catalysis

A complete understanding of enzyme mechanisms requires atomistic details of chemical reactions. Quantum-based molecular dynamics simulations (QMD) are a potential source of this information, but trade-offs between accuracy and computational cost have limited their use. We previously developed extended Lagrangian Born–Oppenheimer molecular dynamics (XL-BOMD) methods that leverage a negligible compromise in accuracy to substantially decrease the cost of QMD simulations. Here, we develop a reactive QMD approach using the latest XL-BOMD formulation, which enables efficient simulations of highly reactive systems, and use it to investigate mechanisms of intermediate formation in isocyanide hydratase (ICH) catalysis. In QMD simulations, molecular analogs of ICH active site residues reacted with para-nitrophenyl isocyanide, forming a thioimidate. Analysis of simulated atomic configurational and charge dynamics revealed a pathway where protonation of the isocyanide carbon occurs prior to thioimidate formation and suggested a possible role of Asp17 as a proton donor in the early phase of ICH catalysis. To test whether the pathway seen using the reactive QMD approach might be relevant to ICH catalysis, we performed X-ray crystallography and pre-steady-state enzyme kinetics studies of wild-type and D17N mutant ICH. Both the structure and kinetics are sensitive to the D17N mutation in a manner that is consistent with the order of the reaction steps seen in the simulations. Mobile protons play essential roles in many enzymes, yet they are difficult to observe experimentally, making the ordering of proton-dependent steps ambiguous in many enzyme mechanisms. The ability to directly simulate model reactions for the design of experiments that provide information about enzyme mechanisms involving mobile protons demonstrates the significance of our reactive QMD approach and motivates further biological applications.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Characteristics of Precipitation and Mesoscale Convective Systems Over the Peruvian Central Andes in Multi 5‐Year Convection‐Permitting Simulations

Abstract Using the Weather Research and Forecasting model with two planetary boundary layer schemes, ACM2 and MYNN, convection‐permitting model (CPM) regional climate simulations were conducted for a 6‐year period, including a one‐year spin‐up period, at a 15‐km grid spacing covering entire South America and a nested convection‐permitting 3‐km grid spacing covering the Peruvian central Andes region. These two CPM simulations along with a 4‐km simulation covering South America produced by National Center for Atmospheric Research (NCAR), three gridded precipitation products, and rain gauge data in Peru and Brazil, are used to document the characteristics of precipitation and mesoscale convective systems (MCSs) in the Peruvian central Andes region. Results show that all km‐scale simulations generally capture the spatiotemporal patterns of precipitation and MCSs at both seasonal and diurnal scales, although biases exist in aspects such as precipitation intensity and MCS frequency, size, propagation speed, and associated precipitation intensity. The 3‐km simulation using MYNN scheme generally outperforms the other simulations in capturing seasonal and diurnal precipitation over the mountain, while both it and the 4‐km simulation demonstrate superior performance in the western Amazon Basin, based on the comparison to the gridded precipitation products and gauge data. Dynamic factors, primarily low‐level jet and terrain‐induced uplift, are the key drivers for precipitation and MCS genesis along the east slope of the Andes, while thermodynamic factors control the precipitation and MCS activity in the western Amazon Basin and over elevated mountainous regions. The study suggests model improvements and better model configurations for future regional climate projections.

Meteorology & Atmospheric Sciences↗

DOE OSTI2025

Implementation and Evaluation of Emission‐Driven Land‐Atmosphere Coupled Simulation in E3SMv2.1

Emissions-driven (prognostic CO 2 ) simulations are essential for representing two-way carbon-climate feedback in Earth System Models. We present an emissions-driven land–atmosphere coupled biogeochemistry (BGC) configuration (BGCLNDATM_progCO2) in version 2.1 of the Energy Exascale Earth System Model (E3SMv2.1). This is the first E3SM configuration that performs land-atmosphere emission-hindcasts. Here, we document its implementation, evaluate the model's performance against observations and other models, and propose a structured evaluation protocol for such emissions-driven simulations. We conducted transient historical simulations (1850–2014) with BGCLNDATM_progCO2 and compare them to reference simulations—a land-atmosphere coupled simulation without BGC and a standalone land simulation with BGC, both using prescribed CO 2 concentrations—and to observations. BGCLNDATM_progCO2 overestimates atmospheric CO 2 concentrations by 11–23 ppm yet stays within the 40-ppm spread CMIP6 emission-driven models and retains physical climate properties comparable to the reference runs. The CO 2 biases are partly attributed to underrepresented oceanic CO 2 uptake and inadequate representations of some terrestrial processes. In general, introducing prognostic CO 2 did not change physical climate metrics at the global scale but had larger regional effects, particularly over land where spatially heterogeneous CO 2 and prognostic leaf area index influenced surface energy balance. Finally, we propose a general evaluation protocol including spin-up assessment, atmospheric CO 2 benchmarking, physical climate evaluation, and land biogeochemical analysis to support scientific rigor and facilitate inter-model comparisons. The new configuration lays the groundwork for future enhancements, including improved terrestrial biogeochemical processes, integrated marine biogeochemistry, and additional human–Earth system interactions. These developments advance E3SM toward fully coupled emissions-driven simulations, enabling more accurate carbon–climate feedback projections and informing mitigation policy by providing physically consistent carbon-budget metrics for mitigation scenarios.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Large-scale simulations of Floquet physics on near-term quantum computers

Abstract Periodically driven quantum systems exhibit a diverse set of phenomena but are more challenging to simulate than their equilibrium counterparts. Here, we introduce the Quantum High-Frequency Floquet Simulation (QHiFFS) algorithm as a method to simulate fast-driven quantum systems on quantum hardware. Central to QHiFFS is the concept of a kick operator which transforms the system into a basis where the dynamics is governed by a time-independent effective Hamiltonian. This allows prior methods for time-independent simulation to be lifted to simulate Floquet systems. We use the periodically driven biaxial next-nearest neighbor Ising (BNNNI) model, a natural test bed for quantum frustrated magnetism and criticality, as a case study to illustrate our algorithm. We implemented a 20-qubit simulation of the driven two-dimensional BNNNI model on Quantinuum’s trapped ion quantum computer. Our error analysis shows that QHiFFS exhibits not only a cubic advantage in driving frequency ω but also a linear advantage in simulation time t compared to Trotterization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Numerical challenges for energy conservation in N -body simulations of collapsing self-interacting dark matter halos

Dark matter (DM) halos can be subject to gravothermal collapse if the DM is not collisionless, but engaged in strong self-interactions instead. When the scattering is able to efficiently transfer heat from the centre to the outskirts, the central region of the halo collapses and reaches densities much higher than those for collisionless DM. This phenomenon is potentially observable in studies of strong lensing. Current theoretical efforts are motivated by observations of surprisingly dense substructures. However, a comparison with observations requires accurate predictions. One method to obtain such predictions is to use N-body simulations. Collapsed halos are extreme systems that pose severe challenges when applying state-of-the-art codes to model self-interacting dark matter (SIDM). In this work, we investigate the root of such problems, with a focus on energy non-conservation. Moreover, we discuss possible strategies to avoid them. We ran N-body simulations, both with and without SIDM, of an isolated DM-only halo and we adjusted the numerical parameters to check the accuracy of the simulation. We find that not only the numerical scheme for SIDM can lead to energy non-conservation, but also the modelling of gravitational interaction and the time integration are problematic. The main issues we find are: (a) particles changing their time step in a non-time-reversible manner; (b) the asymmetry in the tree-based gravitational force evaluation; and (c) SIDM velocity kicks breaking the time symmetry. Tuning the parameters of the simulation to achieve a high level of accuracy allows us to conserve energy not only at early stages of the evolution, but also later on. However, the cost of the simulations becomes prohibitively large as a result. Some of the problems that make the simulations of the gravothermal collapse phase inaccurate can be overcome by choosing appropriate numerical schemes. However, other issues still pose a challenge. Our findings motivate further works on addressing the challenges in simulating strong DM self-interactions.

dark matter↗

DOE OSTI2024

Data Science Shows that Entropy Correlates with Accelerated Zeolite Crystallization in Monte Carlo Simulations

We have performed a data science study of Monte Carlo simulation trajectories to understand factors that can accelerate formation of zeolite nanoporous crystals, a process that can take days or even weeks. In previous work, Monte Carlo simulations predicted and experiments confirmed that using a secondary organic structure-directing agent (OSDA) accelerates crystallization of all-silica LTA zeolite, with experiments finding a three-fold speedup [PCCP 24, 142-148 (2022)]. However, it remains unclear what physical factors cause the speed-up. Here, we apply data science to analyze the simulation trajectories to discover what drives accelerated zeolite crystallization in Monte Carlo going from a one-OSDA synthesis (1OSDA) to a two-OSDA version (2OSDA). We encoded simulation snapshots using the Smooth Overlap of Atomic Positions approach, which represents all 2- and 3-body correlations within a given cutoff distance. Principal component analyses failed to discriminate datasets of structures from 1OSDA and 2OSDA simulations, while the Support Vector Machine (SVM) approach succeeded at classifying such structures with an area-under-curve (AUC) score of 0.99 (where AUC = 1 is a perfect classification) with all 3-body correlations, and as high as 0.94 with only 2-body correlations. SVM decision functions reveal relatively broad / narrow histograms for 1OSDA / 2OSDA datasets, suggesting that the two simulations differ strongly in information heterogeneity. Informed by these results, we performed pair (2-body) entropy calculations during crystallization, resulting in entropy differences that semi-quantitatively account for the speedup observed in the previous Monte Carlo simulations. We conclude that altering synthesis conditions in ways that substantially changes the entropy of labile silica networks may accelerate zeolite crystallization, and we discuss possible approaches for achieving such acceleration.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2026

Comparing ICME simulations with scaled laboratory experiment

In stellar physics and astrophysics, numerical simulations and laboratory experiments are often compared to observational data to support their representation of the real world. However, there is also merit in comparing numerical simulations to properly scaled experiments, especially when the experiment and the simulation are both emulating the solar phenomena. Confirming the credibility of scaled experiments and their scaling with well-validated models is important to expand our knowledge of the associated physical phenomena. This is significant because experiments and simulations can be performed frequently, whereas observations may be limited by location, field of view, and missing data. In this work, we use the Alfvén Wave Solar atmosphere Model, a well-validated magnetohydrodynamic model, to simulate an interplanetary coronal mass ejection (ICME) and compare it to an experiment which provides a scaled analog to a physical ICME. The experiment was performed on the Big Red Ball facility and scaled using dimensionless parameters such as plasma β and magnetosonic Mach number to reproduce the main structure of an ICME. We compare the model-simulated temperature, density, and magnetic field to those from the experiment, as well as the scaling parameters used in the experiment, to those calculated from the simulation. This comparison is performed to further justify the scaling arguments made by the experiment. Additionally, the comparison would lead to the development of stronger scaling arguments for future experiments.

Bryant, K. [University of Michigan, Ann Arbor, MI ↗

DOE OSTI2024

Agora : Multicomponent simulation for cross-survey science

ABSTRACT Next-generation cosmological surveys will observe large portions of the sky, with significant overlap between them. Multi-wavelength observations will enable us to analyse the same large-scale structure from different angles using a variety of tracers and astrophysical effects. The complex interplay between these observables calls for a model that can accurately and coherently describe their collective behaviour, posing a challenge that can only be met through the use of simulations. In this work, a suite of simulated extragalactic skies is presented, including maps and/or catalogues of cosmic microwave background (CMB) lensing, thermal and kinetic Sunyaev–Zel’dovich (tSZ/kSZ) effects, cosmic infrared background (CIB), radio sources, galaxy overdensity and galaxy weak lensing. Each of these probes is implemented in the lightcone using halo catalogues and/or particles from the Multidark-Planck2 ($\small {MDPL2}$) N-body simulation, and the modelling is calibrated using hydrodynamic simulations and publicly available data. The auto and cross-spectra of the individual probes, as well as the cross-spectra between the observables, are shown to be consistent with theoretical models and measurements from data. The simulation is shown to have a wide range of applications, including forecasting, pipeline testing, and evaluating astrophysical biases in cross-correlation measurements. It is further demonstrated that the simulation products produced in this work have sufficient accuracy to recover the input cosmology when subjected to a full cosmological analysis and are ready for application in real-world analyses for ongoing and future surveys. The simulation products presented in this work can be accessed at: https://yomori.github.io/agora/index.html.

Astronomy & Astrophysics↗

DOE OSTI2025

Quantum dynamics simulation of the advection-diffusion equation

The advection-diffusion equation is simulated via several quantum algorithms. Three formulations are considered: (1) Trotterization, (2) variational quantum time evolution (VarQTE), and (3) adaptive variational quantum dynamics simulation (AVQDS). These schemes were originally developed for the Hamiltonian simulation of many-body quantum systems. The finite-difference discretized operator of the transport equation is formulated as a Hamiltonian and solved without the need for ancillary qubits. Computations are conducted on a quantum simulator (IBM Qiskit Aer) and a superconducting quantum hardware (IBM Fez). The former emulates the latter without the noise. The actual hardware implementation experiences significant noise. The results of the quantum simulator are compared with data from direct numerical simulation (DNS) with infidelities of the order 10 −5 . In the quantum simulator, Trotterization is observed to have the lowest infidelity and is suitable for fault-tolerant computation. The AVQDS algorithm requires the lowest gate count and circuit depth. The VarQTE algorithm is the next best in terms of gate counts, but the number of its optimization variables is directly proportional to the number of qubits. Due to current hardware limitations, Trotterization cannot be implemented, as it has an overwhelmingly large number of operations. Meanwhile, AVQDS and VarQTE can be executed at the hardware level. These algorithms present a new paradigm for computational transport phenomena on quantum computers.

Alipanah, Hirad [Univ. of Pittsburgh, PA (United S↗