The traditional methods for modelling the electronic excitation in direct simulation Monte Carlo (DSMC) simulations treat each internal mode individually and disregard any interaction between modes. To address this, a vibronic model was developed by Civrais et al. (Phys. Fluids 36:086112, 2024) allowing each electronic excited state to excite its unique vibrational quantum levels. This work expands on previous work by providing complementary physical insights into the modelling of the vibrational quantum levels of electronic states. The fundamental differences between the uncoupled and coupled approaches in terms of the internal energies and distribution functions are outlined. Then, the scalability of the vibronic model against the traditional approach is demonstrated for elementary operations. It is shown that the coupled approach demonstrates a comparable runtime as the uncoupled approach. Finally, the traditional uncoupled and coupled approaches are applied to the modelling of the electronic excited states on the forebody of the Space Shuttle at an altitude of 99.49 km, demonstrating the inaccuracy of the traditional assumption of the electronic excited states being distributed according to the Boltzmann statistics. It is also shown that the population of the electronic excited states and their vibrational quantum levels strongly deviate between the two approaches, suggesting a significant impact on the line intensity of molecular species’ absorption spectrum.

Quantum computing is a very active and diverse area, with immense research and development occurring in quantum hardware design and algorithm creation for applications in various scientific fields. The key motivation behind such efforts is the potential for significant speed-up relative to simulations on classical computers. Quantum Monte Carlo Integration (QMCI) is a quantum algorithm that promises a quadratic advantage in terms of the required number of samples for a required accuracy over classical Monte Carlo Integration (MCI), which is a key statistical resource for integrating multi-dimensional space. In this study, we explore the reality of this potential, specifically for applications in Computational Fluid Dynamics (CFD). We perform an eigenvalue stability analysis for a 1D convection-diffusion equation, in which the coefficients depend on a random number. The quantum algorithm utilized uses quantum amplitude estimation (QAE) to accelerate the integral estimation process. Numerical values obtained from QMCI results are compared against numerical integration techniques, and acceptably low errors are observed. The performance of QMCI is compared against MCI by equating the number of oracle calls in QMCI with the number of samples required in MCI. No significant difference in this metric is observed, with QMCI requiring more oracle calls. This suggests that the expected quantum supremacy is not attainable for the considered numerical integration problem and its quantum-circuit implementation. Extension to available Noisy-Intermediate-Scale-Quantum (NISQ) hardware is expected to reveal more about the algorithm implementation and the simulator emulation. Potential future directions that can be explored in algorithmic development based on this preliminary research are outlined.

The present work investigates the ability of the Partially-Averaged Navier-Stokes (PANS) method to reproduce transonic buffet, occurring on airfoils and wings at transonic regime under specific flow conditions. The designed test case for this analysis is the OAT15A unswept wing at Mach number M-infinity = 0.73 and Reynolds number Re-c = 3 x 10(6). The three-dimensional flow is studied by accounting for the wind tunnel walls in the experiments of Jacquin et al. [1]. The computations on a large-span, confined configuration revealed a strong three-dimensionality of the flow both before and after the buffet onset. The comparison with unsteady Reynolds-averaged Navier Stokes (URANS) results showed the benefits of PANS in resolving flow unsteadiness at different flow resolutions, especially on affordable CFD grids, at limited additional cost.

Efficient and robust uncertainty quantification (UQ) is essential in aerospace systems, as emphasized by both NASA's CFD Vision 2030 and Certification by Analysis (CbA) 2040 initiatives. However, the extensive computational resources required by traditional UQ methods, especially when coupled with high-fidelity computational fluid dynamics (CFD) simulations, pose significant barriers. Quantum computing (QC) has been identified by the CFD Vision 2030 study as a promising technology to address these challenges, but has not yet been extensively explored in the context of UQ. In this study, a Quantum Computing-based Monte Carlo (QCMC) algorithm is implemented using a Qiskit simulator. This method utilizes Quantum Amplitude Estimation (QAE), specifically tailored for near-term Noisy Intermediate-Scale Quantum (NISQ) computers. The QCMC method demonstrates comparable accuracy to classical Monte Carlo (MC) methods on a two-dimensional heat diffusion problem while reducing the required number of samples (oracle calls) by similar to 8X. By substantially lowering the computational overhead of UQ, this quantum computing-based algorithm could be a promising tool required to enable robust uncertainty-informed aerospace design.

Quantum computing is an advancing area of research in which computer hardware and algorithms are developed to take advantage of quantum mechanical phenomena. In recent studies, quantum algorithms have shown promise in solving linear systems of equations as well as systems of linear ordinary differential equations (ODEs) and partial differential equations (PDEs). Reduced-order modeling (ROM) algorithms for studying fluid dynamics have shown success in identifying linear operators that can describe flowfields, where dynamic mode decomposition (DMD) is a particularly useful method in which a linear operator is identified from data. In this work, DMD is reformulated as an optimization problem to propagate the state of the linearized dynamical system on a quantum computer. This reformulation was chosen as a means of facilitating implementation on a near-term quantum computer. Quadratic unconstrained binary optimization (QUBO), a technique for optimizing quadratic polynomials in binary variables, allows for quantum annealing algorithms to be applied. A quantum circuit model (quantum approximation optimization algorithm, QAOA) is utilized to obtain predictions of the state trajectories. Results are shown for the quantum-ROM predictions for flow over a 2D cylinder at Re = 220 and flow over a NACA0009 airfoil at Re = 500 and α=15∘. The quantum-ROM predictions are found to depend on the number of bits utilized for a fixed point representation and the truncation level of the DMD model. Comparisons with DMD predictions from a classical computer algorithm are made, as well as an analysis of the computational complexity and prospects for future, more fault-tolerant quantum computers.

This article introduces a novel model for describing the electronic excited states in the direct simulation Monte Carlo (DSMC) technique. The model involves the coupling the vibrational and electronic modes of molecular species, enabling each electronic excited state to excite its unique vibrational quantum levels. Numerical techniques are developed for equilibrium and post-collision sampling, as well as for measuring the internal temperature. The DSMC results demonstrate excellent agreement with theoretical predictions, providing verification of the successful implementation in a DSMC solver. For important thermophysical properties of molecular oxygen, such as the specific heat capacity, it is shown that the new model provides a better prediction than a compilation of past studies in comparison to the standard uncoupled approach in DSMC. The model is then applied to simulate a canonical nonreactive oxygen hypersonic flow past a cylindrical body. The population distribution of electronic excited states exhibit significant deviation from the standard approach typically used in the coupling between DSMC and radiation transport solvers.

This work proposes an extended version of the quantum-kinetic chemistry models, aiming to accurately reproduce experimental measurements and high-fidelity calculations in both thermal equilibrium and non-equilibrium. The extension involves the development of new formulations, incorporating a set of tunable parameters obtained from a non-linear least squares fit on the dataset. The newly derived analytical expressions are implemented in a direct simulation Monte Carlo (DSMC) solver. These formulations are applied to the 19 most representative chemical reactions of an air mixture involving dissociation and exchange reactions. The DSMC reaction rates demonstrate excellent agreement with the newly derived analytical expressions, providing verification of the successful implementation in the DSMC solver. The study demonstrates excellent reproduction of the baseline dataset for both thermal equilibrium and non-equilibrium. Furthermore, the new formulations are applied to simulate the surface heat flux during the second space transport system (STS-II) mission at an altitude of 92.35 km.

An extension to the normal shock relations for a thermally perfect, calorically imperfect gas, modelling the vibrational excitation with an anharmonic oscillator model and including the influence of electronic modes, is derived and studied. Such additional considerations constitute an extension to the work achieved in the past, which modelled the caloric imperfections with a harmonic oscillator for vibrational energy and did not consider the effect of electronic energy. Additionally, the newly derived expressions provide physical insights into the limitations of experimentation for replicating flight conditions, which is demonstrated through providing solutions at different upstream temperatures. The results are compared with direct simulation Monte Carlo simulations for nitrogen and air, with the extent of the caloric imperfection of the gas showing excellent agreement. For low upstream temperatures, the extended relations are found to be in good agreement with the original normal shock wave expressions, but the results diverge for higher upstream temperatures that would be more representative of real flows. The results show that the new expressions depart from ideal gas theory for Mach numbers in excess of 4.9 at wind-tunnel conditions and for any Mach number above 3.0 at flight conditions. It is also shown that the traditional harmonic oscillator model and the anharmonic oscillator model begin to diverge at Mach number 3.0 for molecular oxygen gas and at Mach number 5.0 for an air mixture at flight conditions.

This work presents a new formulation of the quantum-kinetic (QK) chemistry models, in which the vibrational excitation is modeled with an anharmonic oscillator model. The new formulations are applied to some of the most representative dissociation reactions occurring during an Earth re-entry. The newly derived analytical expressions are implemented in a direct simulation Monte Carlo (DSMC) solver. The DSMC reaction rates demonstrate excellent agreement with the newly derived analytical expressions, verifying the successful implementation in the DSMC solver. The new models suggest that dissociation reactions are more likely to occur than with the original QK models. Furthermore, the new formulations are compared against experimental measurements, high-fidelity calculations, and well-established chemistry models for both thermal equilibrium and non-equilibrium conditions, presenting reasonable agreement with the baseline database. Additionally, the limitations of the new formulations are assessed for thermal non-equilibrium conditions where an excessive utilization of the relative translational energy and insufficient utilization of the pre-collision vibrational energy to promote dissociation reactions is found.

At hypersonic speeds, vehicles are subjected to extreme aerothermodynamic conditions, which require accurate predictions of the internal degrees of freedom of molecules. The harmonic oscillator (HO) model is commonly used to model the vibrational excitation of molecules in the framework of direct simulation Monte Carlo. Although it benefits from a simple computation, the HO model is known to have serious shortcomings as the temperature becomes significantly high. To address these limitations, an alternative model, called an anharmonic oscillator (aHO), has been developed and implemented in the dsmcFoam+ solver. The current work aims at evaluating an aHO model for an air mixture at Mach 6 and quantifying its influence on a pure oxygen gas flow at Mach 16. The gas mixture study suggests the predictions for the two vibrational models agree very well for four flow properties along the stagnation streamline. The pure oxygen gas study indicates a different topology of the vibrational temperature flow fields when calculated with an aHO model, which can be attributed to the increased Mach number relative to the air mixture case. When an aHO model is considered, the internal modes along the stagnation streamline result in a lower peak temperature that is closer to the surface of the cylinder. The inclusion of the electronic mode of the molecules amplifies this behaviour and results in a significantly lower temperature in the thermal equilibrium state. The surface heat flux and surface pressure appear to be less impacted by the two vibrational models.

Implementation of floating-point arithmetic with consistent rounding is a critical component of many quantum algorithms. Quantum circuit implementations for squaring and division serve as examples here. This work was motivated by ongoing work in developing quantum algorithms for scientific and engineering computing applications, where this type of arithmetic often forms part of the algorithm. A key feature of the work is the use of a reduced-precision floating-point representation of real data specifically designed for near-term future quantum computing hardware with a limited number of qubits (e.g., less than 100) and with an increased level of fault tolerance as compared to current quantum computing hardware. The quantum circuit implementations of the squaring of a floating-point number and the division of two floating-point numbers are detailed here, highlighting similarities in the quantum circuit implementation for the logical steps required for rounding-to-nearest in line with the IEEE 754 standard for the two arithmetic operations. This similarity is an important feature regarding future work where an automated generation of this type of quantum circuit from a set of standard modules and circuit templates is employed.

As the field of quantum computing grows, novel algorithms which take advantage of quantum phenomena need to be developed. As we are currently in the NISQ (noisy intermediate scale quantum) era, quantum algorithm researchers cannot reliably test their algorithms on real quantum hardware, which is still too limited. Instead, quantum computing simulators on classical computing systems are used. In the quantum circuit model, quantum bits (qubits) are operated on by quantum gates. A quantum circuit is a sequence of such quantum gates operating on some number of qubits. A quantum gate applied to a qubit can be controlled by other qubits in the circuit. This applies the gate only to the states which satisfy the required control qubit state. We particularly target FPGAs as our main simulation platform, as these offer potential energy savings when compared to running simulations on CPUs/GPUs. In this work, we present a memory access pattern to optimise the number of iterations that need to be scheduled to execute a quantum gate such that only the iterations which access the required pairs (determined according to the control qubits imposed on the gate) are scheduled. We show that this approach results in a significant reduction in the time required to simulate a gate for each added control qubit. We also show that this approach benefits the simulation time on FPGAs more than CPUs and GPUs and allows to outperform both CPU and GPU platforms in terms of energy efficiency, which is the main factor for scalability of the simulations.

We discuss the viability of ensemble simulations of fluid flows on quantum computers. The basic idea is to formulate a functional Liouville equation for the probability distribution of the flow field configuration and recognize that, due to its linearity, such an equation is in principle more amenable to quantum computing than the dynamic equations of fluid motion. After suitable marginalization and associated closure, the Liouville approach is shown to require several hundreds of logical qubits, hence calling for a major thrust in current noise correction and mitigation techniques.

Vehicles undergoing hypersonic speed experience extreme aerothermodynamic conditions. Real gas effects cannot be neglected, and thus internal degrees of freedom of molecules being partially/fully excited must be carefully predicted in order to accurately capture the physics of the flowfield. Within direct simulation Monte Carlo solvers, a harmonic oscillator (HO) model, where the quantum levels are evenly spaced, is typically used for vibrational energy. A more realistic model is an anharmonic oscillator (aHO), in which the energy between quantum levels is not evenly spaced. In this work, the Morse-aHO model is compared against HO. The Morse-aHO model is implemented in the dsmcFoam+ solver, and the numerical results are in excellent agreement with analytical and potential energy surface solutions for the partition function, mean vibrational energy, and degrees of freedom. A method for measuring the vibrational temperature of the gas when using the anharmonic model in a direct simulation Monte Carlo solver is presented, which is essential for returning macroscopic fields. For important thermophysical properties of molecular oxygen, such as the specific heat capacity, it is shown that the aHO and HO models begin to diverge at temperatures above 1000 K, making the use of HO questionable for all but low-enthalpy flows. For the same gas, including the electronic energy mode significantly improves the accuracy of the specific heat prediction, compared to experimental data, for temperatures above 2000 K. For relaxation from a state of thermal nonequilibrium, it is shown that the aHO model results in a slightly lower equilibrium temperature. When applied to hypersonic flow over a cylinder, the aHO model results in a smaller shock standoff distance and lower peak temperatures.

We present a pedagogical introduction to the current state of quantum computing algorithms for the simulation of classical fluids. Different strategies, along with their potential merits and liabilities, are discussed and commented on.

As quantum computing technology continues to develop, the need for research into novel quantum algorithms is growing. However, such algorithms cannot yet be reliably tested on actual quantum hardware, which is still limited in several ways, including qubit coherence times, connectivity, and available qubits. To facilitate the development of novel algorithms despite this, simulators on classical computing systems are used to verify the correctness of an algorithm, and study its behaviour under different error models. In general, this involves operating on a memory space that grows exponentially with the number of qubits. In this work, we introduce quantum circuit transformations that allow for the construction of parameterised circuits for quantum algorithms. The parameterised circuits are in an ideal form to be processed by quantum compilation tools, such that the circuit can be partially evaluated prior to simulation, and a smaller specialised circuit can be constructed by eliminating fixed input qubits. We show significant reduction in the number of qubits for various quantum arithmetic circuits. Divide-by-n-bits quantum integer dividers are used as an example demonstration. It is shown that the complexity reduces from 4n+2 to 3n+2 qubits in the specialised versions. For quantum algorithms involving divide-by-8 arithmetic operations, a reduction by 2(8)=256 in required memory is achieved for classical simulation, reducing the memory required from 137 GB to 0.53 GB.

In this work, brownout simulations using both Lagrangian and Eulerian frames of reference are presented. The work compares results between these two methods and with experimental results. The numerical models used for the carrier and dispersed phases are presented along with the obtained results. Then, follows a description of the simulations performed for brownout clouds around aircraft at different flight configurations. Different flight configurations involve several thrust coefficients, taxiing speeds and the presence of the fuselage. Finally, analyses have been conducted on the influence on the computational efficiency of Eulerian and Lagrangian approaches, and the two models are compared in terms of parallel efficiency. Results show that Eulerian model can be more affordable in terms of computational cost.

while the third article constitutes a detailed review of existing work and prospects for quantum computing 15 for partial differential equations in structural mechanics.Focusing on the concept of quantum annealing, the article by Navamita Ray, Tirtha Banerjee, Balu 17 Nadiga and Satish Karra investigates the viability of using quantum annealers for the simulation of fluid 18 flows. In the literature, this approach has not been widely investigated. In their article, Ray et al. consider 19 the well-studied flow problem comprising the fully-developed pressure-driven flow between two infinite 20 flat plates, such that a linear, quasi one-dimensional problem results. Then, a framework is described to 2020)). Reviewing these algorithms certainly benefits a wider research community beyond computational structural mechanics.In summary, it is clear that the three articles cover a wide range of contributions in a very active area 49 of research. We hope that readers will enjoy reading the articles and will find these works useful and 50 stimulating.R.S prepared the initial version of this editorial, with further additions and edits by R.M.

The application of Quantum Computing (QC) to fluid dynamics simulation has developed into a dynamic research topic in recent years. With many flow problems of scientific and engineering interest requiring large computational resources, the potential of QC to speed-up simulations and facilitate more detailed modeling forms the main motivation for this growing research interest. Despite notable progress, many important challenges to creating quantum algorithms for fluid modeling remain. The key challenge of non-linearity of the governing equations in fluid modeling is investigated here in the context of lattice-based modeling of fluids. Quantum circuits for the D1Q3 (one-dimensional, three discrete velocities) Lattice Boltzmann model are detailed along with design trade-offs involving circuit width and depth. Then, the design is extended to a one-dimensional lattice model for the non-linear Burgers equation. To facilitate the evaluation of non-linear terms, the presented quantum circuits employ quantum computational basis encoding. The second part of this work introduces a novel, modular quantum-circuit implementation for non-linear terms in multi-dimensional lattice models. In particular, the evaluation of kinetic energy in two-dimensional models is detailed as the first step toward quantum circuits for the collision term of two- and three-dimensional Lattice Boltzmann methods. The quantum circuit analysis shows that with O(100) fault-tolerant qubits, meaningful proof-of-concept experiments could be performed in the near future.