arXiv subjects

Sylvain Laizet

Publications and source records attributed to Sylvain Laizet.

At least 19 recordsLinked to original sources

arXiv2025

Spectral quantum algorithm for passive scalar transport in shear flows

The mixing of scalar substances in fluid flows by stirring and diffusion is ubiquitous in natural flows, chemical engineering, and microfluidic drug delivery. Here, we present a spectral quantum algorithm for scalar mixing by solving the advection-diffusion equation in a quantum computational fluid dynamics framework. The exact gate decompositions of the advection and diffusion operators in spectral space are derived. For all but the simplest one-dimensional flows, these operators do not commute. Therefore, we use operator splitting to construct quantum circuits capable of simulating arbitrary polynomial velocity profiles in multiple dimensions, such as the Blasius profile of a laminar boundary layer. Periodic, Neumann, and Dirichlet boundary conditions can be imposed with the appropriate quantum spectral transform. We evaluate the approach in statevector simulations of a Couette flow, plane Poiseuille flow, and a polynomial Blasius profile approximation. For an advection-diffusion problem in one dimension, we compare the time evolution of an ideal quantum simulation with those of real quantum computers with superconducting and trapped-ion qubits. The required number of two-qubit gates grows with the logarithm of the number of grid points raised to one higher power than the order of the polynomial velocity profile.

quant-ph↗

arXiv2025

Reinforcement Learning Increases Wind Farm Power Production by Enabling Closed-Loop Collaborative Control

Traditional wind farm control operates each turbine independently to maximize individual power output. However, coordinated wake steering across the entire farm can substantially increase the combined wind farm energy production. Although dynamic closed-loop control has proven effective in flow control applications, wind farm optimization has relied primarily on static, low-fidelity simulators that ignore critical turbulent flow dynamics. In this work, we present the first reinforcement learning (RL) controller integrated directly with high-fidelity large-eddy simulation (LES), enabling real-time response to atmospheric turbulence through collaborative, dynamic control strategies. Our RL controller achieves a 4.30% increase in wind farm power output compared to baseline operation, nearly doubling the 2.19% gain from static optimal yaw control obtained through Bayesian optimization. These results establish dynamic flow-responsive control as a transformative approach to wind farm optimization, with direct implications for accelerating renewable energy deployment to net-zero targets.

physics.flu-dyn↗

arXiv2025

Variational quantum algorithm based on Lagrange polynomial encoding to solve differential equations

Differential equations (DEs) serve as the cornerstone for a wide range of scientific endeavors, their solutions weaving through the core of diverse fields such as structural engineering, fluid dynamics, and financial modeling. DEs are notoriously hard to solve, due to their intricate nature, and finding solutions to DEs often exceeds the capabilities of traditional computational approaches. Recent advances in quantum computing have triggered a growing interest from researchers for the design of quantum algorithms for solving DEs. In this work, we introduce two different architectures of a novel variational quantum algorithm (VQA) with Lagrange polynomial encoding in combination with derivative quantum circuits using the Hadamard test differentiation to approximate the solution of DEs. To demonstrate the potential of our new VQA, two well-known ordinary differential equations are used: the damped mass-spring system from a given initial condition and the Poisson equation for periodic, Dirichlet, and Neumann boundary conditions. It is shown that the proposed new VQA has a reduced gate complexity compared to previous variational quantum algorithms, for a similar or better quality of the solution.

quant-ph↗

arXiv2025

Quantum Algorithm for the Advection-Diffusion Equation by Direct Block Encoding of the Time-Marching Operator

A quantum algorithm for simulating multidimensional scalar transport problems using a time-marching strategy is presented. A direct unitary block encoding of the explicit time-marching operator is constructed, resulting in the intrinsic success probability of the squared solution norm without the need for amplitude amplification, thereby retaining a linear dependence on the simulation time. The algorithm separates the explicit time-marching operator into an advection-like component and a corrective shift operator. The advection-like component is mapped to a Hamiltonian simulation and combined with the shift operator through the linear combination of unitaries algorithm. State-vector simulations of a scalar transported in a steady two-dimensional Taylor-Green vortex support the theoretical findings.

quant-ph↗

arXiv2024

A Distributed-memory Tridiagonal Solver Based on a Specialised Data Structure Optimised for CPU and GPU Architectures

Various numerical methods used for solving partial differential equations (PDE) result in tridiagonal systems. Solving tridiagonal systems on distributed-memory environments is not straightforward, and often requires significant amount of communication. In this article, we present a novel distributed-memory tridiagonal solver algorithm, DistD2-TDS, based on a specialised data structure. DistD2-TDS algorithm takes advantage of the diagonal dominance in tridiagonal systems to reduce the communications in distributed-memory environments. The underlying data structure plays a crucial role for the performance of the algorithm. First, the data structure improves data localities and makes it possible to minimise data movements via cache blocking and kernel fusion strategies. Second, data continuity enables a contiguous data access pattern and results in efficient utilisation of the available memory bandwidth. Finally, the data layout supports vectorisation on CPUs and thread level parallelisation on GPUs for improved performance. In order to demonstrate the robustness of the algorithm, we implemented and benchmarked the algorithm on CPUs and GPUs. We investigated the single rank performance and compared against existing algorithms. Furthermore, we analysed the strong scaling of the implementation up to 384 NVIDIA H100 GPUs and up to 8192 AMD EPYC 7742 CPUs. Finally, we demonstrated a practical use case of the algorithm by using compact finite difference schemes to solve a 3D non-linear PDE. The results demonstrate that DistD2 algorithm can sustain around 66% of the theoretical peak bandwidth at scale on CPU and GPU based supercomputers.

cs.DC↗

arXiv2024

Multi-Fidelity Bayesian Optimisation of Wind Farm Wake Steering using Wake Models and Large Eddy Simulations

Improving the power output from wind farms is vital in transitioning to renewable electricity generation. However, in wind farms, wind turbines often operate in the wake of other turbines, leading to a reduction in the wind speed and the resulting power output whilst also increasing fatigue. By using wake steering strategies to control the wake behind each turbine, the total wind farm power output can be increased. To find optimal yaw configurations, typically analytical wake models have been utilised to model the interactions between the wind turbines through the flow field. In this work we show that, for full wind farms, higher-fidelity computational fluid dynamics simulations, in the form of large eddy simulations, are able to find more optimal yaw configurations than analytical wake models. This is because they capture and exploit more of the physics involved in the interactions between the multiple turbine wakes and the atmospheric boundary layer. As large eddy simulations are much more expensive to run than analytical wake models, a multi-fidelity Bayesian optimisation framework is introduced. This implements a multi-fidelity surrogate model, that is able to capture the non-linear relationship between the analytical wake models and the large eddy simulations, and a multi-fidelity acquisition function to determine the configuration and fidelity of each optimisation iteration. This allows for fewer configurations to be evaluated with the more expensive large eddy simulations than a single-fidelity optimisation, whilst producing comparable optimisation results. The same total wind farm power improvements can then be found for a reduced computational cost.

physics.flu-dyn↗

arXiv2024

Quantum Algorithm for Solving the Advection Equation using Hamiltonian Simulation

A quantum algorithm for solving the advection equation by embedding the discrete time-marching operator into Hamiltonian simulations is presented. One-dimensional advection can be simulated directly since the central finite difference operator for first-order derivatives is anti-Hermitian. Here, this is extended to industrially relevant, multi-dimensional flows with realistic boundary conditions and arbitrary finite difference stencils. A single copy of the initial quantum state is required and the circuit depth grows linearly with the required number of time steps, the sparsity of the time-marching operator and the inverse of the allowable error. Statevector simulations of a scalar transported in a two-dimensional channel flow and lid-driven cavity configuration are presented as a proof of concept of the proposed approach.

quant-ph↗

arXiv2024

Asymptotic scaling laws for periodic turbulent boundary layers and their numerical simulation up to Re_theta = 8300

We provide a rigorous analysis of the self-similar solution of the temporal turbulent boundary layer, recently proposed in [2], in which a body force is used to maintain a statistically steady turbulent boundary layer with periodic boundary conditions in the streamwise direction. We derive explicit expressions for the forcing amplitudes which can maintain such flows, and identify those which can hold either the displacement thickness or the momentum thickness equal to unity. This opens the door to the first main result of the paper, which is to prove upper bounds on skin friction for the temporal turbulent boundary layer. We use the Constantin-Doering-Hopf bounding method to show, rigorously, that the skin friction coefficient for periodic turbulent boundary layer flows is bounded above by a uniform constant which decreases asymptotically with Reynolds number. This asymptotic behaviour is within a logarithmic correction of well-known empirical scaling laws for skin friction. This gives the first evidence, applicable at asymptotically high Reynolds numbers, to suggest that the self-similar solution of the temporal turbulent boundary layer exhibits statistical similarities with canonical, spatially evolving, boundary layers. Furthermore, we show how the identified forcing formula implies an alternative, and simpler, numerical implementation of periodic boundary layer flows. We give a detailed numerical study of this scheme presenting direct numerical simulations up to Re_theta = 2000 and implicit large-eddy simulations up to Re_theta = 8300, and show that these results compare well with data from canonical spatially evolving boundary layers at equivalent Reynolds numbers.

physics.flu-dyn↗

arXiv2024

Quantum Computing for nonlinear differential equations and turbulence

A large spectrum of problems in classical physics and engineering, such as turbulence, is governed by nonlinear differential equations, which typically require high-performance computing to be solved. Over the past decade, however, the growth of classical computing power has slowed down because the miniaturisation of chips has been approaching the atomic scale. This is marking an end to Moore's law, which calls for a new computing paradigm: Quantum computing is a prime candidate. In this paper, we offer a perspective on the current challenges that need to be overcome in order to use quantum computing for the simulation of nonlinear dynamics. We review and discuss progress in the development of both quantum algorithms for nonlinear equations and quantum hardware. We propose pairings between quantum algorithms for nonlinear equations and quantum hardware concepts. These avenues open new opportunities for the simulation of nonlinear systems and turbulence.

physics.flu-dyn↗

arXiv2023

Unsupervised Random Quantum Networks for PDEs

Classical Physics-informed neural networks (PINNs) approximate solutions to PDEs with the help of deep neural networks trained to satisfy the differential operator and the relevant boundary conditions. We revisit this idea in the quantum computing realm, using parameterised random quantum circuits as trial solutions. We further adapt recent PINN-based techniques to our quantum setting, in particular Gaussian smoothing. Our analysis concentrates on the Poisson, the Heat and the Hamilton-Jacobi-Bellman equations, which are ubiquitous in most areas of science. On the theoretical side, we develop a complexity analysis of this approach, and show numerically that random quantum networks can outperform more traditional quantum networks as well as random classical networks.

quant-ph↗

arXiv2023

FR3D: Three-dimensional Flow Reconstruction and Force Estimation for Unsteady Flows Around Extruded Bluff Bodies via Conformal Mapping Aided Convolutional Autoencoders

In many practical fluid dynamics experiments, measuring variables such as velocity and pressure is possible only at a limited number of sensor locations, \textcolor{black}{for a few two-dimensional planes, or for a small 3D domain in the flow}. However, knowledge of the full fields is necessary to understand the dynamics of many flows. Deep learning reconstruction of full flow fields from sparse measurements has recently garnered significant research interest, as a way of overcoming this limitation. This task is referred to as the flow reconstruction (FR) task. In the present study, we propose a convolutional autoencoder based neural network model, dubbed FR3D, which enables FR to be carried out for three-dimensional flows around extruded 3D objects with different cross-sections. An innovative mapping approach, whereby multiple fluid domains are mapped to an annulus, enables FR3D to generalize its performance to objects not encountered during training. We conclusively demonstrate this generalization capability using a dataset composed of 80 training and 20 testing geometries, all randomly generated. We show that the FR3D model reconstructs pressure and velocity components with a few percentage points of error. Additionally, using these predictions, we accurately estimate the Q-criterion fields as well lift and drag forces on the geometries.

physics.flu-dyn↗

arXiv2022

Investigating Bayesian optimization for expensive-to-evaluate black box functions: Application in fluid dynamics

Bayesian optimization provides an effective method to optimize expensive-to-evaluate black box functions. It has been widely applied to problems in many fields, including notably in computer science, e.g. in machine learning to optimize hyperparameters of neural networks, and in engineering, e.g. in fluid dynamics to optimize control strategies that maximize drag reduction. This paper empirically studies and compares the performance and the robustness of common Bayesian optimization algorithms on a range of synthetic test functions to provide general guidance on the design of Bayesian optimization algorithms for specific problems. It investigates the choice of acquisition function, the effect of different numbers of training samples, the exact and Monte Carlo based calculation of acquisition functions, and both single-point and multi-point optimization. The test functions considered cover a wide selection of challenges and therefore serve as an ideal test bed to understand the performance of Bayesian optimization to specific challenges, and in general. To illustrate how these findings can be used to inform a Bayesian optimization setup tailored to a specific problem, two simulations in the area of computational fluid dynamics are optimized, giving evidence that suitable solutions can be found in a small number of evaluations of the objective function for complex, real problems. The results of our investigation can similarly be applied to other areas, such as machine learning and physical experiments, where objective functions are expensive to evaluate and their mathematical expressions are unknown.

cs.LG↗

arXiv2022

Direct numerical simulations of shocklet-containing turbulent channel counter-flows

Counter-flow or counter-current configurations can maintain high turbulence intensities and exhibit a significant level of mixing. We have previously introduced a wall-bounded counter-flow turbulent channel configuration (Physical Review Fluids, 6(9), p.094603.) as an efficient framework to study compressibility effects on turbulence. Here, we extend our previous direct numerical simulation study to a relatively higher Mach number (M=0.7) to investigate strong compressibility effects (also by reducing the Prandtl number from Pr=0.7 to 0.2), and the formation and evolution of unsteady shocklet structures. It is found that the configuration is able to produce highly turbulent flows with embedded shocklets and significant asymmetry in probability density functions of dilatation. A peak turbulent Mach number close to unity is obtained, for which the contribution of the dilatational dissipation to total dissipation is nevertheless found to be limited to 6%.

physics.flu-dyn↗

arXiv2022

Deep learning fluid flow reconstruction around arbitrary two-dimensional objects from sparse sensors using conformal mappings

The usage of neural networks (NNs) for flow reconstruction (FR) tasks from a limited number of sensors is attracting strong research interest, owing to NNs' ability to replicate high dimensional relationships. Trained on a single flow case for a given Reynolds number or over a reduced range of Reynolds numbers, these models are unfortunately not able to handle flows around different objects without re-training. We propose a new framework called Spatial Multi-Geometry FR (SMGFR) task, capable of reconstructing fluid flows around different two-dimensional objects without re-training, mapping the computational domain as an annulus. Different NNs for different sensor setups (where information about the flow is collected) are trained with high-fidelity simulation data for a Reynolds number equal to approximately $300$ for 64 objects randomly generated using Bezier curves. The performance of the models and sensor setups are then assessed for the flow around 16 unseen objects. It is shown that our mapping approach improves percentage errors by up to 15\% in SMGFR when compared to a more conventional approach where the models are trained on a Cartesian grid, and achieves errors under 3\%, 10\% and 30\% for pressure, velocity and vorticity fields predictions, respectively. Finally, SMGFR is extended to predictions of snapshots in the future, introducing the Spatio-temporal MGFR (STMGFR) task. A novel approach is developed for STMGFR involving splitting DNNs into a spatial and a temporal component. We demonstrate that this approach is able to reproduce, in time and in space, the main features of flows around arbitrary objects.

physics.flu-dyn↗

arXiv2021

Poisson CNN: Convolutional neural networks for the solution of the Poisson equation on a Cartesian mesh

The Poisson equation is commonly encountered in engineering, for instance in computational fluid dynamics (CFD) where it is needed to compute corrections to the pressure field to ensure the incompressibility of the velocity field. In the present work, we propose a novel fully convolutional neural network (CNN) architecture to infer the solution of the Poisson equation on a 2D Cartesian grid with different resolutions given the right hand side term, arbitrary boundary conditions and grid parameters. It provides unprecedented versatility for a CNN approach dealing with partial differential equations. The boundary conditions are handled using a novel approach by decomposing the original Poisson problem into a homogeneous Poisson problem plus four inhomogeneous Laplace sub-problems. The model is trained using a novel loss function approximating the continuous $L^p$ norm between the prediction and the target. Even when predicting on grids denser than previously encountered, our model demonstrates encouraging capacity to reproduce the correct solution profile. The proposed model, which outperforms well-known neural network models, can be included in a CFD solver to help with solving the Poisson equation. Analytical test cases indicate that our CNN architecture is capable of predicting the correct solution of a Poisson problem with mean percentage errors below 10%, an improvement by comparison to the first step of conventional iterative methods. Predictions from our model, used as the initial guess to iterative algorithms like Multigrid, can reduce the RMS error after a single iteration by more than 90% compared to a zero initial guess.

physics.comp-ph↗

arXiv2021

Lagrangian Coherent Track Initialisation (LCTI)

Advances in time-resolved Particle Tracking Velocimetry (4D-PTV) techniques have been consistently revealed more accurate Lagrangian particle motions. A novel track initialisation technique as a complementary part of 4D-PTV, based on local temporal and spatial coherency of neighbour trajectories, is proposed. The proposed Lagrangian Coherent Track Initialisation (LCTI) applies physics-based Finite Time Lyapunov Exponent (FTLE) to build four frame coherent tracks. We locally determine the boundaries (i.e., ridges) of Lagrangian Coherent Structures (LCS) among neighbour trajectories by using FTLE to distinguish clusters of coherent motions. To evaluate the proposed technique, we created an open-access synthetic Lagrangian and Eulerian dataset of the wake downstream of a smooth cylinder at a Reynolds number equal to 3900 obtained from 3D Direct Numerical Simulation (DNS). The dataset is available to the public. Performance of the proposed method based on three characteristic parameters, temporal scale, particle concentration (i.e., density), and noise ratio, showed robust behaviour in finding true tracks compared to the recent initialisation algorithms. Sensitivity of LCTI to the number of untracked and wrong tracks are also discussed. We address the capability of using the proposed method as a function of a 4D-PTV scheme in the Lagrangian Particle Tracking challenge for a flow with high particle densities. Finally, the LCTI behaviour was assessed in a real jet impingement experiment. LCTI was found to be a reliable tracking tool in complex flow motions, with a strength revealed for flows with high particle concentrations.

physics.flu-dyn↗

arXiv2019

Flows Over Periodic Hills of Parameterized Geometries: A Dataset for Data-Driven Turbulence Modeling From Direct Simulations

Computational fluid dynamics models based on Reynolds-averaged Navier--Stokes equations with turbulence closures still play important roles in engineering design and analysis. However, the development of turbulence models has been stagnant for decades. With recent advances in machine learning, data-driven turbulence models have become attractive alternatives worth further explorations. However, a major obstacle in the development of data-driven turbulence models is the lack of training data. In this work, we survey currently available public turbulent flow databases and conclude that they are inadequate for developing and validating data-driven models. Rather, we need more benchmark data from systematically and continuously varied flow conditions (e.g., Reynolds number and geometry) with maximum coverage in the parameter space for this purpose. To this end, we perform direct numerical simulations of flows over periodic hills with varying slopes, resulting in a family of flows over periodic hills which ranges from incipient to mild and massive separations. We further demonstrate the use of such a dataset by training a machine learning model that predicts Reynolds stress anisotropy based on a set of mean flow features. We expect the generated dataset, along with its design methodology and the example application presented herein, will facilitate development and comparison of future data-driven turbulence models.

physics.flu-dyn↗

arXiv2018

A model under location uncertainty to predict the mean velocity in wall bounded flows

To date no satisfying model exists to explain the mean velocity profile within the whole turbulent layer of canonical wall bounded flows. We propose a modification of the velocity profile expression that ensues from a recently proposed stochastic representation of fluid flows dynamics. This modeling, called modeling under location uncertainty introduces in a rigorous way a subgrid term generalizing the eddy-viscosity assumption and an eddy-induced advection term resulting from turbulence inhomogeneity. This latter term gives rise to a theoretically well-grounded model for the transitional zone between the viscous sublayer and the turbulent sublayer. An expression of the small-scale velocity component is also provided in the viscous zone. Numerical assessment of the results are provided for turbulent boundary layer flows, for pipe flows and channel flows at various Reynolds numbers.

physics.flu-dyn↗