Session: 34-04 Computing architectures and solvers

Paper Number: 151210

Towards Quantum Computing for Turbomachinery CFD: Advancing Periodic Flow Simulations With Simplified Transport Equations 

Simulating turbulent flows in turbomachinery is a demanding task in computational engineering due to the complex interactions of nonlinearities and energy transfer phenomena, at high Reynolds number. Scale resolved approaches, such as Direct Numerical Simulation and Large Eddy Simulation, are impractical for most industrial applications, constrained by the computational limits even of the most powerful classical computers, that rely on classical physics and Boolean logic. Quantum computers, on the other hand, operate under the quantum mechanical principles of superposition and entanglement, allowing to process information nondeterministically and operate simultaneously over an exponentially large set of quantum states (quantum parallelism) - with theoretical exponential speedup in specific problems. Our research is seeking to explore these quantum principles to address periodic flow problems, aiming at more refined simulations of unsteady turbomachinery phenomena in larger computational domains. Due to the early emergent technology readiness level of current quantum hardware, we focus on the theoretical analysis and simulation of our quantum algorithms on classical machines.  

As the foundation of our numerical solver, we adopt the Nonlinear Harmonic Balance (NHB) method, commonly used for simulating unsteady flows in turbomachinery, requiring only a few harmonics to achieve engineering accuracy. In particular, we study the Quantum Fourier Transform (QFT) as a potential replacement for the Fast Fourier Transform, exploiting its theoretical exponential reduction in time complexity. To this end we developed a hybrid classical-quantum NHB (h-NHB) solver, which has been tested through classical simulation using IBM's Qiskit library for noiseless computations without decoherence of quantum states. 

We have derived upper bounds on the error of our QFT algorithm, studied its convergence capability and analyzed the effects of quantum nondeterminism. The h-NHB solver has shown promising results when applied to 1D and 2D unsteady Burgers equations with periodic inlet conditions, being capable of reproducing qualitatively the time-responses predicted by classical solvers, including shock capturing. However, due to quantum nondeterminism, the h-NHB becomes a stochastic solver, leading to convergence stagnation (not divergence), which needs to be addressed. Additionally, we explored the effects of decoherence through quantum noise models, highlighting its negative impact on both the QFT and h-NHB solver’s convergence. The results obtained in this research provide a valuable outlook on quantum CFD and allow us to identify and characterize challenges and limitations that will steer our future research towards the solution of the Navier Stokes equations. 

Presenting Author: Gonçalo Das Neves Carneiro von Karman Institute for Fluid Dynamics

Presenting Author Biography: Gonçalo das Neves Carneiro began his research activity in the Mechanical Engineering Department of the Faculty of Engineering of the University of Porto, as a Master's student, developing p-type finite element models for the study of non-linear vibrations of damaged beams, achieving his first publication in an international scientific journal as first author. He earned his PhD in 2020, in the University of Porto, on the fields of Evolutionary Computation, Structural Optimization and Probabilistic Structural Mechanics.

From 2020 to 2023, he was an Invited Assistant Professor in the Mathematics Section of Faculty of Engineering of the Unviersity of Porto and was a postdoc researcher in the Associated Laboratory for Energy, Transport and Aeronautics. Since 2023, he integrates the Turbomachinery and Propulsion Department of the von Karman Institute for Fluid Dynamics, where he carries out research in the field of Quantum Computing applied to the numerical solution of transport equations in Fluid Dynamics.

Authors:

Gonçalo Das Neves Carneiro von Karman Institute for Fluid Dynamics
Loïc Dewitte Oxford Thermofluids Institute
Jérémie Roland QuIC, École Polytechnique de Bruxelles, Université libre de Bruxelles,
Wim Munters von Karman Institute for Fluid Dynamics
Frank Eulitz von Karman Institute for Fluid Dynamics