Loic Dewitte

Abstract:

Abstract Quantum computing (QC) has emerged as a new computational paradigm with the potential for exponential speedup in specific applications. However, current limitations of quantum technology, including decoherence, noise, and restricted qubit counts, pose significant challenges. In this work, we present a proof-of-concept for a hybrid quantum-classical Harmonic Balance (h-HB) solver for time-periodic flow problems. The method leverages the Quantum Fourier Transform (QFT) for Fourier coefficient computation, motivated by its theoretical exponential time-complexity advantage over the Fast Fourier Transform (FFT). We derive error bounds, analyze convergence, and directly compare the hybrid solver’s performance with a classical HB solver for a time-periodic flow problem modeled by the 2D Burgers equation. While practical quantum advantage remains beyond reach, our results demonstrate that the hybrid solver qualitatively reproduces classical solutions. This work provides valuable insights into quantum CFD for periodic flow problems, highlights key challenges, and lays the groundwork for future research toward solving the Navier-Stokes equations with quantum-assisted methods.

Abstract:

This paper explores the potential of quantum computing for computational fluid dynamics (CFD) applications, with a focus on turbomachinery CFD. A harmonic balance solver is developed for Burgers’ equation, in which discrete Fourier transforms are approximated using a hybrid quantum-classical algorithm based on the quantum Fourier transform (QFT). Three novel algorithms are presented to estimate Fourier coefficients, providing complete knowledge of their amplitudes and phases, which is not possible with the standard QFT. Their behaviour is studied theoretically and numerically, under noiseless and noisy conditions. The algorithms, whose performance is limited by the extensive sampling required to achieve a small error on the Fourier coefficients, tolerate low levels of depolarising noise. The behaviour of the hybrid solver is investigated for a baseline case with a Reynolds number of 1000, 7 harmonics and 100 grid cells, using the best performing algorithm in a noiseless setting with up to 10^8 samples per QFT. Residuals decrease until errors introduced by statistical uncertainty dominate the total error on the solution. Nevertheless, the hybrid solutions match the classical one closely, with RMS residuals as low as 10^{–4}. The impact of several solver parameters on convergence and solution quality is also assessed, including the effect of noise. Although the latter rapidly degrades the solution, the solver achieves satisfactory approximations to the classical solution with 0.001% of depolarising noise. Without seeking to demonstrate a quantum advantage, this work offers valuable insights into the opportunities and challenges of quantum computing, helping readers understand how to design, implement and study quantum algorithms, as well as evaluate their impact in CFD applications.

Abstract:

In recent years, significant research efforts have focused on increasing power extraction using wake steering through yaw misalignment. In the current work, we evaluate the potential increase in annual energy production (AEP) for the Belgian offshore wind farm cluster using the FLORIS framework. The 2.2 GW Belgian cluster is an excellent test case to explore cooperation between wind farms as the concession zone is split into nine individual farms, resulting in a mix of intra- and inter-farm wakes to be considered in one of the largest wind farm clusters operational to date. Furthermore, the cluster high power density with relatively low turbine spacings is found to be responsive to wake mitigation strategies. Three different cost functions are compared. The first one is the complete cluster yaw angles optimization. The other two are farm-based optimizations seeking to maximize either their own AEP or the cluster AEP. Results show that all wind farms benefit from every optimization, encouraging operators to implement this strategy. The cluster optimization is found to be the one providing the best AEP increase for all wind farms individually and thus for the cluster. The farm-based function optimizing the cluster AEP is in second place, encouraging wind farm operators to collaborate for their own profits.