Implicit Hybrid Quantum-Classical CFD Calculations using the HHL Algorithm

Implicit methods are attractive for hybrid quantum-classical CFD solvers as the flow equations are combined into a single coupled matrix that is solved on the quantum device, leaving only the CFD discretisation and matrix assembly on the classical device. In this paper, an implicit hybrid solver is investigated using emulated HHL circuits. The hybrid solutions are compared with classical solutions including full eigen-system decompositions. A thorough analysis is made of how the number of qubits in the HHL eigenvalue inversion circuit affect the CFD solver's convergence rates. Loss of precision in the minimum and maximum eigenvalues have different effects and are understood by relating the corresponding eigenvectors to error waves in the CFD solver. An iterative feed-forward mechanism is identified that allows loss of precision in the HHL circuit to amplify the associated error waves. These results will be relevant to early fault tolerant CFD applications where every (logical) qubit will count. The importance of good classical estimators for the minimum and maximum eigenvalues is also relevant to the calculation of condition number for Quantum Singular Value Transformation approaches to matrix inversion

Evaluation of block encoding for sparse matrix inversion using QSVT

Three block encoding methods are evaluated for solving linear systems of equations using QSVT (Quantum Singular Value Transformation). These are ARCSIN, FABLE and PREPARE-SELECT. The performance of the encoders is evaluated using a suite of 30 test cases including 1D, 2D and 3D Laplacians and 2D CFD matrices. A subset of cases is used to characterise how the degree of the polynomial approximation to $1/x$ influences the performance of QSVT. The results are used to guide the evaluation of QSVT as the linear solver in hybrid non-linear pressure correction and coupled implicit CFD solvers. The performance of QSVT is shown to be resilient to polynomial approximation errors. For both CFD solvers, error tolerances of $10^{-2}$ are more than sufficient in most cases and in some cases $10^{-1}$ is sufficient. The pressure correction solver allows subnormalised condition numbers, $\kappa_s$, as low as half the theoretical values to be used, reducing the number of phase factors needed. PREPARE-SELECT encoding relies on a unitary decomposition, e.g. Pauli strings, that has significant classical preprocessing costs. Both ARCSIN and FABLE have much lower costs, particularly for coupled solvers. However, their subnormalisation factors, which are based on the rank of the matrix, can be many times higher than PREPARE-SELECT leading to more phase factors being needed. For both the pressure correction and coupled CFD calculations, QSVT is more stable than previous HHL results due to the polynomial approximation errors only affecting long wavelength CFD errors. Given that lowering $\kappa_s$ increases the success probability, optimising the performance of QSVT within a CFD code is a function of the number QSVT phase factors, the number of non-linear iterations and the number of shots. Although phase factor files can be reused, the time taken to generate them impedes scaling QSVT to larger test cases.Comment: 26 pages, 24 figure

Virtual certification of gas turbine engines - visualizing the DLR Rig250 compressor

High Performance Computing (HPC) critically underpins the design of aero-engines. With global emissions targets, engine designs require a fundamental change including designs utilizing sustainable aviation fuels and electric/hybrid flight. Virtual certification of designs with HPC is recognized as a key technology to meet these challenges, but require analysis on models with higher fidelity, using ultra-large scale executions. In this explanatory SC-SciVis showcase, we present results from time-accurate simulations of a 4.6B-element full 360-degree model of a production-representative gas turbine engine compressor, the Rig250 at DLR. This represents a grand challenge problem, at the fidelity for virtual certification standards. The results are achieved through Rolls-Royce’s Hydra CFD suite on ARCHER2. The compressor is visualized under off-design conditions, demonstrating flow contours of velocity, Mach number and iso-surfaces of vorticity. The level of detail and the HPC simulations leading to the visualizations demonstrate a step-change towards achieving virtual certification objectives under production settings

Adjoint harmonic sensitivities for forced response minimization

This paper presents an adjoint analysis for three-dimensional unsteady viscous flows aimed at the calculation of linear worksum sensitivities involved in turbomachinery forced response predictions. The worksum values are normally obtained from linear harmonic flow calculations but can also be computed using the solution to the adjoint of the linear harmonic flow equations. The adjoint method has a clear advantage over the linear approach if used within a rotor forced vibration minimization procedure which requires the structural response to a large number of different flow excitation sources characterized by a unique frequency and interblade phase angle. Whereas the linear approach requires a number of linear flow calculations at least equal to the number of excitation sources, the adjoint method reduces this cost to a single adjoint solution for each structural mode of rotor response. A practical example is given to illustrate the dramatic computational saving associated with the adjoint approach