Quantum-enriched large-eddy simulation with the incompressible Schrödinger flow

We propose a hybrid quantum-classical method, the quantum-enriched large-eddy simulation (QELES), for simulating turbulence. The QELES combines the large-scale motion of the large-eddy simulation (LES) and the subgrid motion of the incompressible Schrödinger flow (ISF). The ISF is a possible way to be simulated on a quantum computer, and it generates subgrid scale turbulent structures to enrich the LES field. The enriched LES field can be further used in turbulent combustion and multi-phase flows in which the subgrid scale motion plays an important role. As a conceptual study, we perform the simulations of ISF and LES separately on a classical computer to simulate decaying homogeneous isotropic turbulence. Then, the QELES velocity is obtained by the time matching and the spectral blending methods. The QELES achieves significant improvement in predicting the energy spectrum, probability density functions of velocity and vorticity components, and velocity structure functions, and reconstructs coherent small-scales vortices in the direct numerical simulation (DNS). On the other hand, the vortices in the QELES are less elongated and tangled than those in the DNS, and the magnitude of the third-order structure function in the QELES is less than that in the DNS, due to the different constitutive relations in the viscous flow and ISF.