Quantum advantage for probability-density-function-based sub-grid scale and wall modeling

Recent advancements in quantum computing have shown limited advantages over classical computing for direct numerical simulation of turbulent flows. This talk explores a novel application of quantum computing for large-eddy simulation (LES), specifically focusing on sub-grid scale and wall modeling. We investigate the use of probability-density-function (PDF) based methods, which solve for the PDFs of unresolved eddies. While these methods provide realistic sub-grid information, they are often considered too computationally expensive due to the additional dimensions of the PDFs. However, quantum computing overcomes this challenge by encoding PDF information into qubits, thus achieving quantum advantage. As a proof of concept, we present results from Burgers turbulence and turbulent channel flow simulations.