High-Resolution Turbulence Modeling Using the HHL Algorithm for the Poisson Navier-Stokes Equations
By Taiki
This project explores how the Harrow-Hassidim-Lloyd (HHL) quantum algorithm can accelerate high-resolution turbulence simulations by solving linearized fluid equations, such as the pressure Poisson equation, on a quantum computer. Classical methods for solving these equations are computationally expensive, especially on high-resolution grids, which limits their scalability. The HHL algorithm, however, offers an exponential speedup for solving linear systems, making it a promising alternative to overcome these challenges.
My focus is on optimizing the HHL algorithm for fluid dynamics. By incorporating preconditioning techniques specifically designed for this problem, I aim to reduce the condition number of the pressure Poisson equation, improving computational efficiency. Additionally, by leveraging the sparsity and symmetry of these fluid equations, I work toward bridging the gap between quantum computing and turbulence modeling. My goal is to enable high-resolution simulations that were previously infeasible due to computational constraints.
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Proposal
The proposed research aims to investigate the application of quantum computing techniques, specifically the HHL (Harrow-Hassidim-Lloyd) algorithm, to enhance the solutions of the Pressure Poisson Equation (PPE) in computational fluid dynamics (CFD). The PPE is a fundamental partial differential equation that describes potential fields in various physical systems, including fluid flow. Classical methods for solving the PPE can be computationally expensive, especially for high-dimensional problems. This research seeks to leverage quantum algorithms to reduce computational time and improve resolution for turbulence modeling.