Quantum-Inspired High-Fidelity Solver for Simulating Incompressible Two-Phase Turbulence

In Computational Fluid Dynamics (CFD), accurately computing two-phase incompressible turbulent flows is essential for many problems. Traditionally, the flow is solved using methods like finite difference and finite volume, coupled with a linear solver for pressure and velocity fields. However, these methods face limitations due to the curse of dimensionality: the ratio of the largest eddy to the Kolmogorov scale eddy is proportional to the Reynolds number raised to the power of 9/4, leading to a formidable increase in the grid number and computing resources required to fully resolve turbulence.

Inspired by quantum algorithms that mitigate the curse of dimensionality in many-body systems, we introduce a tensor networks-based method for simulating incompressible two-phase turbulence. In this approach, the velocities and pressure are encoded as matrix product states (MPS), while the finite difference scheme is implemented using matrix product operators (MPO). To simulate the interface between the two flow phases, we propose a tensor networks-based level set method. We enhance the computational performance by employing a cross-interpolation method to optimize the solving of the tensorized level-set equation and the re-initialization equation. Numerical experiments demonstrate that the quantum-inspired method achieves accuracy comparable to traditional methods and successfully captures complex two-phase turbulent structures with a significantly reduced data load size. Additionally, data analysis suggests potential speed-ups for complex multiphase turbulence cases under realistic conditions.