Quantum algorithm for the Navier–Stokes equations by using the streamfunction-vorticity formulation and the lattice Boltzmann method

In this paper, a new algorithm for solving the Navier–Stokes equations (NSE) on quantum device is presented. For fluid flow equations, stream function-vorticity formulation adopted, while lattice Boltzmann method (LBM) utilized corresponding system of numerically one time step. Following nature method, proposed consists five major sections: initialization, collision, propagation, boundary condition implementation and calculation macroscopic quantities. The collision step quantumly implemented by applying standard-form encoding approach, walk procedure applied propagation using IBM’s computing software development framework Qiskit, verification purposes, two-dimensional (2D) cavity simulated compared with classical code.