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

Understand

A new algorithm for solving the Navier-Stokes equations (NSE) on a quantum device is presented.

• For the fluid flow equations the stream function-vorticity formulation is adopted, while the lattice Boltzmann method (LBM) is utilized for solving the corresponding system of equations numerically for one time step.
• Following the nature of the lattice Boltzmann method, the proposed quantum algorithm consists of five major sections: initialization, collision, propagation, boundary condition implementation, and calculation of macroscopic quantities.
• The collision and boundary condition step is quantumly implemented by applying the standard-form encoding approach, while the quantum walk procedure is applied for the propagation step.