An efficient algorithm for the numerical integration of the incompressible Navier-Stokes equations for turbulent flows

Despite the current increase in computing power, Direct Numerical Simulations (DNS) of turbulent flows of industrial interest are still out of reach and more efficient algorithms are necessary to obtain accurate results in a satisfactory amount of time. The common projection method approach for the integration of the incompressible Navier-Stokes (NS) equations requires the onerous resolution of a Pressure Poisson Equation (PPE) to enforce the divergence-free constraint on the velocity field. Runge-Kutta methods ordinarily imply the resolution of the PPE multiple times for each time step, significantly increasing the computational cost. Throughout the years, various fast-projection (FPJ) methods trying to circumvent this drawback have been proposed. In this work, an analysis of the performances of a broad class of existing and newly derived FPJ methods is presented. The accuracy of the schemes is tested on benchmarks of increasing complexity. The analysis here presented revealed that, while the technique generally has second-order accuracy, a specific family of schemes can attain third-order accuracy. Turbulent channel flow, a more realistic wall-bounded configuration, is investigated to assess the performances of the schemes. The use of the fast-projection methods reduced by almost 26% the wall-clock time of the simulation