Robust Fully Explicit Method for Solving the Navier-Stokes Equations

Abstract The motion of viscous fluids is described by the Navier-Stokes equations. The inherent nonlinearity in the Navier-Stokes equations prevents us from the analytic solutions. This paper introduces a robust fully explicit method for numerically solving the discretized Navier-Stokes equations, applicable to various flow types without tuning parameters or artificial models. The numerical analysis results demonstrating the stability and the robustness of the proposed fully explicit method imply the discovery of the rigorous spatial integration of the Navier-Stokes equations over the subdomain uniquely defined for the discrete sampling points in the analysis domain. We anticipate that our findings could serve as a milestone to the comprehensive resolution of the millennium problem regarding the Navier-Stokes equations.