Robust Fully Explicit Method for Solving the Navier-Stokes Equations

Abstract The motion of viscous fluids is described by the Navier-Stokes equations. Theinherent nonlinearity in the Navier-Stokes equations preventsus from the analyticsolutions. This paper introduces a robust fully explicit method for numericallysolving the discretized Navier-Stokes equations, applicable to various flow typeswithout tuning parameters or artificial models. The numerical analysis resultsdemonstrating the stability and the robustness of the proposedfully explicitmethod imply the discovery of the rigorous spatial integration of the Navier-Stokes equations over the subdomain uniquely defined for the discrete samplingpoints in the analysis domain. We anticipate that our findings could serve as amilestone to the comprehensive resolution of the millennium problem regardingthe Navier-Stokes equations.