Exact Variational Principles of 3-D Unseady Navier-Stokes Equations

摘要

As is well known, the search for the exact variational principles (VP) for the full Navier-Stokes equations of 3-D viscous flow is an extremely difficult, still open problem in fluid mechanics. Just recently this problem for the steady flow case has been successfully solved for the first time via a systematic reversed deduction approach incorporating a method of undetermined function. As a further development of that, two VP families are generated herein for the unsteady flow case, providing a new rigorous theoretical basis for the finite element analysis of unsteady viscous flow, especially for the direct numerical simulation (DNS) of turbulent flow.