.... Assoc. Editor: Zhongquan Charlie Zheng. 23 01 2014 02 02 2015 09 03 2015 In this paper, we present a new shape optimization method by using sensitivities obtained from the Arbitrary Lagrangian–Eulerian (ALE) form of the Navier–Stokes equations. In the ALE description, the nodes...

...E. Sansone; C. Pellone; T. Maitre The noncavitating and cavitating flows over a cross-flow water turbine are simulated by using an unsteady Navier–Stokes formulation. For the cavitating flow case, a homogeneous mixture with a varying density is considered and one additional transport equation...

... the standard form found in the classical Navier–Stokes equations, but generally follows the form suggested by Brenner (2005, “Navier-Stokes Revisited,” Physica A, 349(1–2), pp. 60–133) in a modification of Navier–Stokes necessary to successfully reproduce some experimentally measured phenomena...