Stable and time‐dissipative finite element methods for the incompressible Navier–Stokes equations in advection dominated flows

Abstract

AbstractThis paper examines a new Galerkin method with scaled bubble functions which replicates the exact artificial diffusion methods in the case of 1‐D scalar advection–diffusion and that leads to non‐oscillatory solutions as the streamline upwinding algorithms for 2‐D scalar advection–diffusion and incompressible Navier–Stokes. This method retains the satisfaction of the Babuska–Brezzi condition and, thus, leads to optimal performance in the incompressible limit. This method, when, combined with the recently proposed linear unconditionally stable algorithms of Simo and Armero (1993), yields a method for solution of the incompressible Navier–Stokes equations ideal for either diffusive or advection‐dominated flows. Examples from scalar advection–diffusion and the solution of the incompressible Navier–Stokes equations are presented.