Energy Stable and Momentum Conserving Hybrid Finite Element Method for the Incompressible Navier–Stokes Equations

A hybrid method for the incompressible Navier–Stokes equations is presented. The ethod inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods hen momentum advection becomes significant, equal-order interpolations can be used for the velocity nd pressure fields, and mass can be conserved locally. Using continuous...

Energy stable finite element schemes and their applications to two-fluid flow problems

We present energy stable finite element schemes for two-fluid problems with interfacial tension. The interface is captured by solving numerically ordinary differential equations and the interface tension is brought in into the weak formulation of the finite element scheme. Some numerical results of rising bubble problems show the robustness and...

On finite element variational multiscale methods for incompressible turbulent flows

Two realizations of finite element variational multiscale (VMS) methods for the simulation of incompressible turbulent flows are studied. The difference between the two approaches consists in the way the spaces for the large scales and the resolved small scales are chosen. The paper addresses issues of the implementation of these methods, the...