An Implicit Staggered Hybrid Finite Volume/Finite Element Solver for the Incompressible Navier-Stokes Equations

Finite Element Methods for the Incompressible Navier-Stokes Equations

These notes are based on lectures given in a Short Course on Theoretical and Numerical Fluid Mechanics in Vancouver, British Columbia, Canada, July 27-28, 1996, and at several other places since then. They provide an introduction to recent developments in the numerical solution of the Navier-Stokes equations by the finite element method. The material is presented in eight sections:

Staggered discontinuous Galerkin methods for the incompressible Navier-Stokes equations

Article history: Received 20 May 2015 Received in revised form 5 August 2015 Accepted 18 August 2015 Available online 10 September 2015

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

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

An Adaptive Finite Element Method for the Incompressible Navier{stokes Equations on Time-dependent Domains

A Fast Poisson Solver for the Finite Difference Solution of the Incompressible Navier-Stokes Equations

In this paper, a fast direct solver for the Poisson equation on the half-staggered grid is presented. The Poisson equation results from the projection method of the finite difference solution of the incompressible Navier–Stokes equations. To achieve our goal, new algorithms for diagonalizing a semidefinite pair are developed. The fast solver can also be extended to the three-dimensional case. T...