Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Doi
Abstract
In the numerical simulation of the incompressible Navier-Stokes
equations different numerical instabilities can occur. While instability in
the discrete velocity due to dominant convection and instability in the
discrete pressure due to a vanishing discrete LBB constant are well-known,
instability in the discrete velocity due to a poor mass conservation at high
Reynolds numbers sometimes seems to be underestimated. At least, when using
conforming Galerkin mixed finite element methods like the Taylor-Hood
element, the classical grad-div stabilization for enhancing discrete mass
conservation is often neglected in practical computations. Though simple
academic flow problems showing the importance of mass conservation are
well-known, these examples differ from practically relevant ones, since
specially designed force vectors are prescribed. Therefore we present a
simple steady Navier-Stokes problem in two space dimensions at Reynolds
number 1024, a colliding flow in a cross-shaped domain, where the instability
of poor mass conservation is studied in detail and where no force vector is
prescribed