WIAS Preprint No. 1408, (2009)

Collision in a cross-shaped domain --- A steady 2D Navier--Stokes example demonstrating the importance of mass conservation in CFD


  • Linke, Alexander
    ORCID: 0000-0002-0165-2698

2010 Mathematics Subject Classification

  • 35Q30 76D07 76M10

2008 Physics and Astronomy Classification Scheme

  • 47.10.ad


  • incompressible Navier-Stokes equations, mixed finite elements, poor mass conservation, numerical instability


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.

Appeared in

  • Comput. Methods Appl. Mech. Engrg., 198 (2009) pp. 3278--3286.

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