Collision in a cross-shaped domain - A steady 2D Navier-Stokes example demonstrating the importance of mass conservation in CFD. (English) Zbl 1230.76028
Summary: 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 Ladyzhenskaya-Babuska-Brezzi (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.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
Keywords:
incompressible Navier-Stokes equations; mixed finite elements; poor mass conservation; numerical instabilityReferences:
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