Stabilizing poor mass conservation in incompressible flow problems with large irrotational forcing and application to thermal convection
- Galvin, Keith
- Linke, Alexander
- Rebholz, Leo
- Wilson, Nicholas
2010 Mathematics Subject Classification
- 76D05 76M10
- mixed finite elements, incompressible Navier-Stokes equations, poor mass conservation, grad-div stabilization, natural convection, Scott-Vogelius element
We consider the problem of poor mass conservation in mixed finite element algorithms for flow problems with large rotation-free forcing in the momentum equation. We provide analysis that suggests for such problems, obtaining accurate solutions necessitates either the use of pointwise divergence-free finite elements (such as Scott-Vogelius), or heavy grad-div stabilization of weakly divergence-free elements. The theory is demonstrated in numerical experiments for a benchmark natural convection problem, where large irrotational forcing occurs with high Rayleigh numbers.
- Comput. Methods Appl. Mech. Engrg., 237--240 (2012) pp. 166--176.