On the enforcement of discrete mass conservation in incompressible flow simulations with continuous velocity approximation (Q2869162)

The authors present numerical examples to compare the accuracy of Taylor-Hood finite elements with and without grad-div stabilization and Scott-Vogelius elements for discretizing the incompressible Navier-Stokes equations. The discrete mass conservation is discussed and it is shown that Scott-Vogelius elements yield better results for problems where the pressure is large. For a benchmark flow past a cylinder it is found that Scott-Vogelius elements and Taylor-Hood elements with grad-div stabilization give almost identical results for the drag and lift coefficients, while Taylor-Hood elements without stabilization yield poor results. Applications to a heated cavity problem using the Boussinesq approximation are also presented.NEWLINENEWLINEFor the entire collection see [Zbl 1264.65002].