A little more on stabilized Q1Q1 for transient viscous incompressible flow

In an attempt to overcome some of the well-known 'problems' with the Q i P 0 element, we have devised two 'stabilized' versions of the Q 1 Q 1 element, one based on a semi-implicit approximate projection method and the other based on a simple forward Euler technique. While neither one conserves mass in the most desirable manner, both generate a velocity field that is usually 'close enough' to divergence-free. After attempting to analyse the two algorithms, each of which includes some ad hoc 'enhancements', we present some numerical results to show that they both seem to work well enough. Finally, we point out that any projection method that uses a 'pressure correction' approach is inherently limited to time-accurate simulations and, even if treated fully implicitly, is inappropriate for seeking steady states via large time steps.

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