This benchmark is taken from Donea and Huerta’s book [Donea and Huerta, 2003].
The domain is a unit square and the viscosity and density are set to 1.
The components of the gravity vector \(\mathbf g\) are prescribed as
Note that the pressure satisfies
\(\int_{\Omega} p \; \text{d}x = 0\). The gravity, pressure and velocity fields
are shown in Fig. 219 to Fig. 221.
The convergence of the numerical error of this benchmark has been analyzed by
changing the mesh refinement level in the input file, and results show that
the velocity shows cubic error convergence, while the pressure shows quadratic
convergence in the \(L_2\) norm, as expected when using the \(Q_2\times Q_1\)
element.