Bubble-Enriched Least-Squares Finite Element Method for Transient Advective Transport

Table 4

Advection of cosine hill in rotation.

		CN-LSFEM		ST-LSFEM		BE-LSFEM		Improvements		Range of PCG iterations^*
Δt	Courant no.^‡	$U_{\min \hspace{0.17em}}$	$U_{\max \hspace{0.17em}}$	$U_{\min \hspace{0.17em}}$	$U_{\max \hspace{0.17em}}$	$U_{\min \hspace{0.17em}}$	$U_{\max \hspace{0.17em}}$	%redn. in $U_{\min \hspace{0.17em}}$	%gain in $U_{\max \hspace{0.17em}}$
2π/120	0.2618	$-$0.0265	0.9691	$-$0.0405	0.958	$-$0.0189	0.9769	28.8	0.81	7-8
2π/60	0.5236	$-$0.0615	0.9165	$-$0.1138	0.8872	$-$0.0270	0.9713	56.1	5.98	8-8
2π/30	1.047	$-$0.2009	0.8369	$-$0.2192	0.7398	$-$0.2129	0.8418	$-$5.97	0.6	15-16

^‡Courant number based on velocity of the peak.^*Range of PCG iterations/time step: number of iterations with one bubble—the number with six bubbles. % Reduction and % gain calculated on Crank-Nicolson LSFEM results as baseline.