Mesh independence

Three meshes, refinement ratios 1.51 and 1.53. The tank-wide quantities converge and the two codes coincide; the impact peak moves with the mesh in both, by more than they differ.

Three quantities against the cell count

front reaches H1 (s)

braeOpenFOAM

P1 impact peak (Pa)

braeOpenFOAM

peak kinetic energy (J)

braeOpenFOAM

The front's arrival and the tank's peak kinetic energy converge monotonically and the two codes coincide. The impact peak (the raw step value at P1) does not: it oscillates with the mesh in both codes, by more than they differ. OpenFOAM's 4.89 M run wrote its fields at 3 s and 6 s only, so its kinetic energy exists on two meshes.

Grid convergence index

After Celik et al. (2008), given only where the three values change monotonically and the fine pair differs by less than the coarse pair. With $\phi_1, \phi_2, \phi_3$ the values on the fine, medium and coarse mesh of $N_1 > N_2 > N_3$ cells, the refinement ratios and the differences are

r_{21}=\Bigl(\frac{N_1}{N_2}\Bigr)^{1/3}=1.53,\qquad r_{32}=\Bigl(\frac{N_2}{N_3}\Bigr)^{1/3}=1.51,\qquad \varepsilon_{21}=\phi_2-\phi_1,\quad \varepsilon_{32}=\phi_3-\phi_2

(1)

The apparent order $p$ solves

p=\frac{1}{\ln r_{21}}\,\Bigl\lvert\,\ln\Bigl\lvert\frac{\varepsilon_{32}}{\varepsilon_{21}}\Bigr\rvert+\ln\frac{r_{21}^{\,p}-s}{r_{32}^{\,p}-s}\Bigr\rvert,\qquad s=\operatorname{sgn}\frac{\varepsilon_{32}}{\varepsilon_{21}}

(2)

and gives the extrapolated value and the index of the fine mesh:

\phi_{\mathrm{ext}}=\frac{r_{21}^{\,p}\,\phi_1-\phi_2}{r_{21}^{\,p}-1},\qquad \mathrm{GCI}_{\mathrm{fine}}=\frac{1.25}{r_{21}^{\,p}-1}\,\Bigl\lvert\frac{\phi_1-\phi_2}{\phi_1}\Bigr\rvert

(3)

For brae 19 of 69 quantities qualify; the tank-wide ones do:

Quantity (brae)	0.4 M	1.37 M	4.89 M	Apparent order	Extrapolated	Index, fine mesh
Peak kinetic energy	746.8 J	763.6 J	773.5 J	1.37	785.9 J	2.0%
Peak momentum toward the box	−727.2	−735.0	−739.1 kg m/s	1.60	−743.4	0.72%
Front's arrival at H1	0.2420 s	0.2440 s	0.2450 s	1.71	0.2460 s	0.48%
Reservoir gauge H4, peak	0.5405 m	0.5472 m	0.5502 m	1.97	0.5525 m	0.52%

The front's arrival at H1 has the same index, 0.48%, in OpenFOAM. OpenFOAM's peak kinetic energy is 746.7 and 762.8 J on the two meshes where it exists.