3. Modeling A

3.1. Characteristics of modeling

Mensi’s law of diffusion is used.

3.2. Characteristics of the mesh

The test piece is meshed using 80 QUAD4 evenly distributed. There is only one element in the height.

Number of knots: 162

Number of meshes and type: 80 QUAD4

3.3. Characteristics of time discretization

Initial Instant ( \(s\) )) **	Instant Final (:math:`s`**) **	Number of time steps
0	3600	10
3600	259 200	10
259 200	2 419 200	10
2 419 200	39 420 000	10
39,420,000	94,608,000	10
94 608 000	1 57 680 000	10

3.4. Tested sizes and results

Water concentration at point \(x\mathrm{=}0.0\):

Identification	Reference	Aster	\(\text{\%}\) difference
after 1 hour	128.80	128.80	2.21 10-14
after 3 days	128.80	128.80	-2.21 10-14
after 28 days	128.80	128.80	-3.67 10-5
after 1.25 years	117.49	117.49	117.76	0.231
after 3 years	105.06	105.38	0.307
after 5 years	96.77	97.09	0.332

Water concentration at point \(x\mathrm{=}0.04\):

Identification	Reference	Aster	\(\text{\%}\) difference
after 1 hour	128.80	128.80	1.31 10-13
after 3 days	128.80	128.80	-1.77 10-13
after 28 days	128.61	128.66	0.038
after 1.25 years	117.74	117.74	112.35	0.543
after 3 years	99.43	100.06	0.634
after 5 years	91.39	91.99	0.661

Water concentration at point \(x\mathrm{=}0.06\):

Identification	Reference	Aster	\(\text{\%}\) difference
after 1 hour	128.80	128.80	2.53 10-11
after 3 days	128.80	128.80	0.002
after 28 days	124.98	125.67	0.552
after 1.25 years	101.32	102.42	1.089
after 3 years	89.60	90.64	1.158
after 5 years	82.33	83.27	1.140

3.5. Comments

Here we check that the error committed is small since it is less than \(\text{1.5\%}\), which is entirely correct given the relatively crude time discretization used, especially at the end of the calculation.