12. J modeling#

This modeling is based on all the characteristics of the 2D reference problem described on page 2., except that axisymmetric modeling is considered. It is therefore a cylindrical bar, but the analytical solution described on page 4 remains valid for this problem.

12.1. Characteristics of modeling#

For this modeling, the bar is cylindrical and its dimensions are as follows:

  • radius \(\mathit{Lx}=\mathrm{0,5}m\)

  • height \(\mathit{Ly}=\mathrm{5m}\)

The interface is introduced halfway up the bar by a level set \(\mathit{LSN}\) equation:

\(\mathit{LSN}\): \(y\)

We use the AXIS model of the THERMIQUE phenomenon.

12.2. Characteristics of the mesh#

The mesh includes 5 TRIA3 meshes.

_images/10000201000000EB0000023FF4A3DC63BDBE1701.png

Figure 12.2-1: J mesh

12.3. Tested sizes and results#

We first test the values of the classical degrees of freedom TEMP and Heaviside H1 of the temperature field at the output of the THER_LINEAIRE operator, at the nodes located just below (2 knots) and above the interface (2 nodes).

Identification

Reference type

Reference value

Tolerance

All nodes just above the interface - \(\mathit{TEMP}\)

“ANALYTIQUE”

“”

20

0.1%

All nodes just below the interface - \(\mathit{TEMP}\)

“ANALYTIQUE”

“”

10

0.1%

All nodes located just below/above the interface - \(\mathit{H1}\)

“ANALYTIQUE”

5

0.1%

We then test the value of the degree of freedom TEMP of the temperature field at the outlet of POST_CHAM_XFEM, at the nodes located just below and above the interface.

Identification

Reference type

Reference value

Tolerance

All nodes just below the interface - \(\mathit{TEMP}\)

“ANALYTIQUE”

“”

10

0.1%

All nodes located just above the interface \(\mathit{TEMP}\) -

“ANALYTIQUE”

20

0.1%

Finally, we test the value of the TEMP component of the TEMP_ELGA field on the Gauss points located below and above the interface (cf. note page 6).

Identification

Reference type

Reference value

Tolerance

On the Gauss points below the interface - \(\mathit{TEMP}\)

“ANALYTIQUE”

“”

10

0.1%

On the Gauss points above the interface - \(\mathit{TEMP}\)

“ANALYTIQUE”

“”

20

0.1%