10. H modeling#
For this modeling, we change the values of the dimensions of the bar, the level-set equation, as well as the mesh. Boundary conditions remain the same.
The geometric position of the chosen interface generates a configuration that is a prima facie unfavorable for the X- FEM method. However, with the new formulation of enrichment X- FEM [R7.02.12], we see that the conditioning of the problem is not degraded. And the precision of the solution is comparable to other models. It would even be possible to lower the analytical tolerances to the point of machine precision.
10.1. Characteristics of modeling#
For this modeling, the dimensional values of the bar are:
\(\mathit{Lx}=\mathrm{1m}\) and \(\mathit{Ly}=\mathrm{7m}\)
as well as the level-set equation, we consider here a plane interface with normal \(n\mathrm{=}{(\mathrm{1,1})}^{T}\) and passing through the point \(A\) with coordinates \((\mathrm{-}0.5(1\mathrm{-}\delta ),\text{}0.5)\).
The interface is introduced by an equation level set \(\mathit{LSN}\) (see Figure):
\(\mathit{LSN}\): \(x+y-\delta\)
Finally, we use the PLAN model of the THERMIQUE phenomenon.
10.2. Characteristics of the mesh#
The mesh includes 7 QUAD4 meshes. This choice makes it possible to ensure that there are « classical » elements (not X- FEM) at both ends of the bar (see Figure), and therefore to impose boundary conditions on nodes that do not carry enriched degrees of freedom.
Figure 10.2-1: H mesh and level-set position
10.3. 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, on the two nodes that constitute the « low plane » group and on the two nodes that constitute the « high plane » group (see Figure). Since these nodes are shared by classical and enriched elements, the Heaviside H1 degrees of freedom must be zero and the classical degrees of freedom TEMP must correspond to the physical temperature (\(\text{}\stackrel{ˉ}{T}{\text{}}^{\text{inf}}\) or \(\text{}\stackrel{ˉ}{T}{\text{}}^{\text{sup}}\)).
We then test the value of the degree of freedom TEMP of the temperature field at the outlet of POST_CHAM_XFEM, on the two nodes that constitute the « low plane » group and on the two nodes that constitute the « high plane » group (see Figure).
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 |
|
On the Gauss points above the interface - \(\mathit{TEMP}\) |
“ANALYTIQUE” |
“” |
20 |
|