4. Implemented in Code_Aster

In order to eliminate temperature oscillations in space and time, the models AXIS_DIAG, PLAN_DIAG and 3D_ DIAG perform the diagonalization of the mass matrices during linear (THER_LINEAIRE) and non-linear (THER_NON_LINE) thermal calculations. To guarantee its effectiveness, we have seen that it must be carried out on linear elements.

In the case where the mesh is linear, the mass matrices are simply diagonalized by integration into the nodes.

The available models are therefore:

4.1. 2D modellings

Modeling	PLAN_DIAG	AXIS_DIAG
Mesh	Element	Element
TRIA3	THPLTL3	THAXTL3
QUAD4	THPLQL4	THAXQL4
SEG2	THPLSL2	THAXSL2

Comments on 2D elementary calculations:

For linear elements: the mass terms (matrix on the first member and vector on the second member) are lumped by integration at the nodes. The new elements have basic calculation options that are the same as the classical elements. So the only basic options changed are MASS_THER and CHAR_THER_EVOL.

In axisymmetry: if elements of the mesh touch the axis, you should not step into the nodes that are on the axis. It is therefore necessary to isolate this layer of elements and assign modeling AXIS to it.

4.2. 3D modeling

Modeling	3D_ DIAG
Mesh	Element
HEXA8	THER_HEXA8_D
PENTA6	THER_PENTA6_D
TETRA4	THER_TETRA4_D
QUAD4	THER_FACE4_D
TRIA3	THER_FACE3_D

Comments on 3D elementary calculations:

For linear elements: as in 2D, the mass terms (matrix on the 1st member and vector on the 2nd member) are lumped by integration at the nodes (3rd family of Gauss points).

We therefore currently only diagonalize linear 3D elements.

For 5-node pyramids, node integration has been tried but does not work well. Cf. [§3.1.1.3] (we don’t know if all extra-diagonal terms are negative). The “3D_ DIAG “modeling therefore does not exist for pyramids with 5 nodes. In any case, these elements are in the minority in a 3D mesh.