Modeling A ==== Characteristics of modeling ---- The mesh is made with elements of the TRIA3 type. The calculation is done in isotropic stationary linear thermal with the operator THER_LINEAIRE in lumpé (modeling PLAN_DIAG). The spatial error maps for the pure residue indicator (ERTH_ELEM) are calculated. Beforehand it is necessary to have smoothed the heat flow from the Gauss points to the nodes (FLUX_ELNO) and, to post-process the error map (via GIBI), it must be transformed from a CHAM_ELEM per element to a CHAM_ELEM at the nodes by element. The value of the average of the temperature over GM35 (POST_RELEVE_T) and that of the potential deformation energy (POST_ELEM) are also determined. Everything is placed in a PYTHON loop allowing the implementation of a free refinement procedure in nb_calc=4 levels (via MACR_ADAP_MAIL option LIBRE =' RAFF_DERA ') coupled to the error map previously unearthed. This process is controlled by the component ERTREL of ERTH_ELEM (relative component of the residual indicator). With the criteria CRIT_RAFF_PE =0.2 and CRIT_DERA_PE =0.1 (we refine 20% of the worst elements and we deraffine 10% of the best). We can thus observe the convergence of the values of temperature and energy, the increase in their relative errors with respect to the errors provided by the indicator (themselves in relative terms and over the whole structure), the variations in the efficiency indices of the indicator and its good verification of the saturation hypothesis. In order to illustrate "good practice" advice for the quality of studies, on the aspects of mesh geometry, mesh itself and the type of finite elements, we use the adhoc options of LIRE_MAILLAGE, MACR_ADAP_MAIL and MACR_INFO_MAIL. .. image:: images/1000000000000330000001C293F17668BDD4E15E.png :width: 4.25in :height: 2.2965in .. _RefImage_1000000000000330000001C293F17668BDD4E15E.png: Figure 3.1-a: Isovalues of the exchange component (TERME2) of the error indicator .. image:: images/100000000000028A000001DEDBEE734E1B35F93D.png :width: 3.3854in :height: 2.4898in .. _RefImage_100000000000028A000001DEDBEE734E1B35F93D.png: Figure 3.1-b: Decreases in the relative errors of the deformation energy and the mean temperature compared to that of the total relative component of the indicator (ERTREL) Characteristics of the mesh ---- Initially: 1619 TRIA3, 102 SEG2, 911 knots After free refinement: 3088 TRIA3, 134 SEG2, 1681 knots After two free refinements: 6105 TRIA3, 180 SEG2, 3253 knots After three free refinements: 12345 TRIA3, 245 SEG2, 6462 knots After four free refinements: 25063 TRIA3, 347 SEG2, 12962 knots Tested sizes and results ---- We test the values of the relative errors in mean temperature and in potential deformation energy with respect to the reference solutions (cf. [:ref:`§2.2 <§2.2>`]). And this, on the initial mesh and after four free refinements. Since the tests must be multi-platform, the relative tolerance, which is on initial errors set at 10—6%, is deliberately relaxed on errors after four refinements: 10— 4%. These tests are carried out on variables PYTHON (via TEST_FONCTION) previously inserted into functions ASTER (via FORMULE). .. csv-table:: "**Identification**", "**Values** **Code_Aster**", "**Values of** **reference**", "**Tolerance**", "**Relative variance**" **(in%)**", "**Variable** **ASTER**", "**Variable PYTHON**" ":math:`{E}_{p}(0)` ", "0.491819%", "same", "10— 6% ", "1.1010—11" ~ 0% "," ERREEN0 ", "eren0" ":math:`{E}_{p}(4)` ", "0.016287%", "same", "10— 4% ", "3.05 10—12" ~ 0% "," ERREEN4 ", "eren4" "", "", "", "", "", "", "" ":math:`T(0)` "," 4.797588% ", "same", "10— 6% ", "2.42 10—12" ~ 0% "," ERRETM0 ", "ertm0" ":math:`T(4)` "," 0.042547% ", "same", "10— 4% ", "—6.65 10—13 ~ 0% "," ERRETM4 ", "ertm4" notes ---- It should be borne in mind that, as a "simple post-treatment" of the thermo-mechanical problem, **the indicator unfortunately cannot provide a more reliable diagnosis in areas where the resolution of the initial problem is not achieved** (crack, corners, corners, multi-material, embedment, shock...). It is therefore necessary to start an adaptation process (UNIFORME or LIBRE), with a mesh that is already a bit refined by the user near areas of discontinuity (materials, geometric...). MACR_ADAP_MAIL does not have a regularization process, so a bad initial mesh will produce, even when coupled with an indicator, probably a bad adapted mesh! As in mechanics, **the "thermal operators/ MACR_ADAP_MAIL OPTION 'LIBRE'" sequence makes it possible to optimally converge the mesh**. In addition, you can **"juggle" with the components of the thermal indicator** and boundary conditions, "fictional" or not, to **guide the construction of a refined or de-refined mesh by zones** (cf. [:ref:`§6.3 <§6.3>`] [:ref:`R4.10.03 `]).