9. Summary of results

Summary of results

+——————————+————————————————-+———————————————————————–+++——————————————+++ |**modelling** |**Flow at nodes or at** :math:`\mathit{PG}` **with linear temperature** |**Node flow with a quadratic temperature** | +------------------------------+-------------------------------------------------+-----------------------------------------------------------------------+++------------------------------------------+++ |**Item type** |**Discretization in** :math:`X` **and** :math:`Y`|**Max relative error %** ||**Max relative error %** | | +------------------------------+-------------------------------------------------+-----------------------------------------------------------------------+++------------------------------------------+++ |*2D modelling* *' PLAN '* | +------------------------------+-------------------------------------------------+-----------------------------------------------------------------------+++------------------------------------------+++ |QUAD4 |:math:`10\mathit{el}\mathrm{/}m` |0% | |5% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |TRIA3 |:math:`10\mathit{el}\mathrm{/}m` |0% | |1% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |QUAD8 |:math:`10\mathit{el}\mathrm{/}m` |0% | |0% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |QUAD9 |:math:`10\mathit{el}\mathrm{/}m` |0% | |0% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |*2D modelling* *' PLAN_DIAG '* | +------------------------------+-------------------------------------------------+-----------------------------------------------------------------------+++------------------------------------------+++ |QUAD4 |:math:`10\mathit{el}\mathrm{/}m` |0% | |10% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |TRIA3 |:math:`10\mathit{el}\mathrm{/}m` |0% | |10% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |TRIA6 |:math:`10\mathit{el}\mathrm{/}m` |0% | |5% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |QUAD9 |:math:`10\mathit{el}\mathrm{/}m` |0% | |1% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |*2D modelling* *' AXIS '* | +------------------------------+-------------------------------------------------+-----------------------------------------------------------------------+++------------------------------------------+++ |QUAD4 |:math:`10\mathit{el}\mathrm{/}m` |0% | |5% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |TRIA3 |:math:`10\mathit{el}\mathrm{/}m` |0% | |1% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |QUAD8 |:math:`10\mathit{el}\mathrm{/}m` |0% | |0% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |QUAD9 |:math:`10\mathit{el}\mathrm{/}m` |0% | |0% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |*2D modelling* *' AXIS_DIAG '* | +------------------------------+-------------------------------------------------+-----------------------------------------------------------------------+++------------------------------------------+++ |QUAD4 |:math:`10\mathit{el}\mathrm{/}m` |0% | |10% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |TRIA3 |:math:`10\mathit{el}\mathrm{/}m` |0% | |10% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |TRIA6 |:math:`10\mathit{el}\mathrm{/}m` |0% | |5% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |QUAD9 |:math:`10\mathit{el}\mathrm{/}m` |0% | |1% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |*Modeling* *'3D'* | +------------------------------+-------------------------------------------------+-----------------------------------------------------------------------+++------------------------------------------+++ |HEXA8 |:math:`10\mathit{el}\mathrm{/}m` |0% | |5% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |PENTA6 |:math:`10\mathit{el}\mathrm{/}m` |0% | |5% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |PYRAM5 |:math:`5\mathit{el}\mathrm{/}m` |0% | |10% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |TETRA4 |:math:`5\mathit{el}\mathrm{/}m` |0% | |5% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |HEXA20 |:math:`10\mathit{el}\mathrm{/}m` |0% | |0% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |HEXA27 |:math:`10\mathit{el}\mathrm{/}m` |0% | |0% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |PENTA15 |:math:`10\mathit{el}\mathrm{/}m` |0% | |0% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |PYRAM13 |:math:`5\mathit{el}\mathrm{/}m` |0% | |0% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |TETRA10 |:math:`5\mathit{el}\mathrm{/}m` |0% | |0% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |*Modeling* *'3D_ DIAG '* | +------------------------------+-------------------------------------------------+-----------------------------------------------------------------------+++------------------------------------------+++ |HEXA8 |:math:`10\mathit{el}\mathrm{/}m` |0% | |5% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |PENTA6 |:math:`10\mathit{el}\mathrm{/}m` |0% | |5% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |PYRAM5 |:math:`5\mathit{el}\mathrm{/}m` |0% | |10% || +——————————+————————————————-+———————————————————————–+++——————————————+++ |TETRA4 |:math:`5\mathit{el}\mathrm{/}m` |0% | |5% || +——————————+————————————————-+———————————————————————–+++——————————————+++

With a linear temperature field (and a constant flow):

• All models give accurate results.

With a quadratic temperature field (and a linear flow):

• The results are accurate with items of order 2 and modeling not DIAG. These elements having quadratic functions can represent exactly the imposed temperature field. The flows are accurate and would be even more accurate with a coarser discretization.

• Items of order 2 with modeling DIAG are treated as items of order 1 for the calculation of the flow. For these elements, the flows are constant per element. So the error is directly related to the size of the elements.