# Dimensions¶

Real microstructures typically are 3-D. MICRESS® can treat all. 1-D, 2-D and 3-D problems, but, naturally, 3-D simulations are most time-consuming. For this reason it is worth checking whether a specific 3-D problem can be reduced to an equivalent 2-D or 1-D problem with sufficient accuracy.

Some problems are inherently 3-D, like e.g. fibrous eutectic growth or fluid flow through a dendritic mushy zone. But in many other cases, a 2-D simulation with high spatial resolution can give more exact information than a poorly resolved 3-D simulation. Therefore it is important to think about the consequences of a 2-D approximation and to check how they can be eventually corrected.

In general, a 2-D calculation domain can be constructed as:

• a section through the structure. As a consequence, however, if there are various small particles like in the figure below, only a few of them will be found in the 2-D cut. The mean distance between the particles will not be correct and the interaction between the diffusion fields will not be described well. Thus, this is not a good option for microstructure simulation, although experimental micrographs typically are like that!

Graphical representation of a 2-D section

• a projection of the 3-D structure onto 2-D. This will result in correct average particle distance, but in wrong average phase fractions. The release of latent heat, if used in the simulation, will be predicted incorrectly. In early solidification stages when the solid fraction is small and growing grains are far apart, solutal interactions between the structures can be neglected. Then an analytical correction of the phase fraction of the growing phase is possible. In case of latent heat, this correction needs to be done already during simulation; it is done automatically if the option "latheat_3D" is selected. For more information see[1].

Graphical representation of a 2-D projection of a 3-D structure

1. Ingo Steinbach. Phase-field models in materials science. Modelling and Simulation in Materials Science and Engineering, 17$7$:073001, jul 2009. doi:10.1088/0965-0393/17/7/073001