4.1. A first casting problem

Let us consider the Finite Element model in Figure 1. 40 time steps are used to describe the evolution of the state variables. The two sub-domains ? ₁ and ? ₂ are elastic bodies, respectively in aluminium and sand. There is no initial gap between the two sub-domains. This is a plan strain problem.

Figure 1: Meshes on each sub-domain

The way ? ₁ is cooled down depends on the contact conditions between the two sub-domains. Moreover these contact conditions are defined by the thermal expansion of each sub-domain. The thermo-mechanical coupling is strong and similar to the one encountered in casting problems.

4.2. Few stages to obtain the main part of the state evolution

To forecast the defaults in a process with a simulation, it is interesting to obtain a quick overview of the evolution of the state variables. After 20 correction stages a good overview of the displacements and temperature fields is obtained (Figure 2).

Figure 2: An interesting overview of the displacement and temperature field after 20 correction stages.

Even accurate local results are quickly available, with few correction stages. In Figure 3 there is the example of the temperature evolution (Figure 1) on the point P obtained after different correction stages.

Figure 3: Different local evolutions of the temperature at the point P.

4.3. Discussion about the reduced-order model and the LATIN-KL subspace

The LATIN subspace is very close to the subspace proposed by...