In the paper, we present the results of solidification simulation taking into account the movement of the liquid phase. The results are obtained from an author software which is implemented on the base of a stabilized finite elements method (Petrov-Galerkin formulation). Using that formulation the Navier-Stokes equation is solved together with the convection term (Boussinesq approximation). The Finite Element Method (FEM) formulation is responsible for solidification, approximating the solution of the heat conduction equation (with the internal heat source term responsible for the heat released during the phase transition). The movement of the liquid phase in a solidifying cast that is caused by convection can significantly affect the process of heat transfer from the casting to the mold, which in turn has an influence on the temperature distribution in the cast and may cause a change in the location of the defects. The presented results allow to assess under what conditions the effect of convection on the solidification process is significant.

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The paper aims to present the possibility of performing engineering calculations in domains of complex shapes expressed by mathematical descriptions. We focus on calculations done with the use of the Finite Element Method. An example of the compound structure is gyroid, which is a periodic structure representing an area close to the porous structure. The presented gyroid structure exhibits circular struts and a spherical core and spatially occupies a cube. The side length of the cube is defined as unit cell size, and the volume percentage of the struts inside the cube is referred to as volume fraction. The periodic cellular lattice structures are generated by our own software module. One of the uses of such structures is their employment in additive manufacturing (AM) of the so-called 3D printing (layer-by-layer AM technique), where they can contribute reducing the weight of an item and limiting the material consumption. It is important to answer the question of what effect does an element with a gyroid structure have on the thermal properties (e.g. the heat flow versus the volume fraction) compared to an element with full structure. The paper will show the results of such a comparison.

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