Efficient single variable Level Set method for capturing moving interfaces in powder densification processes

Among all the different techniques for modeling moving interfaces, the ones that capture the interfaces with a phase function such as Level Set (LS) methods have a great advantage over surface tracking approaches when managing topological changes. However, the standard LS method and the Conservative Level Set (CLS) method only distinguish between two different stable levels or phases using one level set equation, which is a second-order partial differential equation. When managing three or more levels or phases, the formulation requires additional level set equations. The model presented in this work is a modification of the CLS method by which one single level set variable can manage three stable levels. The level set variable can then be interpreted as the average relative density of a specific material with three stable density levels. The presented model is suitable to represent the deposition and densification of powder material, where three different stable levels (void, powder, and fully dense material) coexist, and therefore can be applied to capture the evolving interfaces, as is of particular interest for processes such as powder based additive manufacturing. The main advantage of the proposed model is the large reduction of the number of degrees of freedom compared to the traditional LS formulation, reducing the required computational resources. Several test cases, including densification cases, are addressed in the present article.

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