Unilateral conditions modelling the cut front during plasma cutting: FEM solution

This study is devoted to the application of the moving-boundary methodology in the modelling of thermal plasma cutting of materials. The aim of the model is to determine the temperature distribution in the workpiece and the geometry of the cutting front during the cut. Mathematically, we model the problem as a coupled system of equations; heat conduction equation with Signorini-type boundary conditions and level-set equation as a result of reformulation of Stefan-type boundary condition. The weak formulation of the model is discussed in the framework of variational inequalities and level-set theory. Using the adaptive finite elements method, numerical results are obtained and illustrated in the manuscript. Our formulations provide a conceptually new approach towards the mathematical understanding of physical phenomena involved in the process of thermal plasma cutting.