Stefan-Signorini Moving Boundary ProblemArisen From Thermal Plasma Cutting:Mathematical Modelling, Analysis and Numerical Solution

Abstract

There is a wide range of thermal cutting techniquesavailable for the shaping of materials. One example is the plasma cutting. The cutting of the workpiece occurs as a result of melting/vaporizing the material by an extremely hot cylindrical plasma beam which burns and melts its way through the material, leaving a kerf in its wake. The heat transfer from the plasma beam into the material accounts for most of the phenomena encountered subsequently: shrinkage, residual stresses, metallurgical changes, mechanical deformations, chemical modifications, etc.The work is devoted to the development of a proper mathematical model which must involve the different physical phenomena occurring in the workpiece during the thermal cutting. The aim of the model is then to determine the temperature distribution in the workpiece and thegeometry of the cutting front. 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 mathematicalanalysis and numerical simulations of the model are discussed in the framework of variational inequalities and level-set theory.