Speaker: Arsen Narimanyan, University of Bremen, Germany

Title: A Stefan-Signorini Moving Boundary Problem:  Mathematical  
Modelling of Thermal Plasma Cutting

Abstract:

There is a wide range of thermal cutting techniques available 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 talk 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 process.  The aim of the model is
then to determine the temperature distribution in the workpiece and
the geometry 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
mathematical analysis of the model is discussed in the framework of
variational inequalities and level-set theory. Numerical results are
obtained using adaptive finite elements method.