Contribution to Mathematical Modeling and Numerical Simulation of Welding Processes

Abstract The present work describes a mathematical model for the numerical simulation of the welding process. Initially, the domain Ω is solid to which the heat is released in certain areas. This heat increases the temperature of the solid, and when the fusion temperature is reached, the phase change occurs. At the fusion temperature, there is a mixture between liquid and solid (modelled as a porous medium); above this temperature mentioned; we will find only liquid. Natural convection currents can occur in the liquid due to buoyancy induced by the gravitational field. In order to reproduce all the phenomenology described, the mathematical model will be based on the energy conservation equation, expressed in terms of enthalpy, together with the mass and momentum conservation equations to determine the velocity of the fluid. The numerical resolution of the equations will be carried out with a Lagrange-Galerkin formulation in a finite element framework, where a temporal discretization BDF2 scheme will be used.