The Research Of Numerical Simulation Of Coupling Field In Welding Pools Based On Multi-Grid Method

The welding process is complex, consuming large amounts of labor and financialresources in the experiment of welding technology. Computer numerical simulation iscreating powerful conditions for the development of the welding technology. In Recentyears, the numerical simulation technology has made great progress in the welding process,such as the coupling of molten pool behavior, the flow field, temperature field with otherfields. Many researchers had a lot of numerical simulation researches, presented manydifferent quasi-steady states and transient numerical calculation models, which had adifferent emphasis. As a whole, they can be classified into2D model of fixed electric arc,3D quasi-stationary model of movable electric arc and3D transient model of movableelectric arc. Multi-grid method is one of the most efficient and the fastest convergenceiterative methods to solve partial differential equation of elliptic type, and it is carried outby recursion algorithm. It is meaningful for engineering practice to applied multi-gridmethod to the solving of3D multi-region coupled field.The numerical simulation of TIG welding process is a coupled problem ofincompressible flow field and temperature field. Its mathematical model is a fixed solutionproblem of3D nonconstancy and nonlinear partial differential equation. In order to solvethis fixed solution problem, the mathematical model is given in this dissertation, and a newdirectly coupled method which combines with multi-grid method, finite difference methodand Newton iteration method is carried out. The main content and conclusion are given asbelow:（1）Finite difference method is applied to discrete the control equations, andnonlinear equations is obtained. Then Newton method is applied to solve the nonlinearequations and Newton formats linear equation is obtained. At last, multi-grid method isused to solve the linear equations.（2）To simulate the welding process of Q235mild steel plate which is undermovable heat source, and visual Fortran is used to compile program to solve equations.Numerical example shows that the method given in this paper (finite difference method+Newton iteration method+numerical simulation) reduced at least35%computation time comparing with traditional iterative method (finite difference method+Newton iteration method+successive overrelaxation iteration method).