A Numerical Method for Computing the Profile of Weld Pool Surfaces

• Published in: International journal of computational methods in engineering science and mechanics Vol. 6; no. 2; pp. 115 - 125
• Main Authors: Cai, X., Jeberg, P. V., Langtangen, H. P.
• Format: Journal Article
• Language: English
• Published: Taylor & Francis Group 03.09.2005
• Subjects: Prescribed Mean Curvature Equations; Secant Method; Weld Pool Surface Profile; Welding Simulation
• ISSN: 1550-2287; 1550-2295
• DOI: 10.1080/15502280590891591

An iterative numerical scheme is presented for solving a system of two prescribed mean curvature equations, which are coupled together through a Lagrange multiplier λ and a mass conservation constraint. Such a system of nonlinear partial differential equations may arise from modeling the free surface deformation of a full penetration weld pool. By introducing a cost function dV(λ), we construct the overall numerical strategy as a secant method that iterates on the value of λ, where the two nonlinear prescribed mean curvature equations are solved during each secant step. We analyze the dependence of the solutions on λ, together with the range of allowable λ values, for a special one-dimensional case. For more general cases, we investigate the convergence behavior by numerical experiments. We have observed in all the test cases that the objective cost function dV(λ) is monotonically increasing inside the range of allowable λ values. This ensures a rapid convergence of the numerical scheme, provided that two initial guesses of λ are well chosen. We also report some experience in solving the nonlinear equations.