WIAS Preprint No. 2600, (2019)

Numerical simulation of high-frequency induction welding in longitudinal welded tubes


  • Asperheim, John Inge
  • Das, Prerana
    ORCID: 0000-0001-6040-0311
  • Grande, Bjørnar
  • Hömberg, Dietmar
    ORCID: 0000-0001-9460-5729
  • Petzold, Thomas

2010 Mathematics Subject Classification

  • 35K05 35Q61 65N30


  • Simulation, multi-field problem, Joule heating, welding




In the present paper the high-frequency induction (HFI) welding process is studied numerically. The mathematical model comprises a harmonic vector potential formulation of the Maxwell equations and a quasi-static, convection dominated heat equation coupled through the joule heat term and nonlinear constitutive relations. Its main novelties are twofold: A new analytic approach permits to compute a spatially varying feed velocity depending on the angle of the Vee-opening and additional spring-back effects. Moreover, a numerical stabilization approach for the finite element discretization allows to consider realistic weld-line speeds and thus a fairly comprehensive three-dimensional simulation of the tube welding process.

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