S.P. Iglin, V.V. Dmitrik, V.Yu. Skulskyi
Èlektron. model. 2020, 42(1):51-73
The problem of the movement of liquid metal in a welding pool in arc welding process is solved in three-dimensional formulation. The velocities of liquid metal flows in the bath melt were investigated. Tetrahedral finite elements are used. Discretization of Navier-Stokes equations by coordinates in space is carried out according to the Galerkin scheme with analytical integration along the element's volume. The Eulerian inverse scheme is used to solve the non-stationary problem. Numerical results are presented.
melt, welding pool, Navier-Stokes equations, finite element method, Galerkin scheme, three-dimensional problem.
- Dmitrik, V.V. and Shevchenko, V.V. (2001), “About the efficiency of heat use of the molten pool”, Avtomaticheskaya svarka, no. 4, pp. 25-27.
- Akulov, A.I., Dmitrik, V.V. and Babushkina, V.A. (1992), “The method of determining the direction of motion of the flows of liquid metal from the head to the tail of the weld pool”, s. SSSR, no. 1776524.В23К31.12.
- Zienkiewicz, O.C. (1971), Metod konechnykh elementov v tekhnike [The Finite Element Method in Engineering Science], McGraw-Hill, London, UK.
- Postnov, V.A. and Kharkhurim I.Ya. (1974), Metod konechnyh elementov v raschetah sudovyh konstrukciy [The finite element method in the calculation of ship structures], Sudostroyeniye.
- Segerlind, L.J. (1976), Primeneniye metoda konechnykh elementov [Applied Finite Element Analysis], John Wiley and Sons, New York, USA.
- Donea, J. and Huerta, A. (2003), Finite Element Methods for Flow Problems, Wiley, New York, USA.
- Jaijan, W. (2010), Solution to Incompressible Navier-Stokes Equations by Using Finite Element Method, The University of Texas, Arlington, USA.
- Reusken, A. (2012), Numerical Methods for the Navier-Stokes Equations, RWTH, Aachen.
- Volkov, P.K. (2003), “The finite element method for solving boundary value problems of the regularized equations of an incompressible fluid in the "velocity-pressure" variables”, Matematicheskoe modelirovanie, Vol. 15, no. 3, pp. 15-28, Moscow, Russia.
- Gobysh, A.V. (2006), “Three-dimensional finite element approximations of the Navier-Stokes, Stokes, Euler equations”, Sbornik nauchnyh trudov NTGU, no. 1(43), pp. 55-60.
- Dmitrik, V.V. and Kalinichenko, B.I. (2002), “Numerical solution of boundary value problems of electric arc welding based on the Galerkin scheme”, Dopovidi NANU, no. 5, pp. 59-64.
- Baker, A. (1974), A Finite Element Solution Algorithm for the Navier-Stokes Equations, DC: NASA, Washington, USA.
- Pironneau, O. (1989), Finite Element Methods for Fluids, Wiley, Paris, France.
- Iglin, S.P. (2009), Optimizaciya formy elementiv konstrukciy [The Shape Optimization of Structure Elements], NTU KhPI, Kharkiv, Ukraine.
- “FreeCAD – Your Own 3D Parametric Modeler”, available at: https://www.freecadweb. org/ (accessed January 27, 2020).
- (1995-2018), “Partial Differential Equation Toolbox User’s Guide”, The MathWorks.
- “Computational fluid dynamics & heat transfer solver for MATLAB”, available at: https://quickersim.com/ (accessed January 27, 2020).