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Simulations of 2D and 3D thermocapillary flows by a least‐squares finite element method
Author(s) -
Tang Li Q.,
Wright Jamie L.,
Tsang Tate T. H.
Publication year - 1998
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19981030)28:6<983::aid-fld757>3.0.co;2-c
Subject(s) - finite element method , conjugate gradient method , mathematics , linearization , least squares function approximation , work (physics) , mathematical analysis , coupling (piping) , mechanics , nonlinear system , algorithm , physics , engineering , mechanical engineering , statistics , quantum mechanics , estimator , thermodynamics
Numerical results for time‐dependent 2D and 3D thermocapillary flows are presented in this work. The numerical algorithm is based on the Crank–Nicolson scheme for time integration, Newton's method for linearization, and a least‐squares finite element method, together with a matrix‐free Jacobi conjugate gradient technique. The main objective in this work is to demonstrate how the least‐squares finite element method, together with an iterative procedure, deals with the capillary‐traction boundary conditions at the free surface, which involves the coupling of velocity and temperature gradients. Mesh refinement studies were also carried out to validate the numerical results. © 1998 John Wiley & Sons, Ltd.