FEM and/or BEM for numerical simulation of Marangoni flow

Abstract

The aim of this work is the numerical study of Marangoni effect using three different methods. They are a finite element method, the classical boundary element method (BEM) and a modified BEM taking into account the singularities of the solution at the corners of the computing domain. The Marangoni flow occurs in a pellicle of  triangular transverse section situated on an inclined plane. On the liquid-gas interface a gradient of surface tension acts along or against the gravity. We obtain numerically the velocity field for various surface tension gradients. Modified BEM proved to be the most reliable approach.

Authors

C.I. Gheorghiu
Tiberiu Popoviciu Institute of Numerical Analysis

Keywords

Marangoni flow; Poisson equation; polygonal domain;  mixed boundary value problem; finite element method; boundary element method; corner singularity; velocity field;

References

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Paper coordinates

C.I. Gheorghiu, FEM and/or BEM for numerical simulation of Marangoni flow, Eng. Anal. Bound. Elem., 5 (1988) 195-197

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References

[1] Chifu, E., Gheorghiu, C. and Stan, I., Surface Mobility of Surfactant Solutions. XI. Numerical Analysis for the Marangoni and the Gravity Flow in a Thin Liquid Layer on Triangular Section, Revue Roumaine de Chimie, 1984, 29, 31-42.

[2] Chifu, E., Albu, I., Gheorghiu, C. I., Gavrila, E. and Salajan, M., Marangoni Flow-Induced by Temperature Gradients-Againsts Gravity Forces, Revue Rouraaine de Chimie, 1986, 31, 105-112

[3] Chifu, E. and Gheorghiu, C. I., Surface Mobility of Surfactant Solutions. XII. Remarks Concerning the Marangoni Flow Through an Inclined Surface Canal, Revue Roumaine de Chiraie, 1987, inpress

[4] Costabel, M. and Stephan, E., Boundary Integral Equations for Mixed Boundary Value Problems in Polygonial Domains and Galerkin Approximation, THD-Preprint Nr. 593, 1981

[5] Ingham, B. D. and Kelmanson, M. A., Boundary Integral Equation Analysis of Singular, Potential and Biharmonic Problems, SpringerVerlag, 1984

[6] Piessens, R., de Donker-Kapenga, E., Uberhuber, C. W. and Kahaner, D. K. QUADPACK A Subroutine Package for Automatic Integration, Springer-Verlag, 1983

[7] Petrila, T. and Gheorghiu, C. I. 1987 Metode element finit și aplicalții, Editura Academiei, București, 1987

[8] Brebbia, C. A. The Boundary Element Method for Engineers, Pentech Press, UK

[9] Wendland, W. L. On Asymptotic Error Estimates for Combined BEM and FEM, CISM-Courses, 1986

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