Stability of Marangoni Convection in a MicroGravity Environment
In a recent paper of SHEN et al. energy-stability bounds were computed for the thermocapillary convection in a model of the float-zone crystal-growth process. The main application is expected to be the production of high-quality semiconductor material in low-gravity environments. Here we outline the physical and mathematical background and then describe in detail the numerical method used to solve the resulting nonlinear eigenvalue problem. Some information on the performance of the method is given and numerical results are presented for the zero gravity case.
KeywordsPrandtl Number Marangoni Number Generalize Eigenvalue Problem Thermocapillary Convection Nonlinear Eigenvalue Problem
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- Bank, R., Mittelmann, H. D. (1986) Continuation and multigrid for nonlinear elliptic systems. In Multigrid Methods II(ed. W. Hackbusch, U. Trottenberg) Lect. Notes Math. 1228, Springer.Google Scholar
- Joseph, D. D. (1976) Stability of Fluid Motions I, II, Springer-Verlag, Berlin.Google Scholar
- Shen, Y., Neitzel, G. P., jankowski, D. F., Mittelmann, H. D. (1989) Energy stability of thermocapillary convection in a model of the float-zone, crystal-growth process. Submitted to J. Fluid Mech.Google Scholar