Spectral simulation of thermocapillary convection

Book · Tue Dec 31 04:00:00 EST 1996

OSTI ID:423009

Ahmed, I; Ball, K S ^[1]

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1. Univ. of Texas, Austin, TX (United States). Dept. of Mechanical Engineering

The demand for growing flawless crystals in the semiconductor industry has renewed widespread interest in the thermocapillary problem. A spectral numerical method is presented for the computation of unsteady two-dimensional thermocapillary convection. The problem considered is incompressible flow in a differentially heated square cavity with a flat, fixed free surface (corresponding to negligible capillary number). The free surface is also assumed to be adiabatic. The equations of motion are solved using a pseudospectral Chebyshev collocation technique, with the second-pseudospectral Chebyshev collocation technique, with the second-order Adams-Bashforth/Crank-Nicolson time integration scheme. Results obtained for moderate to high Marangoni number flows show that accurate solutions to this problem can be obtained using spectral methods. Furthermore, globally smooth solutions are obtained and steep gradients near the cold wall are resolved at relatively lower grid resolutions compared to previously reported numerical investigations with lower order schemes. It is shown that despite the apparent singularities at the contact points of the free surface, high convergence rates can be achieved using spectral methods. The implications of proper scaling and grid-stretching are also addressed.

• OSTI ID: 423009
• Report Number(s): CONF-960815--; ISBN 0-7918-1509-9
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
CAPILLARY FLOW
COMPUTERIZED SIMULATION
CRYSTAL GROWTH
HEAT TRANSFER
SEMICONDUCTOR MATERIALS
THEORETICAL DATA
UNSTEADY FLOW