Ebook: Numerical Simulation of Oscillatory Convection on Low-Pr Fluids: A GAMM Workshop

For the last ten years, there has been an ever-increasing awareness that fluid motion and transport processes influenced by buoyancy are of interest in many fields of science and technology. In particular, a lot of research has been devoted to the oscillatory behaviour of metallic melts (low-Pr fluids) due to the very crucial impact of such flow oscillations on the quality of growing crystals, semi-conductors or metallic alloys, for advanced technology applications. Test cases on the 2D oscillatory convection in differentially heated cavities containing low-Pr fluids have been defined by the organizing committee, and proposed to the community in 1987. The GAMM-Worshop was attended by 55 scientists from 12 countries, in Oct. 1988 in Marseille (France). Twenty-eight groups contributed to the mandatory cases coming from France (12), other European countries (7) and other countries: USA, Japan and Australia (9). Several groups also presented solutions of various related problems such as accurate determination of the threshold for the onset of oscillations, thermocapillary effect in open cavities, and 3D simulations. Period doubling, quasi- periodic behaviour, reverse transition and hysteresis loops have been reported for high Grashof numbers in closed cavities. The workshop was also open to complementary contributions (5), from experiments and theory (stability and bifurcation analysis). The book contains details about the various methods employed and the specific results obtained by each contributor.

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Content:
Front Matter....Pages I-VIII
Introduction....Pages 1-2
Benchmark Definition....Pages 3-8
Front Matter....Pages 9-9
Fine Mesh Solutions Using Stream Function-Vorticity Formulation....Pages 11-18
A Comparison of Velocity-Vorticity and Stream Function-Vorticity Formulations for Pr=0....Pages 19-24
Buoyancy-driven oscillatory flows in shallow cavities filled with low-Prandtl number fluids....Pages 25-34
A Finite-Difference Method with Direct Solvers for Thermally-Driven Cavity Problems....Pages 35-42
Contribution to the Gamm Workshop....Pages 43-48
Low Prandtl Number Convection in a Shallow Cavity....Pages 49-56
Numerical Simulation of Oscillatory Convection in Low Prandtl Number Fluids with the TURBIT Code....Pages 57-64
Marangoni Flows in a Cylindrical Liquid Bridge of Silicon....Pages 65-73
Numerical Simulation of Oscillatory Convection in a Low Prandtl Fluid....Pages 74-81
Steady-State Natural Convection in a Rectangular Cavity Filled with Low Prandtl Number Fluids....Pages 82-89
Numerical Simulation of Oscillatory Convection in Low Prandtl Number Fluids Using Aqua Code....Pages 90-97
Pressure correction splitting methods for the computation of oscillatory free convection in low Pr fluids....Pages 98-107
Influence of Thermocapillarity on the Oscillatory Convection in Low Pr Fluids....Pages 108-115
Front Matter....Pages 161-161
Numerical Simulation of Oscillatory Convection in Low Pr-Fluids....Pages 119-127
An Implicit Pressure Velocity Algorithm Applied to Oscillatory Convection in Low Prandtl Fluid....Pages 128-135
Oscillatory Natural Convection in a Long Horizontal Cavity....Pages 136-143
Contribution of the Heat-Transfer Group at Delft University....Pages 144-152
Numerical Simulation of Oscillatory Convection in Low Prandtl Fluids....Pages 153-159
Front Matter....Pages 161-161
Application of the N3S Finite Element Code to Simulation of Oscillatory Convection in Low Prandtl Fluids....Pages 163-170
Two- and Three-Dimensional Finite-Element Simulations of Buoyancy-Driven Convection in a Confined Pr=0.015 Liquid Layer....Pages 171-181
Two and Three-Dimensional Study of Convection in Low Prandtl Number Fluids....Pages 182-188
Numerical Simulation of Oscillatory Convection in Low Prandtl Fluids....Pages 189-198
The Solution of the Boussinesq Equations by the Finite Element Method....Pages 199-206
Numerical Simulation of Oscillatory Convection in Low Pr Fluids by Using the Galerkin Finite Element Method....Pages 207-214
Front Matter....Pages 215-215
Oscillatory Convection in Low Prandtl Fluids: a Chebyshev Solution with Special Treatment of the Pressure Field....Pages 217-226
Contribution to the GAMM Workshop with a pseudo-spectral Chebyshev algorithm on a staggered grid....Pages 227-236
Spectral Calculations of Convection in Low-Pr Fluids....Pages 237-243
Spectral Method for Two-Dimensional Time-Dependent Pr?0 Convection....Pages 244-255
Steady-State Solution of a Convection Benchmark Problem by Multidomain Chebyshev Collocation....Pages 256-261
Front Matter....Pages 263-263
Synthesis of Finite Difference Methods....Pages 265-272
Synthesis of the Results with the Finite-Volume Method....Pages 273-276
Analysis of Finite Element Results....Pages 277-280
Analysis of Spectral Results....Pages 281-284
General Synthesis of the Numerical Results....Pages 285-303
Front Matter....Pages 305-305
Linear and Non Linear Analysis of the Hadley Circulation....Pages 307-318
A Bifurcation Analysis of Oscillatory Convection in Liquid Metals....Pages 319-326
Front Matter....Pages 327-327
A Laboratory Study of Oscillations in Differentially Heated Layers of Mercury....Pages 329-337
Subharmonic Transitions in Convection in a Moderately Shallow Cavity....Pages 338-343
Front Matter....Pages 327-327
Convection in a Shallow Cavity....Pages 344-353
Front Matter....Pages 355-355
Discussions and Conclusions....Pages 357-362
Back Matter....Pages 363-367

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Content:
Front Matter....Pages I-VIII
Introduction....Pages 1-2
Benchmark Definition....Pages 3-8
Front Matter....Pages 9-9
Fine Mesh Solutions Using Stream Function-Vorticity Formulation....Pages 11-18
A Comparison of Velocity-Vorticity and Stream Function-Vorticity Formulations for Pr=0....Pages 19-24
Buoyancy-driven oscillatory flows in shallow cavities filled with low-Prandtl number fluids....Pages 25-34
A Finite-Difference Method with Direct Solvers for Thermally-Driven Cavity Problems....Pages 35-42
Contribution to the Gamm Workshop....Pages 43-48
Low Prandtl Number Convection in a Shallow Cavity....Pages 49-56
Numerical Simulation of Oscillatory Convection in Low Prandtl Number Fluids with the TURBIT Code....Pages 57-64
Marangoni Flows in a Cylindrical Liquid Bridge of Silicon....Pages 65-73
Numerical Simulation of Oscillatory Convection in a Low Prandtl Fluid....Pages 74-81
Steady-State Natural Convection in a Rectangular Cavity Filled with Low Prandtl Number Fluids....Pages 82-89
Numerical Simulation of Oscillatory Convection in Low Prandtl Number Fluids Using Aqua Code....Pages 90-97
Pressure correction splitting methods for the computation of oscillatory free convection in low Pr fluids....Pages 98-107
Influence of Thermocapillarity on the Oscillatory Convection in Low Pr Fluids....Pages 108-115
Front Matter....Pages 161-161
Numerical Simulation of Oscillatory Convection in Low Pr-Fluids....Pages 119-127
An Implicit Pressure Velocity Algorithm Applied to Oscillatory Convection in Low Prandtl Fluid....Pages 128-135
Oscillatory Natural Convection in a Long Horizontal Cavity....Pages 136-143
Contribution of the Heat-Transfer Group at Delft University....Pages 144-152
Numerical Simulation of Oscillatory Convection in Low Prandtl Fluids....Pages 153-159
Front Matter....Pages 161-161
Application of the N3S Finite Element Code to Simulation of Oscillatory Convection in Low Prandtl Fluids....Pages 163-170
Two- and Three-Dimensional Finite-Element Simulations of Buoyancy-Driven Convection in a Confined Pr=0.015 Liquid Layer....Pages 171-181
Two and Three-Dimensional Study of Convection in Low Prandtl Number Fluids....Pages 182-188
Numerical Simulation of Oscillatory Convection in Low Prandtl Fluids....Pages 189-198
The Solution of the Boussinesq Equations by the Finite Element Method....Pages 199-206
Numerical Simulation of Oscillatory Convection in Low Pr Fluids by Using the Galerkin Finite Element Method....Pages 207-214
Front Matter....Pages 215-215
Oscillatory Convection in Low Prandtl Fluids: a Chebyshev Solution with Special Treatment of the Pressure Field....Pages 217-226
Contribution to the GAMM Workshop with a pseudo-spectral Chebyshev algorithm on a staggered grid....Pages 227-236
Spectral Calculations of Convection in Low-Pr Fluids....Pages 237-243
Spectral Method for Two-Dimensional Time-Dependent Pr?0 Convection....Pages 244-255
Steady-State Solution of a Convection Benchmark Problem by Multidomain Chebyshev Collocation....Pages 256-261
Front Matter....Pages 263-263
Synthesis of Finite Difference Methods....Pages 265-272
Synthesis of the Results with the Finite-Volume Method....Pages 273-276
Analysis of Finite Element Results....Pages 277-280
Analysis of Spectral Results....Pages 281-284
General Synthesis of the Numerical Results....Pages 285-303
Front Matter....Pages 305-305
Linear and Non Linear Analysis of the Hadley Circulation....Pages 307-318
A Bifurcation Analysis of Oscillatory Convection in Liquid Metals....Pages 319-326
Front Matter....Pages 327-327
A Laboratory Study of Oscillations in Differentially Heated Layers of Mercury....Pages 329-337
Subharmonic Transitions in Convection in a Moderately Shallow Cavity....Pages 338-343
Front Matter....Pages 327-327
Convection in a Shallow Cavity....Pages 344-353
Front Matter....Pages 355-355
Discussions and Conclusions....Pages 357-362
Back Matter....Pages 363-367
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