Effect of high-frequency vibration on silicon melt in a cavity with cold curved bottom and hot horizontal top

A numerical study of thermovibrational convection in molten silicon confined within a cavity characterized by a curved cold bottom wall and a uniformly heated plane top wall is presented. High-frequency (HF) vibrations are imposed on the system, and their influence on flow structure, symmetry, and intensity is examined under various configurations. Within the framework of the Boussinesq approximation, the governing equations are formulated in a dimensionless streamfunction–temperature form and solved using a spectral collocation method with Gauss–Lobatto–Chebyshev points and Crank–Nicolson time integration. The effects of vibration direction, amplitude, and cavity-bottom curvature are investigated across a wide range of Grashof (Gr) and vibrational Grashof (Grv) numbers. Three distinct situations are analyzed: pure buoyancy-driven convection, purely vibrational flow under microgravity, and the combined state in which HF vibration is applied to buoyant convection. Flow symmetry, pattern, and intensity are found to be highly sensitive to both the bottom deflection parameter and the vibration angle. The obtained results provide insights into the control of convective behavior in low-Prandtl-number melts, with implications for crystal growth and the purification of silicon in photovoltaic technologies.