Transition of thermally induced flow in a square cavity using Spectral Method

Abstract

This study presents a novel mesh-free method for simulating natural convection in a square cavity filled with Newtonian fluid. The proposed algorithm integrates mesh-free Spectral methods with the Moving Collocation Element (MCOE) technique and employs a strong formulation to solve the nonlinear governing equations. Parametric analysis shows that increasing Rayleigh numbers significantly enhance the average Nusselt number, indicating a shift to convection-dominated heat transfer. Validation against benchmark solutions confirms the method’s accuracy and efficiency.

Keywords

• natural convection
• rayleigh number
• nusselt number
• spectral
• mcoe