Simulating natural convection with high Rayleigh numbers using the Smoothed Particle Hydrodynamics method

Abstract

This paper conducts the simulation of natural convection in a differentially heated square cavity at high Rayleigh numbers by using the smoothed particle hydrodynamics (SPH) method. Due to the decrease of the accuracy and stability, it is challenging for the SPH method to simulate natural convection at high Rayleigh numbers, and there are few reported SPH literatures of natural convection at Ra>106 for air (Pr = 0.71). In this study, four integrated SPH models are presented to simulate the natural convection and their accuracy and stability are assessed. These four SPH models are associated with Kernel Gradient Correction (KGC) to improve approximation accuracy and Particle Shifting Technology (PST) to regularize particle distribution while they are different in treating density diffusion and calculating the pressure term. The numerical results show that SPH model_4 (KGC, PST, δ-SPH and asymmetric pressure approximation) is the most suitable for simulating the closed natural convection problems, especially at high Rayleigh numbers. Good agreements with reference solutions are obtained by SPH model_4 for the natural convection at 104≤Ra≤108. Furthermore, the simulation of natural convection at Ra=109 is conducted by SPH model_4. The evolutions of thermal convection are described in detail. It is found that dynamics characteristic reveals that the dominant force is the pressure gradient, rather than the buoyancy force before the quasi-steady state. In addition, the chaotic motion at Ra=109 has significant influence to the heat transfer characteristic in the vertical boundary layers.