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• Four integrated SPH models are presented and compared for simulating natural convection. • The most suitable SPH model for natural convection is provided. • Natural convection for R a = 10 9 and Pr = 0.71 is successfully modeled for the first time by using the SPH method. • Mechanisms of the natural convection in a square cavity at different Rayleigh numbers are discussed. 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 R a > 10 6 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 10 4 ≤ R a ≤ 10 8. Furthermore, the simulation of natural convection at R a = 10 9 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 R a = 10 9 has significant influence to the heat transfer characteristic in the vertical boundary layers. [ABSTRACT FROM AUTHOR]

• A novel coupling approach of ES-FEM-SPH is developed for solving thermal-fluid-structure interaction (TFSI) problems. • The updated Lagrangian ES-FEM is developed for solving the coupled thermal elastic problems. • The SPH method, after integrating with particle shifting technique and kernel gradient correction, is robust and effective in modeling thermal fluid flows. • The ghost particle coupling algorithm is developed for treating fluid structure conjugate heat transfer. Thermal-fluid-structure interaction (TFSI) problems are significant in science and engineering, and usually pose great challenges for numerical simulations due to the coupled effects of thermal convection, fluid flow and structure deformation. In this paper, a novel coupling approach of smoothed finite element method (ES-FEM) with an improved smoothed particle hydrodynamic (SPH) method is developed for TFSI problems. In the coupling approach, the edge based ES-FEM is used to model solid domain and the Lagrangian SPH is used to model fluid flow. In ES-FEM, the temperature and velocity gradient smoothing technique are applied over the edge-based smoothing domain for thermal structure coupling problems. In SPH, some state-of-art algorithms including kernel gradient correction (KGC) and particle shift technique (PST) are integrated to ensure computational accuracy for simulating thermal fluid flows. A ghost particle coupling algorithm is developed to handle fluid-structure interaction and fluid-structure conjugate heat transfer, and the kinematic condition, dynamics conditions and conservation of energy are satisfied. Four numerical examples are tested to demonstrate the effectiveness of the present coupling approach of ES-FEM-SPH for TFSI problems. Image, graphical abstract [ABSTRACT FROM AUTHOR]