Natural convection is a heat transfer mechanism driven by temperature or density differences, leading to fluid motion without external influence. It occurs in various natural and engineering phenomena, influencing heat transfer, climate, and fluid mixing in industrial processes. This work aims to use the Updated Lagrangian Particle Hydrodynamics (ULPH) theory to address natural convection problems. The Navier-Stokes equation is discretized using second-order nonlocal differential operators, allowing a direct solution of the Laplace operator for temperature in the energy equation. Various numerical simulations, including cases such as natural convection in square cavities and two concentric cylinders, were conducted to validate the reliability of the model. The results demonstrate that the proposed model exhibits excellent accuracy and performance, providing a promising and effective numerical approach for natural convection problems.

A fluid-structure interaction approach is proposed in this paper based on Non-Ordinary State-Based Peridynamics (NOSB-PD) and Updated Lagrangian Particle Hydrodynamics (ULPH) to simulate the fluid-structure interaction problem with large geometric deformation and material failure and solve the fluid-structure interaction problem of Newtonian fluid. In the coupled framework, the NOSB-PD theory describes the deformation and fracture of the solid material structure. ULPH is applied to describe the flow of Newtonian fluids due to its advantages in computational accuracy. The framework utilizes the advantages of NOSB-PD theory for solving discontinuous problems and ULPH theory for solving fluid problems, with good computational stability and robustness. A fluid-structure coupling algorithm using pressure as the transmission medium is established to deal with the fluid-structure interface. The dynamic model of solid structure and the PD-ULPH fluid-structure interaction model involving large deformation are verified by numerical simulations. The results agree with the analytical solution, the available experimental data, and other numerical results. Thus, the accuracy and effectiveness of the proposed method in solving the fluid-structure interaction problem are demonstrated. The fluid-structure interaction model based on ULPH and NOSB-PD established in this paper provides a new idea for the numerical solution of fluid-structure interaction and a promising approach for engineering design and experimental prediction.