SIMPLE Algorithm with Staggered Grid for Natural Convection Simulation in a Square Cavity

This article discusses the implementation of the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm with staggered grid arrangement to simulate natural convection phenomena in a square cavity. Natural convection in enclosed cavities represents fluid motion driven by temperature gradients, a phenomenon with significant applications across various engineering and scientific disciplines, making its accurate simulation particularly valuable.

The SIMPLE algorithm implementation employs a staggered grid configuration where velocity components are stored at cell faces while pressure and temperature are defined at cell centers. The computational domain is discretized using finite volume methodology, with momentum equations solved sequentially using the pressure-velocity coupling mechanism. Key computational steps include: pressure correction through iterative solution of the pressure Poisson equation, momentum interpolation using the Rhie-Chow technique to prevent pressure-velocity decoupling, and implementation of the Boussinesq approximation for buoyancy term modeling. This approach effectively handles complex flow systems while accounting for various influencing factors to achieve accurate numerical results.

Through systematic simulation of square cavity natural convection, we gain deeper insights into the fundamental characteristics of thermal-fluid interactions, providing reliable data support for practical engineering applications. This research contributes significantly to advancements in thermal management systems, electronic cooling solutions, and building environment optimization.