Control Volume Free Element Method for Solving Turbulent Forced and Natural Convection Problems

ABSTRACT In this work, the control volume free element method (CVFrEM) is proposed for turbulent forced and natural convection problems. In the proposed method, the control volume at each collocation node is generated locally within the free element formed for the node, based on which the governing equations are discretized using the Green‐Gauss formula. In contrast to conventional segregated SIMPLE‐like algorithms, the newly proposed method achieves fully coupled velocity and pressure, thereby significantly improving convergence characteristics. The computational framework has been validated through the turbulent natural and forced convection problems involving conjugate heat transfer. Comprehensive verification has been carried out by systematically comparing numerical results with benchmark solutions from the literature and experimental measurements. Numerical experiments on several test cases demonstrate the computational efficiency of the proposed method and its numerical robustness.