Comparing Two Numerical Methods in the Case of Aiding and Opposing Natural Double Diffusion in a Square Enclosure

Natural convection is a central topic in fluid mechanics, attracting the interest of researchers for its value in the validation of numerical methods and its multiple applications in engineering due to its significant advantages over experimental approaches. Natural double-diffusive convection is particularly intriguing because of its diverse applications in fields, where simultaneous variations in temperature and concentration generate significant buoyancy forces. In this paper, two numerical methods are used to study natural doublediffusive convection in a cavity containing a binary mixture, subjected to Neumann-type thermal and solutal gradients. The results are compared to previous studies, highlighting the impact of initial conditions and relevant parameters on the flow intensity as well as the average Nusselt and Sherwood numbers. Simulations showed that the finite difference method outperformed the finite volume method in terms of mesh independence and computational time, although not in terms of iterations. Additionally, the opposite flow case presented a multiplicity of solutions requiring careful selection of initial conditions. This work highlights the importance of understanding the nuances of numerical modeling to effectively study double-diffusive natural convection.