Comparative analysis of nondimensionalization approaches for solving the 2-D differentially heated cavity problem

This work reports a numerical study on the effect of three nondimensionalization approaches that are commonly used to solve the classic problem of the 2-D differentially heated cavity. The governing equations were discretized using orthogonal collocation with Legendre polynomials, and the resulting algebraic system was solved via Newton–Raphson method with LU factorization. The simulations were performed for Rayleigh numbers between 10³ and 10⁸, considering the Prandtl number equal to 0.71 and a geometric aspect ratio equal to 1, analyzing the convergence and the computation time on the flow lines, isotherms and the Nusselt number. The mesh size that provides independent results was 51 × 51. Approach II was the most suitable for the nondimensionalization of the differentially heated cavity problem.