Direct numerical simulation of natural convection in a square cavity at high Rayleigh numbers via the Lagrange interpolating polynomial scheme

Abstract

Direct numerical simulation (DNS) is a powerful research technique to solve the Navier–Stokes equations based on turbulent flows. DNS delivers highly reliable physical solutions with extreme accuracy. Unfortunately, present hardware and computing technologies remain limited, making it difficult to implement DNS in practice. The recently proposed Lagrange interpolating polynomial (LIP) scheme is a discretization technique for the finite-volume method. The LIP scheme is easy to use with nonuniform grid simulations and can flexibly increase or decrease the order of accuracy. The objective of this study is to verify that the LIP scheme is suitable for DNS of natural convection in a square cavity at high Rayleigh numbers (Ra). Accordingly, code was developed in-house using a second-order LIP scheme with the finite-volume method and the semi-implicit method for pressure-linked equations (SIMPLE) algorithm. Simulations were performed at Ra values of 109 and 1.58 × 109. The solutions were then verified against experimental benchmark data and published numerical solutions. The maximum differences in the Nusselt numbers between the computed solutions and the experimental benchmark data and published numerical solutions are 19.23% and 5.51%, respectively. However, the comparison results indicate that most of the computed solutions are in good agreement with experimental benchmark data and published numerical solutions.