A Rotational Projection Scheme for the Navier–Stokes Equations Coupled with a Heat Equation with Temperature-Dependent Coefficients

This paper presents a new algorithm based on splitting methods for the numerical solution of the Navier–Stokes equations coupled with the heat equation. This work is set in a context where viscosity and thermal conductivity depend explicitly on temperature We propose an extension of the Coupled Prediction Scheme based on a rotational projection formulation, noted as the Rotational Coupled Prediction Scheme (RCPS). The accuracy and effectiveness of the proposed numerical scheme are demonstrated through a series of numerical tests, and the results obtained are compared with those already existing in the literature. In particular, the Rayleigh–Bénard convection (RBC) problem was used as a reference benchmark.