The gradient discretisation method for the Navier–Stokes problem coupled with the heat equation

In this work, we extend the gradient discretisation method to the Navier–Stokes model coupled with the heat equation. The gradient discretisation method is a framework that covers different numerical methods, conforming and non conforming methods. Using this framework, we provide a comprehensive and unified numerical analysis for the Navier–Stokes model with the heat equation. We present numerical results that demonstrate the efficiency of hybrid mimetic mixed schemes included in the framework we develop here.