A generic Scheme For the time-dependent Navier-Stokes Equation Coupled With The Heat Equation

Abstract

In this work, we study the gradient discretisation method (GDM) of the time-dependent Navier-Stokes equations coupled with the heat equation, where the viscosity depends on the temperature. We design the discrete method and prove its convergence without non-physical conditions. The paper is closed with numerical experiments that confirm the theoretical results.