A collocated finite volume scheme to solve free convection for general non-conforming grids

TL;DR

This paper introduces a new collocated finite volume scheme for simulating free convection in fluid flows on irregular grids, emphasizing stability and accuracy for Navier-Stokes and energy equations.

Contribution

It proposes a novel collocated scheme for Navier-Stokes and energy equations on non-conforming grids, improving stability and accuracy in free convection simulations.

Findings

Scheme demonstrates high accuracy on irregular grids

Stability is achieved through specific pressure gradient and nonlinear term choices

Numerical tests confirm the effectiveness of the method

Abstract

We present a new collocated numerical scheme for the approximation of the Navier-Stokes and energy equations under the Boussinesq assumption for general grids, using the velocity-pressure unknowns. This scheme is based on a recent scheme for the diffusion terms. Stability properties are drawn from particular choices for the pressure gradient and the non-linear terms. Numerical results show the accuracy of the scheme on irregular grids.