A low-order hybrid method for the variable-density incompressible Navier-Stokes equations

TL;DR

This paper introduces a new low-order hybrid numerical method for variable-density incompressible Navier-Stokes equations that supports complex meshes and is proven to be stable, convergent, and validated through numerical tests.

Contribution

The paper presents a novel low-order hybrid method capable of handling general meshes for the variable-density Navier-Stokes equations, with comprehensive theoretical analysis and validation.

Findings

Method supports polygonal and polyhedral meshes

Proven stability, existence, and uniqueness of solutions

Numerical tests confirm theoretical convergence

Abstract

In this work we introduce and analyse a new low-order method for the variable-density incompressible Navier-Stokes equations. The main novelty of the proposed method lies in the support of general meshes, possibly including polygonal or polyhedral elements as well as non-matching interfaces. We carry out a complete analysis, showing stability, existence and uniqueness of a discrete solution, and convergence of the latter to a suitably defined weak solution of the continuous problem. Numerical tests validate the theoretical results.