A high-order artificial compressibility method based on Taylor series time-stepping for variable density flow

In this paper, we introduce a fourth-order accurate finite element method for incom-pressible variable density flow. The method is implicit in time and constructed with the Taylor series technique, and uses standard high-order Lagrange basis functions in space. Taylor series time-stepping relies on time derivative correction terms to achieve high -order accuracy. We provide detailed algorithms to approximate the time derivatives of the variable density Navier-Stokes equations. Numerical validations confirm a fourth -order accuracy for smooth problems. We also numerically illustrate that the Taylor series method is unsuitable for problems where regularity is lost by solving the 2D Rayleigh-Taylor instability problem. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).