A high-order artificial compressibility method based on Taylor series time-stepping for variable density flow
Numerical Analysis
2022-09-21 v1 Numerical Analysis
Abstract
In this paper, we introduce a fourth-order accurate finite element method for incompressible 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.
Cite
@article{arxiv.2209.09698,
title = {A high-order artificial compressibility method based on Taylor series time-stepping for variable density flow},
author = {Lukas Lundgren and Murtazo Nazarov},
journal= {arXiv preprint arXiv:2209.09698},
year = {2022}
}