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arXiv · 2209.09698

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

Lukas Lundgren·Murtazo Nazarov
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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.

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Lukas Lundgren, Murtazo Nazarov. 2022-09-20. A high-order artificial compressibility method based on Taylor series time-stepping for variable density flow. https://arxiv.org/abs/2209.09698

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