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In this paper, we introduce a fourth-order accurate finite element method forincompressible variable density flow. The method is implicit in time andconstructed with the Taylor series technique, and uses standard high-orderLagrange basis functions in space. Taylor series time-stepping relies on timederivative correction terms to achieve high-order accuracy. We provide detailedalgorithms to approximate the time derivatives of the variable densityNavier-Stokes equations. Numerical validations confirm a fourth-order accuracyfor smooth problems. We also numerically illustrate that the Taylor seriesmethod is unsuitable for problems where regularity is lost by solving the 2DRayleigh-Taylor instability problem.

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