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.
Entropy-stable discontinuous Galerkin approximation with summation-by-parts property for the incompressible Navier-Stokes equations with variable density and artificial compressibility
Lattice Boltzmann model approximated with finite difference expressions
Conservatoire National des Arts et Métiers（国立巴黎高等工艺学院）；University Paris-Sud（巴黎第十一大学）；Beijing Computational Science Research Center（北京计算科学研究中心）；Institut National des Sciences Appliquées de Lyon（里昂国立应用科学学院）；University of Tunis El Manar（突尼斯埃尔马纳大学）
