论文标题
基于泰勒序列时间步长的高级人造可压缩方法可变密度流动
A high-order artificial compressibility method based on Taylor series time-stepping for variable density flow
论文作者
论文摘要
在本文中，我们为不可压缩的可变密度流提供了四阶准确的有限元方法。该方法是在时间上隐含的，并使用泰勒系列技术构建，并在空间中使用标准的高阶拉格朗日函数。泰勒串联时间稳定依赖于时间导数校正项来实现高阶精度。我们提供详细的算法，以近似可变密度的Navier-Stokes方程的时间导数。数值验证证实了平滑问题的四阶精度。我们还在数字上说明，泰勒系列方法不适合通过解决2D雷利 - 泰勒不稳定性问题而丢失规律性的问题。
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.
