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首页> 外文期刊>Journal of Computational Physics >Fictitious Domain approach with hp-finite element approximation for incompressible fluid flow
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Fictitious Domain approach with hp-finite element approximation for incompressible fluid flow

机译：hp域有限元逼近的不可压缩流体虚拟域方法

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摘要

We consider the application of Fictitious Domain approach combined with least squares spectral elements for the numerical solution of fluid dynamic incompressible equations. Fictitious Domain methods allow problems formulated on a complicated shaped domain Ω to be solved on a simpler domain Π containing Ω. Least Squares Spectral Element Method has been used to develop the discrete model, as this scheme combines the generality of finite element methods with the accuracy of spectral methods. Moreover the least squares methods have theoretical and computational advantages in the algorithmic design and implementation. This paper presents the formulation and validation of the Fictitious Domain Least Squares Spectral Element approach for the steady incompressible Navier-Stokes equations. The convergence of the approximated solution is verified solving two-dimensional benchmark problems, demonstrating the predictive capability of the proposed formulation.
机译：我们考虑将虚拟域方法与最小二乘谱元素相结合来应用流体动力学不可压缩方程的数值解。通过使用虚拟域方法，可以在包含Ω的简单域Π上解决在复杂形状域Ω上公式化的问题。最小二乘谱元素法已用于开发离散模型，因为该方案将有限元方法的通用性与频谱方法的准确性结合在一起。此外，最小二乘法在算法设计和实现中具有理论和计算优势。本文介绍了稳态不可压缩Navier-Stokes方程的虚拟域最小二乘谱元素方法的制定和验证。通过求解二维基准问题，验证了近似解的收敛性，证明了所提出公式的预测能力。

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