A semi-implicit characteristic-based polynomial pressure projection for FEM to solve incompressible flows
A semi-implicit characteristic-based polynomial pressure projection for FEM to solve incompressible flows
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DOI：
10.1108/hff-04-2020-0184
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发表时间：
2021-02
影响因子：
4.2
通讯作者：
M. Liu;Huifen Zhu;G. Gao;Chen Jiang;Guirong Liu
中科院分区：
文献类型：
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作者：
M. Liu;Huifen Zhu;G. Gao;Chen Jiang;Guirong Liu
目的研究一种新的稳定化格式，以处理有限元法求解不可压层流流动过程中的对流和压力振荡问题。设计/方法/方式半隐式稳定计划，基于特征的多项式压力投影（CBP 3）由特征Galerkin方法和多项式压力投影。理论上，该方案适用于任何类型的元素使用速度和压力的等阶近似。本文重点研究了三节点三角形和四节点四面体单元，它们是压力稳定问题中最简单但最困难的单元。结果-本论文提出了一种新的计划，它可以稳定的FEM解决方案的低和相对较高的雷诺数的流量。并研究了CBP 3格式的稳定化参数对数值结果的影响。研究限制/影响-在这项工作中的研究仅限于层流不可压缩流。实际影响-CBP 3计划的验证和验证进行了几个2 D和3 D的数值例子。该格式可用于处理更实际的流体问题。社会影响-计划的应用，研究复杂的血流动力学的患者特定的腹主动脉瘤，这表明它有潜力解决生物流量。独创性/价值-该文件模拟2 D和3 D的数值例子与上级的结果相比，现有的结果和实验。新的CBP 3格式被证明是非常有效的处理对流和压力振荡。
Purpose The purpose of this paper is to investigate a novel stabilization scheme to handle convection and pressure oscillation in the process of solving incompressible laminar flows by finite element method (FEM). Design/methodology/approach The semi-implicit stabilization scheme, characteristic-based polynomial pressure projection (CBP3) consists of the Characteristic-Galerkin method and polynomial pressure projection. Theoretically, the proposed scheme works for any type of element using equal-order approximation for velocity and pressure. In this work, linear 3-node triangular and 4-node tetrahedral elements are the focus, which are the simplest but most difficult elements for pressure stabilizations. Findings The present paper proposes a new scheme, which can stabilize FEM solution for flows of both low and relatively high Reynolds numbers. And the influence of stabilization parameters of the CBP3 scheme has also been investigated. Research limitations/implications The research in this work is limited to the laminar incompressible flow. Practical implications The verification and validation of the CBP3 scheme are conducted by several 2 D and 3 D numerical examples. The scheme could be used to deal with more practical fluid problems. Social implications The application of scheme to study complex hemodynamics of patient-specific abdominal aortic aneurysm is also presented, which demonstrates its potential to solve bio-flows. Originality/value The paper simulated 2 D and 3 D numerical examples with superior results compared to existing results and experiments. The novel CBP3 scheme is verified to be very effective in handling convection and pressure oscillation.