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.

中文翻译：

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基于半隐式特性的多项式有限元投影法，用于求解不可压缩流

目的

本文的目的是研究一种新颖的稳定方案，以解决有限元方法（FEM）求解不可压缩层流时的对流和压力振荡问题。

设计/方法/方法

半隐式稳定方案是基于特征的多项式压力投影（CBP3），它由特征-Galerkin方法和多项式压力投影组成。从理论上讲，所提出的方案适用于使用速度和压力的等阶近似的任何类型的元素。在这项工作中，线性3节点三角形和4节点四面体元素是重点，它们是压力稳定最简单但最困难的元素。

发现

本文提出了一种新的方案，该方案可以针对低雷诺数和相对高雷诺数的流稳定FEM解。并且还研究了CBP3方案的稳定参数的影响。

研究局限/意义

这项工作的研究仅限于层状不可压缩流。

实际影响

CBP3方案的验证和确认是通过几个2 D和3 D数值示例进行的。该方案可用于处理更实际的流体问题。

社会影响

还介绍了该方案在研究特定于患者的腹主动脉瘤的复杂血流动力学中的应用，证明了其解决生物流的潜力。

创意/价值

本文模拟了2D和3D数值示例，其结果优于现有结果和实验。经验证，新颖的CBP3方案在处理对流和压力波动方面非常有效。