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A semi-implicit characteristic-based polynomial pressure projection for FEM to solve incompressible flows

Mingyang Liu (Central South University, Changsha, China)
Huifen Zhu (Central South University, Changsha, China)
Guangjun Gao (Key Laboratory of Traffic Safety on Track of Ministry of Education, Changsha, China and School of Traffic and Transportation Engineering, Central South University, Changsha, China)
Chen Jiang (Central South University, Changsha, China)
G.R Liu (School of Aerospace Systems, University of Cincinnati, Cincinnati, Ohio, USA)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 11 February 2021

Issue publication date: 3 May 2021



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).


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.


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.


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.



Authors appreciate the supports from, National Key Research and Development Program of China (Grant No. 2016YFB1200401), China Postdoctoral Science Foundation (Grant No. 2017M622611), the Project of Innovation-driven Plan in Central South University (Grant No. 2015CX003), National Natural Science Foundation of China (No. 51405517 and Key Program Grant No. U1534210), Science Foundation of Hunan Province (Grant No. 2016jj3004 and 2016jj3005), Central South University free orientation 2020 (No. 1053320191189). National Natural Science Foundation of China (No. 12002395).


Liu, M., Zhu, H., Gao, G., Jiang, C. and Liu, G.R. (2021), "A semi-implicit characteristic-based polynomial pressure projection for FEM to solve incompressible flows", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 31 No. 5, pp. 1710-1731.



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