The numerical investigation of non-Newtonian fluid filling process via finite element and discontinuous Galerkin method

• Published in: Zhejiang da xue xue bao. Journal of Zhejiang University. Sciences edition. Li xue ban Vol. 50; no. 1; pp. 49 - 55
• Main Author: Gao, Puyang
• Format: Journal Article
• Language: Chinese
• Published: Hangzhou Zhejiang University 01.01.2023; Zhejiang University Press
• Subjects: Finite element method; Galerkin method; Interpolation; Mathematical analysis; Newtonian fluids; Non Newtonian fluids; Polynomials; Shearing; Stability
• ISSN: 1008-9497
• DOI: 10.3785/j.issn.1008-9497.2023.01.008

In this paper, we develop a coupled finite element and discontinuous Galerkin method in three dimension and study the non-Newtonian fluid filling process. To solve two phase Navier-Stokes equations, we employ the incremental pressure correction scheme to accomplish it in three steps. In order to guarantee the computational stability, we take the second order and first order interpolation polynomials for the velocity and pressure, respectively. In addition, the conservative Level Set method is employed to capture the moving interface. The discontinuous Galerkin method is used to solve the Level Set and its re-initialization equations. We take the three dimensional vortex shearing problem and the three dimensional non-Newtonian fluid filling process to verify the proposed approach, compare the result with the numerical results and existing experimental data to illustrate the stability, accuracy and the mass conservation property of the coupled scheme.