scholarly journals A discrete exterior calculus finite element method for solving two phase flow problems

2009 ◽  
Author(s):  
Peter Klimas
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase ◽  
Flow Problems ◽  
Discrete Exterior Calculus ◽  
Exterior Calculus ◽  
Element Method

Variational multi-scale finite element method for the two-phase flow of polymer melt filling process

2019 ◽  
Vol 30 (3) ◽  
pp. 1407-1426 ◽  
Author(s):  
Xuejuan Li ◽  
Ji-Huan He
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Method ◽  
Two Phase Flow ◽  
Polymer Melt ◽  
Phase Flow ◽  
Filling Process ◽  
Two Phase ◽  
Content Type ◽  
Element Method

Purpose The purpose of this paper is to develop an effective numerical algorithm for a gas-melt two-phase flow and use it to simulate a polymer melt filling process. Moreover, the suggested algorithm can deal with the moving interface and discontinuities of unknowns across the interface. Design/methodology/approach The algebraic sub-grid scales-variational multi-scale (ASGS-VMS) finite element method is used to solve the polymer melt filling process. Meanwhile, the time is discretized using the Crank–Nicolson-based split fractional step algorithm to reduce the computational time. The improved level set method is used to capture the melt front interface, and the related equations are discretized by the second-order Taylor–Galerkin scheme in space and the third-order total variation diminishing Runge–Kutta scheme in time. Findings The numerical method is validated by the benchmark problem. Moreover, the viscoelastic polymer melt filling process is investigated in a rectangular cavity. The front interface, pressure field and flow-induced stresses of polymer melt during the filling process are predicted. Overall, this paper presents a VMS method for polymer injection molding. The present numerical method is extremely suitable for two free surface problems. Originality/value For the first time ever, the ASGS-VMS finite element method is performed for the two-phase flow of polymer melt filling process, and an effective numerical method is designed to catch the moving surface.

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