A Numerical Method for Two-Phase Stefan Problems

This study discusses on the implementation of an upwind method for a one-dimensional two-fluid model including the surface tension effect in the momentum equations. This model consists of a complete set of six equations including two-mass, two-momentum, and two-internal energy conservation equations having all real eigenvalues. Based on this equation system with upwind numerical method, the present authors first make a pilot code and then solve some benchmark problems to verify whether this model and numerical method is able to properly solve some fundamental one-dimensional two-phase flow problems or not.

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Solving two‐phase freezing Stefan problems: Stability and monotonicity

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.5787 ◽

2019 ◽

Vol 43 (14) ◽

pp. 7948-7960

Author(s):

Miguel A. Piqueras ◽

Rafael Company ◽

Lucas Jódar

Keyword(s):

Two Phase ◽

Stefan Problems

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

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-07-2019-0599 ◽

2019 ◽

Vol 30 (3) ◽

pp. 1407-1426 ◽

Cited By ~ 12

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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Periodic stability of solutions to two-phase stefan problems with nonlinear boundary condition

Nonlinear Analysis ◽

10.1016/0362-546x(94)90182-1 ◽

1994 ◽

Vol 22 (12) ◽

pp. 1445-1474

Author(s):

Toyohiko Aiki

Keyword(s):

Boundary Condition ◽

Nonlinear Boundary ◽

Nonlinear Boundary Condition ◽

Stability Of Solutions ◽

Two Phase ◽

Stefan Problems

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A Numerical Method for the Analysis of a New Model for Two-Phase Bubbly Flow in Elastic Pipes

Volume 2: Symposia and General Papers, Parts A and B ◽

10.1115/fedsm2002-31219 ◽

2002 ◽

Cited By ~ 1

Author(s):

D. Kim

Keyword(s):

Numerical Method ◽

Surface Deformation ◽

Two Phase Flow ◽

Numerical Technique ◽

Bubbly Flow ◽

Neumann Boundary ◽

Phase Flow ◽

Two Phase ◽

Tube Cross Section ◽

Elastic Pipes

A new approach and numerical method for study gas-liquid two-phase flows in elastic pipes is suggested. “A nonlinear wave dynamical model for liquid containing gas bubbles” is applied to derive governing equations for two-phase flow-filled pipelines. On assuming the hydraulic approximation the continuity and momentum equations of two-phase flow in a pipe are obtained for the first time. From these equations the inhomogeneous wave equation of Lighthill-type for two-phase flow in pipelines is derived. The shear stress at the tube surface, deformation of the tube cross-section, and liquid’s phase compressibility are taken into account. A high effectively and accurate finite difference technique for the exact solution of the basic equations in the case of Neumann boundary conditions is developed. Based on the proposed algorithm various numerical experiments have been carried out to investigate the major fluid dynamical features of hydraulic shocks and shock waves in the horizontal pipes. Comparisons with both the experimental data and computational results obtained with a second-order accurate predictor-corrector method support our numerical technique as well as the model.

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