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A Numerical Method on Eulerian Grids for Two-Phase Compressible Flow

Part of: Optics, electromagnetic theory - General

Published online by Cambridge University Press:  27 January 2016

Yonghui Guo ,
Ruo Li  and
Chengbao Yao
Yonghui Guo
Affiliation:
Northwest Institute of Nuclear Technology, Xi'an 710024, China
Ruo Li*
Affiliation:
HEDPS & CAPT, LMAM & School of Mathematical Sciences, Peking University, Beijing 100871, China
Chengbao Yao
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, andNorthwest Institute of Nuclear Technology, Xi'an 710024, China
*
*Corresponding author. Email: gyh661012@163.com (Y. H. Guo), rli@math.pku.edu.cn (R. Li), yaocheng@pku.edu.cn (C. B. Yao)
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Abstract

We develop a numerical method to simulate a two-phase compressible flow with sharp phase interface on Eulerian grids. The scheme makes use of a levelset to depict the phase interface numerically. The overall scheme is basically a finite volume scheme. By approximately solving a two-phase Riemann problem on the phase interface, the normal phase interface velocity and the pressure are obtained, which is used to update the phase interface and calculate the numerical flux between the flows of two different phases. We adopt an aggregation algorithm to build cell patches around the phase interface to remove the numerical instability due to the breakdown of the CFL constraint by the cell fragments given by the phase interface depicted using the levelset function. The proposed scheme can handle problems with tangential sliping on the phase interface, topological change of the phase interface and extreme contrast in material parameters in a natural way. Though the perfect conservation of the mass, momentum and energy in global is not achieved, it can be quantitatively identified in what extent the global conservation is spoiled. Some numerical examples are presented to validate the numerical method developed.

Keywords

Two-phase flowlevelsetRiemann problem

MSC classification

Secondary: 78A48: Composite media; random media
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 2 , April 2016 , pp. 187 - 212
Copyright
Copyright © Global-Science Press 2016 

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