A new fractional time-stepping method for variable density incompressible flows

Authors:
Ying Li;Liquan Mei;Jiatai Ge;Feng Shi
Affiliations:
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China;School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China and Center for Computational Geosciences, Xi'an Jiaotong University, Xi'an 710049,China;School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China;Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
Venue:
Journal of Computational Physics
Year:
2013

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Abstract

This paper describes a new method for solving variable density incompressible viscous flows. We have dealt with the momentum equation and the divergence free constraint in a new manner by rewriting the original equations. The originality of the proposed approach is that we have used different numerical methods to evaluate the evolution of the velocity and pressure. Compared with some established methods, the proposed approach is parameter-free, more flexible and can avoid the difficulties caused by the original equations. The stability analysis of the method is performed to show that our method is stable. Finally, numerical experiments are given to show the accuracy, efficiency and validness of this method for variable density incompressible flows.