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The Immersed Interface Method for Simulating Two-Fluid Flows

Published online by Cambridge University Press:  09 August 2018

Miguel Uh  and
Sheng Xu
Miguel Uh*
Affiliation:
Department of Mathematics, Southern Methodist University, Dallas, TX 75275-0156, USA.
Sheng Xu*
Affiliation:
Department of Mathematics, Southern Methodist University, Dallas, TX 75275-0156, USA.
*
Email address:muhzapata@gmail.com
* Corresponding author.Email: sxu@smu.edu
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Abstract

We develop the immersed interface method (IIM) to simulate a two-fluid flow of two immiscible fluids with different density and viscosity. Due to the surface tension and the discontinuous fluid properties, the two-fluid flow has nonsmooth velocity and discontinuous pressure across the moving sharp interface separating the two fluids. The IIM computes the flow on a fixed Cartesian grid by incorporating into numerical schemes the necessary jump conditions induced by the interface. We present how to compute these necessary jump conditions from the analytical principal jump conditions derived in [Xu, DCDS, Supplement 2009, pp. 838-845]. We test our method on some canonical two-fluid flows. The results demonstrate that the method can handle large density and viscosity ratios, is second-order accurate in the infinity norm, and conserves mass inside a closed interface.

Keywords

76M2065M0635Q35Immersed interface methodtwo-fluid flowsjump conditionsaugmented variable approachsingular forceCartesian grid methods

Information

Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 7 , Issue 4 , November 2014 , pp. 447 - 472
Copyright
Copyright © Global Science Press Limited 2014

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