Volume 7, Issue 4
The Immersed Interface Method for Simulating Two-Fluid Flows

Miguel Uh & Sheng Xu

Numer. Math. Theor. Meth. Appl., 7 (2014), pp. 447-472.

Published online: 2014-07

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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

Immersed interface method, two-fluid flows, jump conditions, augmented variable approach, singular force, Cartesian grid methods.

  • AMS Subject Headings

76M20, 65M06, 35Q35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-7-447, author = {}, title = {The Immersed Interface Method for Simulating Two-Fluid Flows}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2014}, volume = {7}, number = {4}, pages = {447--472}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2014.1309si}, url = {http://global-sci.org/intro/article_detail/nmtma/5884.html} }
TY - JOUR T1 - The Immersed Interface Method for Simulating Two-Fluid Flows JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 447 EP - 472 PY - 2014 DA - 2014/07 SN - 7 DO - http://doi.org/10.4208/nmtma.2014.1309si UR - https://global-sci.org/intro/article_detail/nmtma/5884.html KW - Immersed interface method, two-fluid flows, jump conditions, augmented variable approach, singular force, Cartesian grid methods. AB -

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.

Miguel Uh & Sheng Xu. (2020). The Immersed Interface Method for Simulating Two-Fluid Flows. Numerical Mathematics: Theory, Methods and Applications. 7 (4). 447-472. doi:10.4208/nmtma.2014.1309si
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