Communications in Applied Mathematics and Computational Science

Hybrid numerical treatment of two-fluid problems with passive interfaces

Nicholas Cogan

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Abstract

We consider the coupled motion of a passive interface separating two immiscible fluids of different viscosities. There are several applications where the velocity of the two fluids is needed everywhere within the domain. Examples include the transport of bacteria and diffusing substances within a biofilm matrix and the transport of cations throughout the mucociliary and periciliary layer in the lung lining. In this investigation, we use a hybrid approach which employs the boundary integral method to determine the interface velocity and the method of regularized stokeslets to determine the velocity elsewhere in the domain.

Our approach capitalizes on the strengths of the two methods, yielding an intuitive, efficient procedure for determining the velocity of a two-fluid system throughout the domain. A key feature of the method is the extension to two-fluid systems with varying viscosity. We describe the results of three numerical simulations designed to test the numerical method and motivate its use.

Article information

Source
Commun. Appl. Math. Comput. Sci., Volume 2, Number 1 (2007), 117-133.

Dates
Received: 13 November 2006
Accepted: 26 August 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.camcos/1513798532

Digital Object Identifier
doi:10.2140/camcos.2007.2.117

Mathematical Reviews number (MathSciNet)
MR2369382

Zentralblatt MATH identifier
1128.76021

Subjects
Primary: 76B70: Stratification effects in inviscid fluids

Keywords
two-fluid boundary integral method regularized stokeslets biofilm

Citation

Cogan, Nicholas. Hybrid numerical treatment of two-fluid problems with passive interfaces. Commun. Appl. Math. Comput. Sci. 2 (2007), no. 1, 117--133. doi:10.2140/camcos.2007.2.117. https://projecteuclid.org/euclid.camcos/1513798532


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