Volume 11, Issue 3
An Immersed Interface Method for the Simulation of Inextensible Interfaces in Viscous Fluids

Zhijun Tan, D. V. Le, K. M. Lim & B. C. Khoo

Commun. Comput. Phys., 11 (2012), pp. 925-950.

Published online: 2012-11

Preview Full PDF 149 1185
Export citation
  • Abstract

In this paper, an immersed interface method is presented to simulate the dynamics of inextensible interfaces in an incompressible flow. The tension is introduced as an augmented variable to satisfy the constraint of interface inextensibility, and the resulting augmented system is solved by the GMRES method. In this work, the arclength of the interface is locally and globally conserved as the enclosed region undergoes deformation. The forces at the interface are calculated from the configuration of the interface and the computed augmented variable, and then applied to the fluid through the related jump conditions. The governing equations are discretized on a MAC grid via a second-order finite difference scheme which incorporates jump contributions and solved by the conjugate gradient Uzawa-type method. The proposed method is applied to several examples including the deformation of a liquid capsule with inextensible interfaces in a shear flow. Numerical results reveal that both the area enclosed by interface and arclength of interface are conserved well simultaneously. These provide further evidence on the capability of the present method to simulate incompressible flows involving inextensible interfaces.

  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-11-925, author = {}, title = {An Immersed Interface Method for the Simulation of Inextensible Interfaces in Viscous Fluids}, journal = {Communications in Computational Physics}, year = {2012}, volume = {11}, number = {3}, pages = {925--950}, abstract = {

In this paper, an immersed interface method is presented to simulate the dynamics of inextensible interfaces in an incompressible flow. The tension is introduced as an augmented variable to satisfy the constraint of interface inextensibility, and the resulting augmented system is solved by the GMRES method. In this work, the arclength of the interface is locally and globally conserved as the enclosed region undergoes deformation. The forces at the interface are calculated from the configuration of the interface and the computed augmented variable, and then applied to the fluid through the related jump conditions. The governing equations are discretized on a MAC grid via a second-order finite difference scheme which incorporates jump contributions and solved by the conjugate gradient Uzawa-type method. The proposed method is applied to several examples including the deformation of a liquid capsule with inextensible interfaces in a shear flow. Numerical results reveal that both the area enclosed by interface and arclength of interface are conserved well simultaneously. These provide further evidence on the capability of the present method to simulate incompressible flows involving inextensible interfaces.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.200110.040511a}, url = {http://global-sci.org/intro/article_detail/cicp/7396.html} }
TY - JOUR T1 - An Immersed Interface Method for the Simulation of Inextensible Interfaces in Viscous Fluids JO - Communications in Computational Physics VL - 3 SP - 925 EP - 950 PY - 2012 DA - 2012/11 SN - 11 DO - http://doi.org/10.4208/cicp.200110.040511a UR - https://global-sci.org/intro/article_detail/cicp/7396.html KW - AB -

In this paper, an immersed interface method is presented to simulate the dynamics of inextensible interfaces in an incompressible flow. The tension is introduced as an augmented variable to satisfy the constraint of interface inextensibility, and the resulting augmented system is solved by the GMRES method. In this work, the arclength of the interface is locally and globally conserved as the enclosed region undergoes deformation. The forces at the interface are calculated from the configuration of the interface and the computed augmented variable, and then applied to the fluid through the related jump conditions. The governing equations are discretized on a MAC grid via a second-order finite difference scheme which incorporates jump contributions and solved by the conjugate gradient Uzawa-type method. The proposed method is applied to several examples including the deformation of a liquid capsule with inextensible interfaces in a shear flow. Numerical results reveal that both the area enclosed by interface and arclength of interface are conserved well simultaneously. These provide further evidence on the capability of the present method to simulate incompressible flows involving inextensible interfaces.

Zhijun Tan, D. V. Le, K. M. Lim & B. C. Khoo. (2020). An Immersed Interface Method for the Simulation of Inextensible Interfaces in Viscous Fluids. Communications in Computational Physics. 11 (3). 925-950. doi:10.4208/cicp.200110.040511a
Copy to clipboard
The citation has been copied to your clipboard