Commun. Comput. Phys., 12 (2012), pp. 528-543.

An Iterative Two-Fluid Pressure Solver Based on the Immersed Interface Method

Sheng Xu 1*

1 Department of Mathematics, Southern Methodist University, Dallas, TX 75275-0156, USA.

Received 9 February 2011; Accepted (in revised version) 22 August 2011
Available online 20 February 2012


An iterative solver based on the immersed interface method is proposed to solve the pressure in a two-fluid flow on a Cartesian grid with second-order accuracy in the infinity norm. The iteration is constructed by introducing an unsteady term in the pressure Poisson equation. In each iteration step, a Helmholtz equation is solved on the Cartesian grid using FFT. The combination of the iteration and the immersed interface method enables the solver to handle various jump conditions across two-fluid interfaces. This solver can also be used to solve Poisson equations on irregular domains.

AMS subject classifications: 76T99, 35J05, 65N06

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Key words: Poisson solver, the immersed interface method, two-fluid flow, jump conditions.

*Corresponding author.
Email: (S. Xu)

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