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Derivation of principal jump conditions for the immersed interface method in two-fluid flow simulation

Pages: 838 - 845, Issue Special, September 2009

 Abstract        Full Text (133.6K)              

Sheng Xu - Department of Mathematics, Southern Methodist University, Dallas, TX 75275, United States (email)

Abstract: In a flow of two immiscible incompressible viscous fluids, jump discontinuities of flow quantities appear at the two-fluid interface. The immersed interface method can accurately and efficiently simulate the flow without smearing the sharp interface by incorporating necessary jump conditions into a numerical scheme. In this paper, we systematically derive the principal jump conditions for the velocity, the pressure, and their normal derivatives.

Keywords:  the immersed interface method, principal jump conditions, two-fluid flow, singular forces, the Navier-Stokes equations
Mathematics Subject Classification:  76D05, 76M20, 65M06

Received: August 2008;      Revised: March 2009;      Published: September 2009.