American Institute of Mathematical Sciences

Advanced
2009, 2009(Special): 838-845. doi: 10.3934/proc.2009.2009.838

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

Sheng Xu 1,

1. 

Department of Mathematics, Southern Methodist University, Dallas, TX 75275, United States

Received  August 2008 Revised  March 2009 Published  September 2009

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: principal jump conditions, the Navier-Stokes equations, singular forces, two-fluid flow, the immersed interface method.
Mathematics Subject Classification: 76D05, 76M20, 65M06.
Citation: Sheng Xu. Derivation of principal jump conditions for the immersed interface method in two-fluid flow simulation. Conference Publications, 2009, 2009 (Special) : 838-845. doi: 10.3934/proc.2009.2009.838
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