Derivation of principal jump conditions for the immersed interface method in two-fluid flow simulation
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
Received: August 2008; Revised: March 2009; Published: September 2009.