The Immersed Interface Method for Simulating Two-Fluid Flows. Issue 4 (9th August 2018)

• Record Type: Journal Article
• Authors: Uh, Miguel; Xu, Sheng
• Is Part Of: Numerical mathematics. Volume 7:Issue 4(2014)
• Page Start: 447
• Page End: 472
• Publication Date: 2018-08-09
• Subjects: 76M20, -- 65M06, -- 35Q35; Immersed interface method, -- two-fluid flows, -- jump conditions, -- augmented variable approach, -- singular force, -- Cartesian grid methods; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.1017/S1004897900001288
• Languages: English
• ISSNs: 1004-8979

Abstract

Abstract: We develop the immersed interface method (IIM) to simulate a two-fluid flow of two immiscible fluids with different density and viscosity. Due to the surface tension and the discontinuous fluid properties, the two-fluid flow has nonsmooth velocity and discontinuous pressure across the moving sharp interface separating the two fluids. The IIM computes the flow on a fixed Cartesian grid by incorporating into numerical schemes the necessary jump conditions induced by the interface. We present how to compute these necessary jump conditions from the analytical principal jump conditions derived in [Xu, DCDS, Supplement 2009, pp. 838-845]. We test our method on some canonical two-fluid flows. The results demonstrate that the method can handle large density and viscosity ratios, is second-order accurate in the infinity norm, and conserves mass inside a closed interface.