TY - CHAP

T1 - A Diffuse Interface Model for Incompressible Two-Phase Flow with Large Density Ratios

AU - Xie, Yu

AU - Wodo, Olga

AU - Ganapathysubramanian, Baskar

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The authors acknowledge partial funding from KAUST CRG, NSF 1236839, and NSF 1149365. Computing support from NSF XSEDE via TG-CTS110007 is gratefully acknowledged.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2016/10/4

Y1 - 2016/10/4

N2 - In this chapter, we explore numerical simulations of incompressible and immiscible two-phase flows. The description of the fluid–fluid interface is introduced via a diffuse interface approach. The two-phase fluid system is represented by a coupled Cahn–Hilliard Navier–Stokes set of equations. We discuss challenges and approaches to solving this coupled set of equations using a stabilized finite element formulation, especially in the case of a large density ratio between the two fluids. Specific features that enabled efficient solution of the equations include: (i) a conservative form of the convective term in the Cahn–Hilliard equation which ensures mass conservation of both fluid components; (ii) a continuous formula to compute the interfacial surface tension which results in lower requirement on the spatial resolution of the interface; and (iii) a four-step fractional scheme to decouple pressure from velocity in the Navier–Stokes equation. These are integrated with standard streamline-upwind Petrov–Galerkin stabilization to avoid spurious oscillations. We perform numerical tests to determine the minimal resolution of spatial discretization. Finally, we illustrate the accuracy of the framework using the analytical results of Prosperetti for a damped oscillating interface between two fluids with a density contrast.

AB - In this chapter, we explore numerical simulations of incompressible and immiscible two-phase flows. The description of the fluid–fluid interface is introduced via a diffuse interface approach. The two-phase fluid system is represented by a coupled Cahn–Hilliard Navier–Stokes set of equations. We discuss challenges and approaches to solving this coupled set of equations using a stabilized finite element formulation, especially in the case of a large density ratio between the two fluids. Specific features that enabled efficient solution of the equations include: (i) a conservative form of the convective term in the Cahn–Hilliard equation which ensures mass conservation of both fluid components; (ii) a continuous formula to compute the interfacial surface tension which results in lower requirement on the spatial resolution of the interface; and (iii) a four-step fractional scheme to decouple pressure from velocity in the Navier–Stokes equation. These are integrated with standard streamline-upwind Petrov–Galerkin stabilization to avoid spurious oscillations. We perform numerical tests to determine the minimal resolution of spatial discretization. Finally, we illustrate the accuracy of the framework using the analytical results of Prosperetti for a damped oscillating interface between two fluids with a density contrast.

UR - http://hdl.handle.net/10754/623504

UR - http://link.springer.com/10.1007/978-3-319-40827-9_16

UR - http://www.scopus.com/inward/record.url?scp=84992313463&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-40827-9_16

DO - 10.1007/978-3-319-40827-9_16

M3 - Chapter

SN - 9783319408255

SP - 203

EP - 215

BT - Advances in Computational Fluid-Structure Interaction and Flow Simulation

PB - Springer Nature

ER -