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

2009 ◽  
Keyword(s):  
Fluid Flow ◽  
Flow Simulation ◽  
Jump Conditions ◽  
Immersed Interface Method ◽  
Immersed Interface ◽  
Two Fluid

On the Jump Conditions for an Immersed Interface Method

2016 ◽  
Vol 38 (3) ◽  
pp. A1280-A1316 ◽  
Author(s):  
Mounir Bennoune ◽  
Jérôme Morin-Drouin ◽  
Robert G. Owens
Keyword(s):  
Jump Conditions ◽  
Immersed Interface Method ◽  
Immersed Interface

An Iterative Two-Fluid Pressure Solver Based on the Immersed Interface Method

2012 ◽  
Vol 12 (2) ◽  
pp. 528-543 ◽  
Author(s):  
Sheng Xu
Keyword(s):  
Fluid Pressure ◽  
Cartesian Grid ◽  
Iteration Step ◽  
Fluid Interfaces ◽  
Order Accuracy ◽  
Immersed Interface Method ◽  
Immersed Interface ◽  
Pressure Poisson Equation ◽  
Poisson Equations ◽  
Two Fluid

AbstractAn iterative solver based on the immersed interface method is proposed to solve the pressure in a two-fluid flow on a Cartesian grid with second-order accuracy in the infinity norm. The iteration is constructed by introducing an unsteady term in the pressure Poisson equation. In each iteration step, a Helmholtz equation is solved on the Cartesian grid using FFT. The combination of the iteration and the immersed interface method enables the solver to handle various jump conditions across two-fluid interfaces. This solver can also be used to solve Poisson equations on irregular domains.

An Immersed Interface Method for the Simulation of Inextensible Interfaces in Viscous Fluids

2012 ◽  
Vol 11 (3) ◽  
pp. 925-950 ◽  
Author(s):  
Zhijun Tan ◽  
D. V. Le ◽  
K. M. Lim ◽  
B. C. Khoo
Keyword(s):  
Present Method ◽  
Incompressible Flows ◽  
Viscous Fluids ◽  
Gmres Method ◽  
Jump Conditions ◽  
Governing Equations ◽  
Immersed Interface Method ◽  
Immersed Interface ◽  
Type Method ◽  
Augmented System

AbstractIn this paper, an immersed interface method is presented to simulate the dynamics of inextensible interfaces in an incompressible flow. The tension is introduced as an augmented variable to satisfy the constraint of interface inextensibility and the resulting augmented system is solved by the GMRES method. In this work, the arclength of the interface is locally and globally conserved as the enclosed region undergoes deformation. The forces at the interface are calculated from the configuration of the interface and the computed augmented variable, and then applied to the fluid through the related jump conditions. The governing equations are discretized on a MAC grid via a second-order finite difference scheme which incorporates jump contributions and solved by the conjugate gradient Uzawa-type method. The proposed method is applied to several examples including the deformation of a liquid capsule with inextensible interfaces in a shear flow. Numerical results reveal that both the area enclosed by interface and arclength of interface are conserved well simultaneously. These provide further evidence on the capability of the present method to simulate incompressible flows involving inextensible interfaces.

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