Three-dimensional volume-conserving immersed boundary model for two-phase fluid flows

Li, Yibao; Yun, Ana; Lee, Dongsun; Shin, Jeeyoung; Jeong, Darae

doi:10.1016/j.cma.2013.01.009

Cited by 28 publications

(15 citation statements)

References 54 publications

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“…Finally, let us mention that developing and analyzing numerical methods for two-phase flows is a very active research field, and we refer to [47,2,15,16,52,32,35] for some examples of recent contributions.…”

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confidence: 99%

A Stable Parametric Finite Element Discretization of Two-Phase Navier–Stokes Flow

2014

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We present a parametric finite element approximation of two-phase flow. This free boundary problem is given by the Navier-Stokes equations in the two phases, which are coupled via jump conditions across the interface. Using a novel variational formulation for the interface evolution gives rise to a natural discretization of the mean curvature of the interface. The parametric finite element approximation of the evolving interface is then coupled to a standard finite element approximation of the two-phase Navier-Stokes equations in the bulk. Here enriching the pressure approximation space with the help of an XFEM function ensures good volume conservation properties for the two phase regions. In addition, the mesh quality of the parametric approximation of the interface in general does not deteriorate over time, and an equidistribution property can be shown for a semidiscrete continuousin-time variant of our scheme in two space dimensions. Moreover, our finite element approximation can be shown to be unconditionally stable. We demonstrate the applicability of our method with some numerical results in two and three space dimensions.

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confidence: 99%

A Stable Parametric Finite Element Discretization of Two-Phase Navier–Stokes Flow

2014

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“…With different projection methods, the gradient pressure term (∇ d p) is added (Kim, 2005;Kim & Moin, 1985;Poux, Glockner, & Azaïez, 2011;Tseng & Huang, 2014) or subtracted (Chorin, 1968;Li, Jung, Lee, Lee, & Kim, 2012;Li, Yun, Lee, Shin, Jeong, & Kim, 2013). Our proposed method for the intermediate velocity will work well if ∇ d p is subtracted.…”

Section: Boundary Condition For Intermediate Velocitymentioning

confidence: 99%

A simple and efficient outflow boundary condition for the incompressible Navier–Stokes equations

Choi

Choic³

et al. 2016

Engineering Applications of Computational Fluid Mechanics

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Many researchers have proposed special treatments for outlet boundary conditions owing to lack of information at the outlet. Among them, the simplest method requires a large enough computational domain to prevent or reduce numerical errors at the boundaries. However, an efficient method generally requires special treatment to overcome the problems raised by the outlet boundary condition used. For example, mass flux is not conserved and the fluid field is not divergence-free at the outlet boundary. Overcoming these problems requires additional computational cost. In this paper, we present a simple and efficient outflow boundary condition for the incompressible Navier-Stokes equations, aiming to reduce the computational domain for simulating flow inside a long channel in the streamwise direction. The proposed outflow boundary condition is based on the transparent equation, where a weak formulation is used. The pressure boundary condition is derived by using the Navier-Stokes equations and the outlet flow boundary condition. In the numerical algorithm, a staggered marker-and-cell grid is used and temporal discretization is based on a projection method. The intermediate velocity boundary condition is consistently adopted to handle the velocity-pressure coupling. Characteristic numerical experiments are presented to demonstrate the robustness and accuracy of the proposed numerical scheme. Furthermore, the agreement of computational results from small and large domains suggests that our proposed outflow boundary condition can significantly reduce computational domain sizes. ARTICLE HISTORY

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“…See [17] for more detailed explanation about the polyhedron volume. Also, we define the percent of relative error of volume (X) with the initial volume (X 0 ) as…”

Section: Volume Preservationmentioning

confidence: 99%

Curve and Surface Smoothing Using a Modified Cahn‐Hilliard Equation

Choi

Jeong

Kim

2017

Mathematical Problems in Engineering

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We present a new method using the modified Cahn-Hilliard (CH) equation for smoothing piecewise linear shapes of two-and three-dimensional objects. The CH equation has good smoothing dynamics and it is coupled with a fidelity term which keeps the original given data; that is, it does not produce significant shrinkage. The modified CH equation is discretized using a linearly stable splitting scheme in time and the resulting scheme is solved by using a Fourier spectral method. We present computational results for both curve and surface smoothing problems. The computational results demonstrate that the proposed algorithm is fast and efficient.

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Three-dimensional volume-conserving immersed boundary model for two-phase fluid flows

Cited by 28 publications

References 54 publications

A Stable Parametric Finite Element Discretization of Two-Phase Navier–Stokes Flow

A Stable Parametric Finite Element Discretization of Two-Phase Navier–Stokes Flow

A simple and efficient outflow boundary condition for the incompressible Navier–Stokes equations

Curve and Surface Smoothing Using a Modified Cahn‐Hilliard Equation

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