An isochoric domain deformation method for computing steady free surface flows with conserved volumes

Xie, Xueying; Musson, Lawrence; Pasquali, Matteo

doi:10.1016/j.jcp.2007.04.028

Cited by 7 publications

(3 citation statements)

References 15 publications

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“…From a computational standpoint, the moving internal boundaries present a numerical challenge, and two classes of methods have been developed to meet it: interface tracking and interface capturing [2]. The former deploys grid points or markers on the interface that track it each time step [3][4][5]. The latter uses an auxiliary scalar field that distinguishes the fluid components.…”

Section: Introductionmentioning

confidence: 99%

3D phase-field simulations of interfacial dynamics in Newtonian and viscoelastic fluids

Zhou

Yue

Feng

et al. 2010

Journal of Computational Physics

119

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-This work presents a three-dimensional finite-element algorithm, based on the phase-field model, for computing interfacial flows of Newtonian and complex fluids. A 3D adaptive meshing scheme produces fine grid covering the interface and coarse mesh in the bulk. It is key to accurate resolution of the interface at manageable computational costs.The coupled Navier-Stokes and Cahn-Hilliard equations, plus the constitutive equation for non-Newtonian fluids, are solved using second-order implicit time stepping. Within each time step, Newton iteration is used to handle the nonlinearity, and the linear algebraic system is solved by preconditioned Krylov methods. The phase-field model, with a physically diffuse interface, affords the method several advantages in computing interfacial dynamics.One is the ease in simulating topological changes such as interfacial rupture and coalescence.Another is the capability of computing contact line motion without invoking ad hoc slip conditions. As validation of the 3D numerical scheme, we have computed drop deformation in an elongational flow, relaxation of a deformed drop to the spherical shape, and drop spreading on a partially wetting substrate. The results are compared with numerical and experimental results in the literature as well as our own axisymmetric computations where appropriate. Excellent agreement is achieved provided that the 3D interface is adequately resolved by using a sufficiently thin diffuse interface and refined grid. Since our model involves several coupled partial differential equations and we use a fully implicit scheme, the matrix inversion requires a large memory. This puts a limit on the scale of problems that can be simulated in 3D, especially for viscoelastic fluids.

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Section: Introductionmentioning

confidence: 99%

3D phase-field simulations of interfacial dynamics in Newtonian and viscoelastic fluids

Zhou

Yue

Feng

et al. 2010

Journal of Computational Physics

119

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“…To address the latter, a number of pioneering studies (Epureanu et al, 2002;Anttonen et al, 2003Anttonen et al, , 2005Feng and Soulaïmani, 2007;Liberge et al, 2008) endeavored to adapt Eulerian-Lagrangian dynamic mesh adaptation methods, that are commonly used in CFD models of aeroelasticity (Batina, 1990;Farhat et al, 1998;Blom, 2000;Schuster et al, 2003;Ishihara and Yoshimura, 2005;Hsu and Chang, 2007;Xie et al, 2007;Braun et al, 2008;Roszak et al, 2009). To address the latter, a number of pioneering studies (Epureanu et al, 2002;Anttonen et al, 2003Anttonen et al, , 2005Feng and Soulaïmani, 2007;Liberge et al, 2008) endeavored to adapt Eulerian-Lagrangian dynamic mesh adaptation methods, that are commonly used in CFD models of aeroelasticity (Batina, 1990;Farhat et al, 1998;Blom, 2000;Schuster et al, 2003;Ishihara and Yoshimura, 2005;Hsu and Chang, 2007;Xie et al, 2007;Braun et al, 2008;Roszak et al, 2009).…”

Section: Lagrangian-ulerian Methods and Deformable Gridsmentioning

confidence: 99%

Reduced-Order Modelling for Flow Control

Noack¹,

Morzyński²,

Tadmor³

2011

CISM International Centre for Mechanical Sciences

193

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“…For steady state flows, one can solve the problem by the domain deformation method [26,91] or even simplify the problem to Laplace equations [55,64] by neglecting viscous effects.…”

Section: Computational Backgroundmentioning

confidence: 99%