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A Rotational Pressure-Correction Scheme for Incompressible Two-Phase Flows with Open Boundaries.

Dong S, Wang X - PLoS ONE (2016)

Bottom Line: Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary.By comparing simulation results with theory and the experimental data, we show that the method produces physically accurate results.We also present numerical experiments to demonstrate the long-term stability of the method in situations where large density contrast, large viscosity contrast, and backflows occur at the two-phase open boundaries.

View Article: PubMed Central - PubMed

Affiliation: Center for Computational & Applied Mathematics, Department of Mathematics, Purdue University, West Lafayette, Indiana, United States of America.

ABSTRACT
Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We present several new forms of open boundary conditions for two-phase outflow simulations within the phase field framework, as well as a rotational pressure correction based algorithm for numerically treating these open boundary conditions. Our algorithm gives rise to linear algebraic systems for the velocity and the pressure that involve only constant and time-independent coefficient matrices after discretization, despite the variable density and variable viscosity of the two-phase mixture. By comparing simulation results with theory and the experimental data, we show that the method produces physically accurate results. We also present numerical experiments to demonstrate the long-term stability of the method in situations where large density contrast, large viscosity contrast, and backflows occur at the two-phase open boundaries.

No MeSH data available.


Related in: MedlinePlus

Bouncing water drop (drop radius 1mm, initial height H0 = 3.2mm): temporal sequence of snapshots of the air-water interface at non-dimensional time instants: (a) t = 0.05, (b) t = 0.25, (c) t = 0.4, (d) t = 0.55, (e) t = 0.7, (f) t = 0.85, (g) t = 1.0, (h) t = 1.15.
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pone.0154565.g004: Bouncing water drop (drop radius 1mm, initial height H0 = 3.2mm): temporal sequence of snapshots of the air-water interface at non-dimensional time instants: (a) t = 0.05, (b) t = 0.25, (c) t = 0.4, (d) t = 0.55, (e) t = 0.7, (f) t = 0.85, (g) t = 1.0, (h) t = 1.15.

Mentions: We consider a rectangular domain (see Fig 4(a)), and , where L is specified later. The domain is periodic in the horizontal direction at . The top and bottom of the domain are two superhydrophobic solid walls. If the air-water interface intersects the walls, the contact angle is assumed to be 170°. The domain is initially filled with air. A water drop, initially circular with a radius , is suspended in the air. The center of the water drop is initially located at a height H0 above the bottom wall, that is, (x0, y0) = (0, H0), where (x0, y0) is the coordinate of the center of mass of the water drop. H0 is varied in the simulations. The gravity is assumed to be in the −y direction. At t = 0, the water drop is released, and falls through the air, impacting and bouncing off the bottom wall. The objective of this problem is to simulate and study the behavior of the water drop.


A Rotational Pressure-Correction Scheme for Incompressible Two-Phase Flows with Open Boundaries.

Dong S, Wang X - PLoS ONE (2016)

Bouncing water drop (drop radius 1mm, initial height H0 = 3.2mm): temporal sequence of snapshots of the air-water interface at non-dimensional time instants: (a) t = 0.05, (b) t = 0.25, (c) t = 0.4, (d) t = 0.55, (e) t = 0.7, (f) t = 0.85, (g) t = 1.0, (h) t = 1.15.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4862665&req=5

pone.0154565.g004: Bouncing water drop (drop radius 1mm, initial height H0 = 3.2mm): temporal sequence of snapshots of the air-water interface at non-dimensional time instants: (a) t = 0.05, (b) t = 0.25, (c) t = 0.4, (d) t = 0.55, (e) t = 0.7, (f) t = 0.85, (g) t = 1.0, (h) t = 1.15.
Mentions: We consider a rectangular domain (see Fig 4(a)), and , where L is specified later. The domain is periodic in the horizontal direction at . The top and bottom of the domain are two superhydrophobic solid walls. If the air-water interface intersects the walls, the contact angle is assumed to be 170°. The domain is initially filled with air. A water drop, initially circular with a radius , is suspended in the air. The center of the water drop is initially located at a height H0 above the bottom wall, that is, (x0, y0) = (0, H0), where (x0, y0) is the coordinate of the center of mass of the water drop. H0 is varied in the simulations. The gravity is assumed to be in the −y direction. At t = 0, the water drop is released, and falls through the air, impacting and bouncing off the bottom wall. The objective of this problem is to simulate and study the behavior of the water drop.

Bottom Line: Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary.By comparing simulation results with theory and the experimental data, we show that the method produces physically accurate results.We also present numerical experiments to demonstrate the long-term stability of the method in situations where large density contrast, large viscosity contrast, and backflows occur at the two-phase open boundaries.

View Article: PubMed Central - PubMed

Affiliation: Center for Computational & Applied Mathematics, Department of Mathematics, Purdue University, West Lafayette, Indiana, United States of America.

ABSTRACT
Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We present several new forms of open boundary conditions for two-phase outflow simulations within the phase field framework, as well as a rotational pressure correction based algorithm for numerically treating these open boundary conditions. Our algorithm gives rise to linear algebraic systems for the velocity and the pressure that involve only constant and time-independent coefficient matrices after discretization, despite the variable density and variable viscosity of the two-phase mixture. By comparing simulation results with theory and the experimental data, we show that the method produces physically accurate results. We also present numerical experiments to demonstrate the long-term stability of the method in situations where large density contrast, large viscosity contrast, and backflows occur at the two-phase open boundaries.

No MeSH data available.


Related in: MedlinePlus