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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

Velocity distributions near the upper domain boundary obtained with various open boundary conditions: (a) OBC Eq (3a), (b) OBC Eq (3b), (c) OBC Eq (3c), (d) OBC Eq (3d), (e) OBC Eq (4), (f) OBC Eq (5).Velocity vectors are plotted on every ninth quadrature points in each direction within each element.
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pone.0154565.g012: Velocity distributions near the upper domain boundary obtained with various open boundary conditions: (a) OBC Eq (3a), (b) OBC Eq (3b), (c) OBC Eq (3c), (d) OBC Eq (3d), (e) OBC Eq (4), (f) OBC Eq (5).Velocity vectors are plotted on every ninth quadrature points in each direction within each element.

Mentions: We observe that the open boundary conditions Eqs (3a)–(3d) proposed here produce flow characteristics that are similar to those based on the boundary conditions Eqs (4) and (5) from [6]. A comparison of the velocity distributions near the upper domain boundary obtained with different open boundary conditions is shown in Fig 12. This corresponds to a configuration where the pair of vortices trailing a free air bubble crosses the upper open boundary. Only the upper portion of the domain has been shown here for clarity. One can clearly observe the backflows into the domain induced by the vortices on sections of the upper boundary. Flows are also sucked into the domain through the side boundaries. The overall characteristics of the velocity fields obtained with these open boundary conditions appear qualitatively quite similar.


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

Dong S, Wang X - PLoS ONE (2016)

Velocity distributions near the upper domain boundary obtained with various open boundary conditions: (a) OBC Eq (3a), (b) OBC Eq (3b), (c) OBC Eq (3c), (d) OBC Eq (3d), (e) OBC Eq (4), (f) OBC Eq (5).Velocity vectors are plotted on every ninth quadrature points in each direction within each element.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0154565.g012: Velocity distributions near the upper domain boundary obtained with various open boundary conditions: (a) OBC Eq (3a), (b) OBC Eq (3b), (c) OBC Eq (3c), (d) OBC Eq (3d), (e) OBC Eq (4), (f) OBC Eq (5).Velocity vectors are plotted on every ninth quadrature points in each direction within each element.
Mentions: We observe that the open boundary conditions Eqs (3a)–(3d) proposed here produce flow characteristics that are similar to those based on the boundary conditions Eqs (4) and (5) from [6]. A comparison of the velocity distributions near the upper domain boundary obtained with different open boundary conditions is shown in Fig 12. This corresponds to a configuration where the pair of vortices trailing a free air bubble crosses the upper open boundary. Only the upper portion of the domain has been shown here for clarity. One can clearly observe the backflows into the domain induced by the vortices on sections of the upper boundary. Flows are also sucked into the domain through the side boundaries. The overall characteristics of the velocity fields obtained with these open boundary conditions appear qualitatively quite similar.

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