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# A Solenoidal Initial Condition for the Numerical Solution of the Navier-Stokes Equations for Two-Phase Incompressible Flow

F. Bierbrauer, S.-P. Zhu1

School of Mathematics and Applied Statistics, University of Wollongong, NSW, 2522, Australia

Computer Modeling in Engineering & Sciences 2007, 19(1), 1-22. https://doi.org/10.3970/cmes.2007.019.001

## Abstract

Recently the use of the one-field formulation in the numerical solution of the Navier-Stokes equations for two-phase incompressible flow has become a very attractive approach in CFD (computational fluid dynamics). While the presence of material discontinuities across fluid interfaces presents some difficulty, it is their combination with a non-solenoidal discontinuous initial velocity field, commonly occurring in the mathematical formulation, that has provided the greatest hindrance in the numerical solution. This paper presents three analytical solutions, the Bounded Creeping Flow, Solenoidal and Conserved Solenoidal Solutions, which are both continuous, incompressible, retain as much of the original mathematical formulation as possible and provide a physically reasonable initial velocity field.

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APA Style
Bierbrauer, F., Zhu, S. (2007). A solenoidal initial condition for the numerical solution of the navier-stokes equations for two-phase incompressible flow. Computer Modeling in Engineering & Sciences, 19(1), 1-22. https://doi.org/10.3970/cmes.2007.019.001
Vancouver Style
Bierbrauer F, Zhu S. A solenoidal initial condition for the numerical solution of the navier-stokes equations for two-phase incompressible flow. Comput Model Eng Sci. 2007;19(1):1-22 https://doi.org/10.3970/cmes.2007.019.001
IEEE Style
F. Bierbrauer and S. Zhu, "A Solenoidal Initial Condition for the Numerical Solution of the Navier-Stokes Equations for Two-Phase Incompressible Flow," Comput. Model. Eng. Sci., vol. 19, no. 1, pp. 1-22. 2007. https://doi.org/10.3970/cmes.2007.019.001

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