Abstract
The subject of the paper is the numerical simulation of two-phase flow of immiscible fluids. Their motion is described by the incompressible Navier-Stokes equations with different constant density and viscosity for different fluids. The interface between the fluids is defined with the aid of the level-set method using a transport first-order hyperbolic equation. The Navier-Stokes system is equipped with initial and boundary conditions and transmission conditions on the interface between the two fluids. This system is discretized by the Taylor-Hood P2/P1 conforming finite elements in space and the second-order BDF method in time. The transport level-set problem is solved with the aid of the space-time discontinuous Galerkin method. Numerical experiments demonstrate that the developed method is accurate and robust.
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Communicated by: Pavel Solin
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This work was supported by the grant No. 17-01747S of the Czech Science Foundation. The research of E. Bezchlebová was also partially supported by the Student Faculty Grant (SFG) of the Faculty of Mathematics and Physics of the Charles University in Prague. The research of P. Sváček was supported by the grant of the Ministry of Education of the Czech Republic No. CZ.02.1.01/0.0/0.0/16_019/0000778.
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Bezchlebová, E., Dolejší, V., Feistauer, M. et al. Numerical simulation of two-phase flow of immiscible fluids by the finite element, discontinuous Galerkin and level-set methods. Adv Comput Math 45, 1993–2018 (2019). https://doi.org/10.1007/s10444-019-09681-1
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DOI: https://doi.org/10.1007/s10444-019-09681-1
Keywords
- Two-phase flow
- Immiscible fluids
- Navier-Stokes equations
- Transport level-set equation
- Finite element method
- BDF time discretization
- Space-time discontinuous Galerkin method
- Numerical experiments