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Numerical simulation of 3D viscoelastic flows with free surfaces. (English) Zbl 1173.76303
Summary: A numerical model is presented for the simulation of viscoelastic flows with complex free surfaces in three space dimensions. The mathematical formulation of the model is similar to that of the volume of fluid (VOF) method, but the numerical procedures are different.
A splitting method is used for the time discretization. The prediction step consists in solving three advection problems, one for the volume fraction of liquid (which allows the new liquid domain to be obtained), one for the velocity field, one for the extra-stress. The correction step corresponds to solving an Oldroyd-B fluid flow problem without advection in the new liquid domain.
Two different grids are used for the space discretization. The three advection problems are solved on a fixed, structured grid made out of small cubic cells, using a forward characteristics method. The Oldroyd-B problem without advection is solved using continuous, piecewise linear stabilized finite elements on a fixed, unstructured mesh of tetrahedrons. Efficient post-processing algorithms enhance the quality of the numerical solution. A hierarchical data structure reduces the memory requirements.
Convergence of the numerical method is checked for the pure extensional flow and the filling of a tube. Numerical results are presented for the stretching of a filament. Fingering instabilities are obtained when the aspect ratio is large. Also, results pertaining to jet buckling are reported.

MSC:
76A10 Viscoelastic fluids
76M10 Finite element methods applied to problems in fluid mechanics
76M25 Other numerical methods (fluid mechanics) (MSC2010)
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
Software:
PROST; SLIC
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