An algorithm for the simulation of transient viscoelastic flows with free surfaces
Journal of Computational Physics
Superconvergence and the superconvergent patch recovery
Finite Elements in Analysis and Design - Special issue: Robert J. Melosh Medal Competition
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This paper presents the filament-stretching problem for Newtonian fluid by Semi-implicit Taylor-Galerkin/Pressure correction finite element methods (STGFEM). The assumptions of incompressible fluid, no gravitational effect, and temperature independence are used. The two-dimensional governing equations are derived through the conservation of mass and momentum in cylindrical coordinate system. The configuration of mesh, which is elaborately and dominantly biased, can reflect true stretching behavior. The large deformation of fluid at free surface will be effected by surface tension force, thus both dynamic and kinematic boundary conditions must be considered. Initial locations of free surface at each stretching step are computed by an elliptic equation. Then, the locations will be adjusted until the volume conserved. As the result, the solutions can be solved with reduced computational time and instability. The simulation program has been created to compute solutions, which are the variation of velocities, pressure, stresses, shear rate, and extension rate. Remeshing and interpolating techniques are used to increase accuracy of the solutions. This paper has produced solutions up to Hencky stain 1.92, which exhibit the same trend as the experimental ones.