scholarly journals Non-Isothermal Free-Surface Viscous Flow of Polymer Melts in Pipe Extrusion Using an Open-Source Interface Tracking Finite Volume Method

Polymers ◽  
2021 ◽  
Vol 13 (24) ◽  
pp. 4454
Author(s):  
Célio Fernandes ◽  
Ahmad Fakhari ◽  
Željko Tukovic
Keyword(s):  
Constitutive Equation ◽  
Viscous Flow ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Large Scale ◽  
Polymer Melts ◽  
Arbitrary Lagrangian Eulerian ◽  
Extrudate Swell ◽  
Ale Formulation ◽  
Volume Method

Polymer extrudate swelling is a rheological phenomenon that occurs after polymer melt flow emerges at the die exit of extrusion equipment due to molecular stress relaxations and flow redistributions. Specifically, with the growing demand for large scale and high productivity, polymer pipes have recently been produced by extrusion. This study reports the development of a new incompressible non-isothermal finite volume method, based on the Arbitrary Lagrangian–Eulerian (ALE) formulation, to compute the viscous flow of polymer melts obeying the Herschel–Bulkley constitutive equation. The Papanastasiou-regularized version of the constitutive equation is employed. The influence of the temperature on the rheological behavior of the material is controlled by the Williams–Landel–Ferry (WLF) function. The new method is validated by comparing the extrudate swell ratio obtained for Bingham and Herschel–Bulkley flows (shear-thinning and shear-thickening) with reference data found in the scientific literature. Additionally, the essential flow characteristics including yield-stress, inertia and non-isothermal effects were investigated.

scholarly journals Local quasigeoid modelling in Slovakia using the finite volume method on the discretized Earth's topography

2020 ◽  
Vol 50 (3) ◽  
pp. 287-302
Author(s):  
Róbert ČUNDERLÍK ◽  
Matej MEDĽA ◽  
Karol MIKULA
Keyword(s):  
Numerical Solution ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Large Scale ◽  
Horizontal Resolution ◽  
Geopotential Model ◽  
Computational Domain ◽  
Disturbing Potential ◽  
Volume Method ◽  
Upper Boundary

The paper presents local quasigeoid modelling in Slovakia using the finite volume method (FVM). FVM is used to solve numerically the fixed gravimetric boundary value problem (FGBVP) on a 3D unstructured mesh created above the real Earth's surface. Terrestrial gravimetric measurements as input data represent the oblique derivative boundary conditions on the Earth's topography. To handle such oblique derivative problem, its tangential components are considered as surface advection terms regularized by a surface diffusion. The FVM numerical solution is fixed to the GOCE-based satellite-only geopotential model on the upper boundary at the altitude of 230 km. The horizontal resolution of the 3D computational domain is 0.002 × 0.002 deg and its discretization in the radial direction is changing with altitude. The created unstructured 3D mesh of finite volumes consists of 454,577,577 unknowns. The FVM numerical solution of FGBVP on such a detailed mesh leads to large-scale parallel computations requiring 245 GB of internal memory. It results in the disturbing potential obtained in the whole 3D computational domain. Its values on the discretized Earth's surface are transformed into the local quasigeoid model that is tested at 404 GNSS/levelling benchmarks. The standard deviation of residuals is 2.8 cm and decreases to 2.6 cm after removing 9 identified outliers. It indicates high accuracy of the obtained FVM-based local quasigeoid model in Slovakia.

A finite-volume method for the Euler equations on arbitrary lagrangian-eulerian grids

1991 ◽  
Vol 20 (4) ◽  
pp. 399-409 ◽  
Author(s):  
J.Y. Trépanier ◽  
M. Reggio ◽  
H. Zhang ◽  
R. Camarero
Keyword(s):  
Finite Volume Method ◽  
Euler Equations ◽  
Finite Volume ◽  
Arbitrary Lagrangian Eulerian ◽  
Volume Method

scholarly journals Three-Dimensional Hydrostatic Curved Channel Flow Simulations Using Non-Staggered Triangular Grids

Water ◽  
2022 ◽  
Vol 14 (2) ◽  
pp. 174
Author(s):  
Wei Zhang ◽  
Miguel Uh Uh Zapata ◽  
Damien Pham Van Pham Van Bang ◽  
Kim Dan Nguyen
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Channel Flow ◽  
Large Scale ◽  
Three Dimensional ◽  
Ocean Modeling ◽  
Curved Channel ◽  
Triangular Grids ◽  
Vortex Pattern ◽  
Volume Method

Non-staggered triangular grids have many advantages in performing river or ocean modeling with the finite-volume method. However, horizontal divergence errors may occur, especially in large-scale hydrostatic calculations with centrifugal acceleration. This paper proposes an unstructured finite-volume method with a filtered scheme to mitigate the divergence noise and avoid further influencing the velocities and water elevation. In hydrostatic pressure calculations, we apply the proposed method to three-dimensional curved channel flows. Approximations reduce the numerical errors after filtering the horizontal divergence operator, and the approximation is second-order accurate. Numerical results for the channel flow accurately calculate the velocity profile and surface elevation at different Froude numbers. Moreover, secondary flow features such as the vortex pattern and its movement along the channel sections are also well captured.

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