Bertoco, J.; Castelo, A.; Ferrás, L.L.; Fernandes, C. Numerical Simulation of Three-Dimensional Free Surface Flows Using the K–BKZ–PSM Integral Constitutive Equation. Polymers2023, 15, 3705.
Bertoco, J.; Castelo, A.; Ferrás, L.L.; Fernandes, C. Numerical Simulation of Three-Dimensional Free Surface Flows Using the K–BKZ–PSM Integral Constitutive Equation. Polymers 2023, 15, 3705.
Bertoco, J.; Castelo, A.; Ferrás, L.L.; Fernandes, C. Numerical Simulation of Three-Dimensional Free Surface Flows Using the K–BKZ–PSM Integral Constitutive Equation. Polymers2023, 15, 3705.
Bertoco, J.; Castelo, A.; Ferrás, L.L.; Fernandes, C. Numerical Simulation of Three-Dimensional Free Surface Flows Using the K–BKZ–PSM Integral Constitutive Equation. Polymers 2023, 15, 3705.
Abstract
This work introduces a novel numerical method designed to address three-dimensional unsteady free surface flows incorporating integral viscoelastic constitutive equations, specifically, the K-BKZ-PSM (Kaye–Bernstein, Kearsley, Zapas - Papanastasiou, Scriven, Macosko) model. The new proposed methodology employs a second-order finite difference approach along with the deformation fields method to solve the integral constitutive equation, and the marker-particle method (known as \emph{Marker-and-Cell}) to accurately capture the evolution of the fluid's free surface. The newly developed numerical method has proven its effectiveness in handling complex fluid flow scenarios, including confined flows and extrudate swell simulations of Boger fluids. Furthermore, a new semi-analytical solution for velocity and stress fields is derived, considering fully developed flows of a K-BKZ-PSM fluid in a pipe.
Computer Science and Mathematics, Applied Mathematics
Copyright:
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