Abstract—The work concerns least-squares (LS) finite element solutions of the Oldroyd-B viscoelastic fluid flows using adaptive grids. To capture the viscoelastic flow region, adaptive grids are automatically generated on the basis of the von Mises stress from stress component transfer functions, and these generated refined grids agree with the physical flow attributes. Model problems considered are the flow past a slot channel problems. Numerical solutions of the flow pass through a slot channel indicate that the viscoelastic polymer solution flow characteristics are described by the refinement results of the von Mises stress. In additions, adaptive grids using the von Mises stress outperform those using functions of velocity, and satisfactory results are obtained using a lower total numbers of elements. The developed method is effective for analyzing viscoelastic fluid flows. Furthermore, the effects of low Weissenberg numbers are also investigated.

Index Terms—Least-squares, viscoelastic fluid, adaptive mesh refinement, von Mises stress, transverse Slot.

Hsueh-Chen Lee is with General Education Center, Wenzao Ursuline University of Languages, Kaohsiung, Taiwan (email: 87013@mail.wzu.edu.tw; hsuehchen.lee@gmail.com).

Cite: Hsueh-Chen Lee, "Numerical Simulations of Viscoelastic Fluid Flows Using a Least-Squares Finite Element Method Based on Von Mises Stress Criteria," International Journal of Applied Physics and Mathematics vol. 7, no. 3, pp. 157-164, 2017.