The characteristic-based split (CBS) scheme for viscoelastic flow past a circular cylinder

• Published in: International journal for numerical methods in fluids Vol. 57; no. 2; pp. 157 - 176
• Main Authors: Liu, Chun-Bin, Nithiarasu, P.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 20.04.2008; Wiley
• Subjects: artificial compressibility (AC); artificial dissipation; CBS scheme; Computational methods in fluid dynamics; Exact sciences and technology; FEM; Fluid dynamics; fractional step; Fundamental areas of phenomenology (including applications); Non-newtonian fluid flows; Oldroyd-B; Physics; Turbulent flows, convection, and heat transfer; Wakes; Rectangular pipe; Viscoelastic fluid; Pipe flow; Computational fluid dynamics; Oldroyd fluid; Digital simulation; Fractional step method; fractional step; Oldroyd-B; artificial dissipation; FEM; Finite element method; Algorithms; CBS scheme; Wakes; Circular cylinder; Modelling; Drag coefficient; artificial compressibility (AC)
• ISSN: 0271-2091; 1097-0363; 1097-0363
• DOI: 10.1002/fld.1625

A fully explicit, characteristic‐based split (CBS) method for viscoelastic flow past a circular cylinder, placed in a rectangular channel, is presented. The pressure equation in its explicit form is employed via an artificial compressibility parameter. The constitutive equations used here are based on the Oldroyd‐B model. No loss of convergence to steady state was observed in any of the results presented in this paper. Comparison of the present results with other available numerical data shows that the CBS algorithm is in excellent agreement with them at lower Deborah numbers. However, at higher Deborah numbers, the present results differ from other numerical solutions. This is due to the fact that the positive definitiveness of the conformation matrix is lost between a Deborah number of 0.6 and 0.7. However, the positive definitiveness is retained when an artificial diffusion is added to the discrete constitutive equations at higher Deborah numbers. It appears that the fractional solution stages used in the CBS scheme and the higher‐order time step‐based convection stabilization clearly reduce the instability at higher Deborah numbers. The Deborah number limit reached in the present work is three without artificial dissipation and two with artificial dissipation. Copyright © 2007 John Wiley & Sons, Ltd.