High-order finite volume method for solving viscoelastic fluid lows

Abstract

Computational Fluid Dynamics (CFD) is widely used by polymer processing industries in order to evaluate polymeric fluid flows. A successful computational code must provide reliable predictions (modeling) in a fast and efficient way (simulation). In this work, a new approach to solve the governing equations of viscoelastic fluid flows is proposed. It is based on the finite-volume method with collocated arrangement of the variables, using high-order approximations for the linear and nonlinear average fluxes in the interfaces and for the nonlinear terms obtained from the discretization of the constitutive equations. The approximations are coupled to the Weighted Essentially Non-Oscillatory (WENO) scheme to avoid oscillations in the solution. The Oldroyd-B model is used to describe the rheological behavior of the viscoelastic fluid. The average values of the variables in the volumes are used during the resolution, and the point values are recovered in the post-processing step by deconvolution of the average values. The nonlinear system, resulting from the discretization of the equations, is solved simultaneously using a Newton-like method. The obtained solutions are oscillation-free and accurate, demonstrated by the application on a classic problem in computational fluid dynamics, the slip-stick flow

Viscoelastic flow analysis using the software OpenFOAM and differential constitutive equations

“…The higher the Weissenberg (or Deborah) number, the more pronounced the elastic effect. In the attempt of solving the HWNP or minimizing its effects, many strategies have been proposed, including special interpolations schemes [3,4] and specific numerical methodologies coupling momentum and constitutive viscoelastic equations [5][6][7][8].…”

Development of a high-order finite volume method with multiblock partition techniques

“…Direct use of the average values avoids numerical approximation schemes for the integrals involved, reducing, as a consequence, the number of discretization points and making the proposed procedure faster and more accurate than conventional procedures (Muniz et al, 2008;Pereira et al, 2001). Values of the variables in each of control volume face are obtained by polynomial interpolation using values of the corresponding variable at the center of neighboring control volumes.…”

“…Using high-order schemes allows one to obtain a solution with equal or better accuracy than low-order interpolation schemes considering less-refined meshes, hence, as a consequence reducing simulation processing time (Muniz et al, 2008;Piller and Stalio, 2004;Leonard, 1995;Kobayashi, 1999;Pereira et al, 2001). Fourth-order Lagrange interpolation schemes have been considered in this paper.…”

“…For this example two flow conditions are studied: the first considering the Reynolds number of 100 and the second considering the Reynolds number of 400. Table 2 presents the results for Re=100 obtained by Botella and Peyret (1998) using a spectral method with Chebyshev collocation, Deng et al (1994) using FVM with Richardson extrapolation, Ghia et al (1982) and Bruneau and Jouron (1990) using the finite difference method with multigrid technique, Yapici et al, (2009) using FVM with CDS scheme, andMuniz et al (2003) using FVM with fourthorder Lagrange and Padé interpolation schemes. The values of the minimum speed v x , taken at the vertical center line (x=0.5), followed by the corresponding y value and also the values of the maximum and minimum velocity v y in the central horizontal line (y=0.5) followed by the corresponding x values, are presented.…”

“…Alternatively, high-order interpolation schemes produce more accurate solutions with low computational costs (Muniz et al, 2008;Piller and Stalio, 2004;Leonard, 1995). However, to maintain the global order of the approximation, it is important that all approximation formulas for the advective, diffusive and nonlinear terms have the same order of accuracy (Leonard, 1995).…”