A finite volume method for the simulation of elastoviscoplastic flows and its application to the lid-driven cavity case

Abstract

We propose a Finite Volume Method for the simulation of elastoviscoplastic flows, modelled after the extension to the Herschel-Bulkley model by Saramito [J. Non-Newton. Fluid Mech. 158 (2009) 154-161]. The method is akin to methods for viscoelastic flows. It is applicable to cell-centred grids, both structured and unstructured, and includes a novel pressure stabilisation technique of the "momentum interpolation" type. Stabilisation of the velocity and stresses is achieved through a "both sides diffusion" technique and the CUBISTA convection scheme, respectively. A second-order accurate temporal discretisation scheme with adaptive time step is employed. The method is used to obtain benchmark results of lid-driven cavity flow, with the model parameters chosen so as to represent Carbopol. The results are compared against those obtained with the classic Herschel-Bulkley model. Simulations are performed for various lid velocities, with slip and no-slip boundary conditions, and with different initial conditions for stress. Furthermore, we investigate the cessation of the flow, once the lid is suddenly halted.

Numerical Methods for Viscoelastic Fluid Flows

“…The scope of the workshops has broadened over the years and covers topics not addressed in this review. Similarly, the benchmark problems have also evolved and currently there seems to be a predilection for the following test cases: (a) flow past a cylinder in a channel, with a ratio of 0.5 between the cylinder diameter and channel width (e.g., Knechtges et al 2014, Carrozza et al 2019); (b) 4:1 planar and axisymmetric contractions (e.g., Pimenta & Alves 2017, Niethammer et al 2019); (c) flow in a lid-driven cavity (e.g., , Fernandes et al 2019, Syrakos et al 2020); (d) flow in cross-slot devices (e.g., Cruz et al 2014, Kalb et al 2018, Zografos et al 2018; and (e) die swell (e.g., Comminal et al 2018, Spanjaards et al 2019, Tang et al 2019. The Oldroyd-B and UCM models continue to be frequent choices, but there is also a significant number of works dealing with other constitutive equations.…”

“…The benchmark problems described clearly show that important progress has been made over the years, and currently for all of these 2D flows, data with good accuracy are available in the steady-flow regime. For transient computations, the lid-driven cavity benchmark has seen some recent progress, with several works presenting accurate data in the transient and steady-state regimes (e.g., , Sousa et al 2016, Syrakos et al 2020). In the future, we suggest that the focus should lean toward 3D flows at very large Wi to improve our understanding of the elastic turbulence regime.…”

Numerical exploration of mixed convection heat transfer features within a copper-water nanofluidic medium occupied a square geometrical cavity

“…In such a heat transfer occurrence, the laminar convective flows of nanofluids can be described mathematically by a system of classical [5][6][7][8][9][10][11][12] fractional [13,14] partial differential equations, which cannot be treated analytically or semi-analytically because of its higher nonlinearity and coupling equations. This is why several researchers [15][16][17][18] conducted similar problems numerically by applying powerful computational procedures, like the finite element method (FEM), finite volume method (FVM), and lattice Boltzmann method (LBM).…”

A unification of least-squares and Green-Gauss gradients under a common projection-based gradient reconstruction framework

“…Gradient reconstruction schemes are among the fundamental ingredients of Finite Volume Methods (FVMs). They are used in the discretisation of diffusion [1,2] and convection [3] terms, of terms of turbulence closure equations [4], of terms of non-Newtonian constitutive equations [5,3,6,7] etc. Although lately a significant amount of research has gone into the development of high-order FVMs, the second-order accurate FVMs continue to be the most popular choice, due to ease of implementation, low memory requirements, faster execution (for the same number of degrees of freedom), better understanding and familiarity with the discretisation and stabilisation schemes etc.…”