Finite volume simulation of viscoelastic laminar flow in a lid-driven cavity

Numerical study of the square-root conformation tensor formulation for confined and free-surface viscoelastic fluid flows

“…This flow is generated by the motion of one or more walls of a closed cavity. There are several experimental and numerical studies involving lid-driven cavity flows, mainly with Newtonian fluids [35], whereas for viscoelastic fluids, the interest is fairly recent, and mainly used to assess numerical methods for highly elastic flows [12,[36][37][38][39][40] which requires a regularization on the lid motion due to the singular behavior near the corners. The standard problem relies on the following regularized parabolic profile for the top lid, u(x, t) = 8[1 + tanh(8t − 4)]x 2 (1 − x) 2 .…”

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

“…It is important to highlight the degree of accuracy obtained by the LAG4 scheme, that, even using meshes with a lower degree of refinement, was able to obtain satisfactory solutions, especially when comparing the results of Ghia et al (1982) and Bruneau and Jouron (1990) using a 129x129 mesh with the results of LAG4 using a 20x20 mesh, and the results of Yapici et al, (2009) using a 305x305 mesh with the results of LAG4 using a 60x60 mesh. When the numerical solution is obtained using a mesh refinement sufficiently fine to ensure monotonic convergence, it is possible to estimate the order of the numerical scheme using the following expression (Ferziger and Peric, 2002):…”

The simpler GMRES method combined with finite volume method for simulating viscoelastic flows on triangular grid

“…Finite difference method (FDM) [11,12], finite element method (FEM) [13] and finite volume method (FVM) [14,15] have been used in the discretization of the governing equations. FDM is generally restricted to simple geometries [16]. FVM is advantageous both in saving computer space and in numerical stability compared to FEM [17].…”

“…Alternatively, the GMRES(m) method has also been employed to solve the resulting linear systems due to the nonlinear problems [22,23]. Sometimes, the alternating direction implicit (ADI) algorithm is used to solve the resulting linear systems due to the pressure-correction equation [16], but it is based on structured grid. The conjugate-gradient (CG) method has been used to solve the resulting linear systems due to the pressure equation while the BiCGSTAB has been used to solve the resulting linear systems due to the constitutive equation [24].…”