An adaptive remeshing strategy for shear-thinning fluid flow simulations

Fortin, A.; Bertrand, François; Fortin, M.; Chamberland, Éric; Boulanger-Nadeau, P. E.; Maliki, A. El; Najeh, N.

doi:10.1016/j.compchemeng.2004.06.007

Cited by 12 publications

(6 citation statements)

References 9 publications

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“…An isotropic remeshing technique which we had developed based on the gradient of the principal stress difference was not able to reach the same order of mesh size, because of highly elongated viscoelastic wakes. The efficiency of the isotropic remeshing technique would need to be improved further allowing the use of anisotropic meshes similar to that of Fortin et al [15].…”

Section: Introductionmentioning

confidence: 99%

A parallel adaptive unstructured finite volume method for linear stability (normal mode) analysis of viscoelastic fluid flows

Şahin

Wilson

2008

Journal of Non-Newtonian Fluid Mechanics

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A parallel unstructured finite volume method is presented for analysis of the stability of two-dimensional steady Oldroyd-B fluid flows to small amplitude three-dimensional perturbations. A semi-staggered dilation-free finite volume discretization with Newton's method is used to compute steady base flows. The linear stability problem is treated as a generalized eigenvalue problem (GEVP) in which the rightmost eigenvalue determines the stability of the base flow. The rightmost eigenvalues associated with the most dangerous eigenfunctions are computed through the use of the shift-invert Arnoldi method. To avoid fine meshing in the regions where the flow variables are changing slowly, a local mesh refinement technique is used in order to increase numerical accuracy with a lower computational cost. The CUBIT mesh generation environment has been used to refine the quadrilateral meshes locally. In order to achieve higher performance on parallel machines the algebraic systems of equations resulting from the steady problem and the GEVP have been solved by implementing the MUltifrontal Massively Parallel Solver (MUMPS). The proposed method is applied to the linear stability analysis of the flow of an Oldroyd-B fluid past a linear periodic array of circular cylinders in a channel and a linear array of circular half cylinders placed on channel walls. Two different leading eigenfunctions are identified for close and wide cylinder spacing for the periodic array of cylinders. The numerical results indicate good agreement with the numerical and experimental results available in the literature. Crown

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Section: Introductionmentioning

confidence: 99%

A parallel adaptive unstructured finite volume method for linear stability (normal mode) analysis of viscoelastic fluid flows

Şahin

Wilson

2008

Journal of Non-Newtonian Fluid Mechanics

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“…An additional advantage of using indirect formulations is that the conditional number of the resulting system of equations is lower than those obtained from direct formulations. This allows for the use of iterative solvers [21] that for 3D cases are necessary as size makes direct solvers prohibitive [8].…”

Section: [G]{t} − [H ]{U} = [F ] −1 ([G]{t} − [H ]{û}){G}mentioning

confidence: 99%

“…This approach although proven to be quite accurate requires large amounts of computational resources and are often accompanied with complex remeshing algorithms [7,8]. Kelly and Gigas [6] use Fluent™ [finite volume method (FVM)] to solve a 3D mixing application requiring 158, 000 cells.…”

Section: Introductionmentioning

confidence: 99%

Indirect boundary integral formulation for the solution of shear-thinning flow inside single rotor mixers

Giraldo

Power

Florez

2010

Numer. Methods Partial Differential Eq.

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An efficient indirect boundary integral formulation for the evaluation of inelastic non-Newtonian shearthinning flows at low Reynolds number is presented in this article. The formulation is based on the solution of a homogeneous Stokes flow field and the use of a particular solution for the nonlinear non-Newtonian terms that yields the complete solution to the problem. Matrix multiplications are reduced in comparison to other means of handling nonlinear terms in boundary integral formulations such as the dual reciprocity method. The iterative solution of the nonlinear system of equations has been performed with a modified Newton-Raphson method obtaining accurate results for values of the power law index as low as 0.4 without domain partitioning. Geometries such as Couette flow and a typical industrial polymer mixer have been analyzed with the proposed method obtaining good results with a reduction in computational cost compared with other equivalent formulations.

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“…The mesh SPH2 is obtained by the procedure of dividing edges of SPH1 by 2. The adapted mesh is coming from the paper of Fortin et al [30].…”

Section: Flow Around a Cylindermentioning

confidence: 99%

Efficient preconditioning techniques for finite‐element quadratic discretization arising from linearized incompressible Navier–Stokes equations

Maliki

Guénette

2010

Numerical Methods in Fluids

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SUMMARYWe develop an efficient preconditioning techniques for the solution of large linearized stationary and non-stationary incompressible Navier-Stokes equations. These equations are linearized by the Picard and Newton methods, and linear extrapolation schemes in the non-stationary case. The time discretization procedure uses the Gear scheme and the second-order Taylor-Hood element P 2 − P 1 is used for the approximation of the velocity and the pressure. Our purpose is to develop an efficient preconditioner for saddle point systems. Our tools are the addition of stabilization (penalization) term r ∇(div(·)), and the use of triangular block matrix as global preconditioner. This preconditioner involves the solution of two subsystems associated, respectively, with the velocity and the pressure and have to be solved efficiently. Furthermore, we use the P 1 − P 2 hierarchical preconditioner recently proposed by the authors, for the block matrix associated with the velocity and an additive approach for the Schur complement approximation. Finally, several numerical examples illustrating the good performance of the preconditioning techniques are presented.

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An adaptive remeshing strategy for shear-thinning fluid flow simulations

Cited by 12 publications

References 9 publications

A parallel adaptive unstructured finite volume method for linear stability (normal mode) analysis of viscoelastic fluid flows

A parallel adaptive unstructured finite volume method for linear stability (normal mode) analysis of viscoelastic fluid flows

Indirect boundary integral formulation for the solution of shear-thinning flow inside single rotor mixers

Efficient preconditioning techniques for finite‐element quadratic discretization arising from linearized incompressible Navier–Stokes equations

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