The simpler GMRES method combined with finite volume method for simulating viscoelastic flows on triangular grid |
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| Affiliation: | 1. Centre for Polymer and Material Technologies, Department of Materials, Textiles and Chemical Engineering, Ghent University, Technologiepark 130, 9052 Zwijnaarde, Belgium;2. Laboratory for Chemical Technology, Department of Materials, Textiles and Chemical Engineering, Ghent University, Technologiepark 125, 9052 Zwijnaarde, Belgium;3. Centre for Textile Science and Engineering, Department of Materials, Textiles and Chemical Engineering, Ghent University, Technologiepark 70a, 9052 Zwijnaarde, Belgium;1. Universidade Federal do Pará, Instituto de Ciências Exatas e Naturais, Faculdade de Matemática, Belém 66075-110, PA, Brasil;2. IPC/i3N – Institute for Polymers and Composites, University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal;3. University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Ivana Lu?i?a 5, Zagreb, Croatia;4. Wikki Ltd, 459 Southbank House, SE1 7SJ, London, United Kingdom |
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| Abstract: | An efficient solver integrating the restarted simpler generalized minimal residual method (SGMRES(m)) with finite volume method (FVM) on triangular grid is developed to simulate the viscoelastic fluid flows. In particular, the SGMRES(m) solver is used to solve the large-scale sparse linear systems, which arise from the course of FVM on triangular grid for modeling the Newtonian and the viscoelastic fluid flows. To examine the performance of the solver for the nonlinear flow equations of viscoelastic fluids, we consider two types of numerical tests: the Newtonian flow past a circular cylinder, and the Oldroyd-B fluid flow in a planar channel and past a circular cylinder. It is shown that the numerical results obtained by the SGMRES(m) are consistent with the analytical solutions or empirical values. By comparing CPU time of different solvers, we find our solver is a highly efficient one for solving the flow equations of viscoelastic fluids. |
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| Keywords: | Modeling Navier–Stokes Oldroyd-B SGMRES Finite volume Triangular grid |
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