A Newton–Krylov finite volume algorithm for the power-law non-Newtonian fluid flow using pseudo-compressibility technique |
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| Authors: | Amir Nejat Alireza Jalali Mahkame Sharbatdar |
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| Institution: | 1. School of Mechanical Engineering, College of Engineering, University of Tehran, North Karegar Ave., Tehran, Iran;2. University of British Columbia, Department of Mechanical Engineering, 2324 Main Mall, Vancouver, BC, Canada V6T 1Z4;1. Dep. Ing. Mecánica y Energía, Universidad Miguel Hernández, Av. Universidad, s/n, 03202 Elche, Spain;2. Dep. Ing. Térmica y de Fluidos, Universidad Politécnica de Cartagena, Dr. Fleming, s/n, 30202 Cartagena, Spain;1. School of Mechanical Engineering, Pusan National University, Jang Jeon 2-Dong, Geum Jeong Gu, Busan 609-735, Republic of Korea;2. Rolls-Royce and Pusan National University Technology Centre in Thermal Management, Jang Jeon 2-Dong, Geum Jeong Gu, Busan 609-735, Republic of Korea;1. Department of Mechanical Engineering, Celal Bayar University, Manisa, Turkey;2. Department of Mechanical Engineering, Technology Faculty, F?rat University, Elaz??, Turkey;1. School of Mechanical Engineering, Pusan National University, Jang Jeon 2-Dong, Geum Jeong Gu, Busan 609-735, Republic of Korea;2. Global Core Research Center for Ships and Offshore Plants, Pusan National University, Jang Jeon 2-Dong, Geum Jeong Gu, Busan 609-735, Republic of Korea |
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| Abstract: | An implicit Newton–Krylov finite volume algorithm has been developed for efficient steady-state computation of the power-law non-Newtonian fluid flows. The pseudo-compressibility technique is used for the coupling of continuity and momentum equations. The spatial discretization is central (second-order) for both convective and diffusive terms and the accuracy of the solution is verified. The nine block diagonal Jacobian matrix (needed for implicit formulation) is computed directly through the flux differentiation. Five-diagonal and three-diagonal block matrices (the simplified versions of the main Jacobian matrix) are used with the ILU(0 & 1) and the Thomas linear solvers for preconditioning, respectively. The performance of the Newton-GMRES solver is examined in detail for different preconditioning strategies. The effects of the power-law behavior index and Re number on the convergence rate are also studied. The performance of the Newton-BiCGSTAB and the Newton-GMRES solvers are compared with each other. The results show, the ILU(1)/Newton-GMRES is the most efficient combination that is robust even in high Reynolds number shear-thinning fluid flow cases. |
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