Parallel domain decomposition method for finite element approximation of 3D steady state non‐Newtonian fluids
Parallel domain decomposition method for finite element approximation of 3D steady state non‐Newtonian fluids
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DOI：
10.1002/fld.4027
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发表时间：
2015-07
影响因子：
1.8
通讯作者：
Wen-Shin Shiu;F. Hwang;X. Cai
中科院分区：
文献类型：
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作者：
Wen-Shin Shiu;F. Hwang;X. Cai
我们引入了一种用于 3D 非牛顿纳维-斯托克斯方程的稳定有限元方法，以及一种用于求解离散化产生的稀疏非线性方程组的并行域分解方法。一般来说，非牛顿流动问题比牛顿流动更具挑战性，因为非线性不仅存在于对流项中，而且存在于取决于剪切速率的粘度项中。许多适用于牛顿流的良好迭代方法和预处理技术不适用于非牛顿流。我们采用伽辽金/最小二乘有限元方法，调整稳定参数以计算非牛顿效应，对方程进行离散化，并通过 Newton-Krylov-Schwarz 算法求解所得的高度非线性方程组。在本研究中，我们将所提出的方法应用于通过内圆柱旋转的偏心环的一些非弹性幂律流体流动，并研究该方法对于一些物理参数（包括幂律指数和雷诺数比）的鲁棒性。然后，我们报告了域分解算法在最多具有 512 个处理器的计算机上实现的超线性加速。版权所有 © 2015 约翰·威利父子有限公司
We introduce a stabilized finite element method for the 3D non‐Newtonian Navier–Stokes equations and a parallel domain decomposition method for solving the sparse system of nonlinear equations arising from the discretization. Non‐Newtonian flow problems are, generally speaking, more challenging than Newtonian flows because the nonlinearities are not only in the convection term but also in the viscosity term, which depends on the shear rate. Many good iterative methods and preconditioning techniques that work well for the Newtonian flows do not work well for the non‐Newtonian flows. We employ a Galerkin/least squares finite element method, with stabilization parameters adjusted to count the non‐Newtonian effect, to discretize the equations, and the resulting highly nonlinear system of equations is solved by a Newton–Krylov–Schwarz algorithm. In this study, we apply the proposed method to some inelastic power‐law fluid flows through the eccentric annuli with inner cylinder rotation and investigate the robustness of the method with respect to some physical parameters, including the power‐law index and the Reynolds number ratios. We then report the superlinear speedup achieved by the domain decomposition algorithm on a computer with up to 512 processors. Copyright © 2015 John Wiley & Sons, Ltd.