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Robust stabilised finite element solvers for generalised Newtonian fluid flows
Journal of Computational Physics ( IF 4.1 ) Pub Date : 2021-05-17 , DOI: 10.1016/j.jcp.2021.110436
Richard Schussnig , Douglas R.Q. Pacheco , Thomas-Peter Fries

Various materials and solid-fluid mixtures of engineering and biomedical interest can be modelled as generalised Newtonian fluids, as their viscosity depends locally on the flow field. Despite the peculiarities of such models, it is common practice to combine them with numerical techniques conceived for Newtonian fluids, which can bring several issues such as spurious pressure boundary layers, unsuitable natural boundary conditions and additional nonlinear terms spoiling the effectiveness of both nonlinear solution procedures and preconditioners. In this context, we present a novel framework dealing with such issues while maintaining low computational cost and simple implementation. The building blocks of the presented algorithm are (i) a novel stabilised formulation for incompressible flow problems preserving consistency for low-order pairs, (ii) robust extrapolation of velocities in the time-dependent case to decouple the rheological law from the overall system, (iii) adaptive time step selection and (iv) a fast physics-based preconditioned Krylov subspace solver, to tackle the relevant range of discretisation parameters including highly varying viscosity. Selected numerical experiments are provided demonstrating the potential of the presented approach in terms of robustness, accuracy and efficiency for problems of practical interest.



中文翻译:

广义牛顿流体流动的鲁棒稳定有限元求解器

工程和生物医学感兴趣的各种材料和固体-流体混合物可以建模为广义牛顿流体,因为它们的粘度局部取决于流场。尽管此类模型具有特殊性,但通常的做法是将它们与为牛顿流体构想的数值技术结合使用,这可能会带来一些问题,例如杂散压力边界层,不合适的自然边界条件以及其他非线性项,这会破坏两种非线性解决方案的有效性和预处理器。在这种情况下,我们提出了一个新颖的框架来处理此类问题,同时保持较低的计算成本和简单的实现。提出的算法的基本组成部分是:(i)针对不可压缩流问题的新型稳定公式,可保持低阶对的一致性,(ii)在与时间有关的情况下进行稳健的速度外推,以使流变规律与整个系统脱钩;(iii)自适应时间步长选择;(iv)基于物理学的快速预处理Krylov子空间求解器,以解决相关的范围离散化参数包括高度变化的粘度。提供了选定的数值实验,从鲁棒性,准确性和效率方面证明了所提出方法解决实际问题的潜力。

更新日期:2021-05-17
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