非牛顿流体的剪切速率投影方案
Shear rate projection schemes for non-Newtonian fluids
AI总结：
本文提出了一种基于旋转投影方案扩展的非牛顿流体投影方法，通过去除压力边界条件，产生一致的压力方程，并通过制造解和圆柱体流动实验验证方法的准确性。
摘要：
应用于纳维-斯托克斯方程的操作分裂方法催生了多种用于模拟流体动力学的数值方法。Chorin和Temam对这一主题的独立工作催生了所谓的投影方法。基本的投影方案，无论是增量还是非增量变体（见[1]），都会在压力上引入一个人工的Neumann边界条件。通过去除压力上的这个边界条件，Timmermans等人[2]提出的所谓旋转增量压力校正方案为常粘度牛顿流体提供了一致的压力方程。在本文中，我们提出了一种基于旋转投影方案扩展的非牛顿流体投影方法家族。称为剪切速率投影，这些方法在应用于广义牛顿流体时会产生一致的压力方程。通过制造解来展示方法的准确性。还将展示使用Carreau流变模型的圆柱体流动数值实验。
英文摘要：
The operator splitting approach applied to the Navier-Stokes equations, gave rise to various numerical methods for the simulations of the dynamics of fluids. The separate work of Chorin and Temam on this subject gave birth to the so-called projection methods. The basic projection schemes, either the incremental or non-incremental variant (see [1]) induces an artificial Neumann boundary condition on the pressure. By getting rid of this boundary condition on the pressure, the so-call rotational incremental pressure-correction scheme as proposed by Timmermans et al. [2] for Newtonian fluids with constant viscosity gives a consistent equation for the pressure. In this work we propose a family of projection methods for generalized Newtonian fluids based on an extension of the rotational projection scheme. Called shear rate projections, these methods produces consistent pressure when applied to generalized Newtonian fluids. Accuracy of the methods will be illustrated using a manufactured solution. Numerical experiments for the flow past a cylinder, with a Carreau rheological model, will also be presented.
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