非牛顿流体蠕动流动的混合高阶方法
A Hybrid High-Order method for creeping flows of non-Newtonian fluids
摘要：
在本文中，我们设计和分析了一个混合高阶离散方法的非牛顿，不可压缩流体的稳态运动的斯托克斯近似的小速度。该方法有几个吸引人的功能，包括支持一般网格和高阶，无条件inf-sup稳定性，并获得的标量Leray-Lions问题相匹配的收敛顺序。一个完整的适定性和收敛性分析的方法进行了新的，一般假设的应变率剪应力法，其中包括几个常见的例子，如幂律和Carreau-Yasuda模型。数值例子完成论述。
英文摘要：
In this paper, we design and analyze a Hybrid High-Order discretization method for the steady motion of non-Newtonian, incompressible fluids in the Stokes approximation of small velocities. The proposed method has several appealing features including the support of general meshes and high-order, unconditional inf-sup stability, and orders of convergence that match those obtained for scalar Leray-Lions problems. A complete well-posedness and convergence analysis of the method is carried out under new, general assumptions on the strain rate-shear stress law, which encompass several common examples such as the power-law and Carreau-Yasuda models. Numerical examples complete the exposition.
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