Weakly imposed boundary conditions for shear-rate dependent non-Newtonian fluids: application to cardiovascular flows.
Weakly imposed boundary conditions for shear-rate dependent non-Newtonian fluids: application to cardiovascular flows.
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DOI：
10.3934/mbe.2021193
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发表时间：
2021-05-06
期刊：
影响因子：
--
通讯作者：
Masud A
中科院分区：
文献类型：
--
作者：
Kang S;Nashar S;Livingston ER;Masud A
本文给出了广义Navier-Stokes方程在弱本质边界条件下的稳定化形式。血液的非牛顿行为通过剪切速率相关的本构方程建模。通过在变分多尺度框架下局部求解细尺度变分方程，得到了弱Dirichlet边界条件下的边界项。所提出的方法再现的一致性和稳定性方面，是目前在Nitsche型的方法。此外，对于剪切速率流体，还出现了两个边界项。其中一项是粘度导数项，是剪切速率的函数，而另一项是零阶项。这些项在获得所考虑规范中速度和压力场的最佳收敛率方面发挥着重要作用。一个最重要的贡献是形式的稳定张量，也变分派生。采用边缘函数的边缘稳定张量进行数值计算，它自适应地调整自己的边界残差的大小。所得到的配方是变分一致的，弱施加无滑移边界条件导致更高的精度的空间梯度粗边界层网格相比，传统的强施加的边界条件。本方法的这一特点将是在施加界面连续性条件在血液动脉相互作用问题的非匹配离散化的意义。给出了一组测试案例来研究该方法的数学属性，并给出了一个特定于患者的案例来显示其临床相关性。
This paper presents a stabilized formulation for the generalized Navier-Stokes equations for weak enforcement of essential boundary conditions. The non-Newtonian behavior of blood is modeled via shear-rate dependent constitutive equations. The boundary terms for weak enforcement of Dirichlet boundary conditions are derived via locally resolving the fine-scale variational equation facilitated by the Variational Multiscale (VMS) framework. The proposed method reproduces the consistency and stabilization terms that are present in the Nitsche type approaches. In addition, for the shear-rate fluids, two more boundary terms appear. One of these terms is the viscosity-derivative term and is a function of the shear-rate, while the other term is a zeroth-order term. These terms play an important role in attaining optimal convergence rates for the velocity and pressure fields in the norms considered. A most significant contribution is the form of the stabilization tensors that are also variationally derived. Employing edge functions the edge stabilization tensor is numerically evaluated, and it adaptively adjusts itself to the magnitude of the boundary residual. The resulting formulation is variationally consistent and the weakly imposed no-slip boundary condition leads to higher accuracy of the spatial gradients for coarse boundary-layer meshes when compared with the traditional strongly imposed boundary conditions. This feature of the present approach will be of significance in imposing interfacial continuity conditions across non-matching discretizations in blood-artery interaction problems. A set of test cases is presented to investigate the mathematical attributes of the method and a patient-specific case is presented to show its clinical relevance.
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影响因子：
3.2
作者：
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通讯作者：
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DOI：
10.1016/j.cma.2013.08.005
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影响因子：
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