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The Biot-Stokes coupling using total pressure: formulation, analysis and application to interfacial flow in the eye
arXiv - CS - Numerical Analysis Pub Date : 2021-06-17 , DOI: arxiv-2106.09191
Ricardo Ruiz-Baier, Matteo Taffetani, Hans D. Westermeyer, Ivan Yotov

We consider a multiphysics model for the flow of Newtonian fluid coupled with Biot consolidation equations through an interface, and incorporating total pressure as an unknown in the poroelastic region. A new mixed-primal finite element scheme is proposed solving for the pairs fluid velocity - pressure and displacement - total poroelastic pressure using Stokes-stable elements, and where the formulation does not require Lagrange multipliers to set up the usual transmission conditions on the interface. The stability and well-posedness of the continuous and semi-discrete problems are analysed in detail. Our numerical study {is framed in} the context of different interfacial flow regimes in Cartesian and axisymmetric coordinates that could eventually help describe early morphologic changes associated with glaucoma development in canine species.

中文翻译:

使用总压的 Biot-Stokes 耦合:公式化、分析和应用到眼睛界面流动

我们考虑了牛顿流体流动的多物理场模型,通过接口与 Biot 固结方程耦合,并将总压力作为多孔弹性区域中的未知数。提出了一种新的混合原始有限元方案,使用 Stokes 稳定单元求解成对的流体速度 - 压力和位移 - 总多孔弹性压力,并且该公式不需要拉格朗日乘子来在界面上设置通常的传输条件。详细分析了连续和半离散问题的稳定性和适定性。我们的数值研究{基于}笛卡尔坐标和轴对称坐标中不同界面流动状态的背景,最终可以帮助描述与犬类青光眼发展相关的早期形态变化。
更新日期:2021-06-18
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