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.

翻译：我们考虑的是牛顿流体流动的多物理学模型,加上通过接口的比奥特合并方程式,并纳入总压力,这是在多孔弹性区域未知的。我们建议采用斯托克斯可调质元素来解决对等体流体流体速度-压力和离位-总脉压压力,如果配方不需要拉格朗乘数来设置界面上通常的传输条件。我们详细分析了连续和半分解问题的稳定性和稳妥性。我们的数字研究 {以}碳酸盐和轴对称坐标中不同阻流系统的背景,最终可以帮助描述与峡谷物种的青光学发育相关的早期红外光学变化。