论文标题
流体孔弹性结构相互作用的混合弹性配方
A mixed elasticity formulation for fluid-poroelastic structure interaction
论文作者
论文摘要
我们开发了一种混合有限元方法，用于在由stokes方程控制的自由流体与流动的相互作用中产生的耦合问题，该相互作用是由可变形的多孔培养基中的流动性，该培养基由生物弹性的生物弹性系统建模。质量保护，压力的平衡和海狸 - 约瑟夫 - 萨夫曼条件施加在界面上。我们考虑基于弱对称应力 - 置换弹性弹性系统和Darcy速度压力流动配方的完全混合的生物剂公式。速度压力公式用于Stokes方程。界面条件通过引入结构速度的痕迹和Darcy压力作为Lagrange乘数。为连续的弱公式建立了解决方案的存在和独特性。对于半分化连续的混合有限元近似，得出了稳定性和误差估计。提出了数值实验以验证理论结果并说明了该方法相对于物理参数的鲁棒性。
We develop a mixed finite element method for the coupled problem arising in the interaction between a free fluid governed by the Stokes equations and flow in deformable porous medium modeled by the Biot system of poroelasticity. Mass conservation, balance of stress, and the Beavers--Joseph--Saffman condition are imposed on the interface. We consider a fully mixed Biot formulation based on a weakly symmetric stress-displacement-rotation elasticity system and Darcy velocity-pressure flow formulation. A velocity-pressure formulation is used for the Stokes equations. The interface conditions are incorporated through the introduction of the traces of the structure velocity and the Darcy pressure as Lagrange multipliers. Existence and uniqueness of a solution are established for the continuous weak formulation. Stability and error estimates are derived for the semi-discrete continuous-in-time mixed finite element approximation. Numerical experiments are presented to verify the theoretical results and illustrate the robustness of the method with respect to the physical parameters.
