This paper presents a numerical method for the simulation of elastic solid materials coupled to fluid inclusions. The application is motivated by the modeling of vascularized tissues and by problems in medical imaging which target the estimation of effective (i.e., macroscale) material properties, taking into account the influence of microscale dynamics, such as fluid flow in the microvasculature. The method is based on the recently proposed Reduced Lagrange Multipliers framework. In particular, the interface between solid and fluid domains is not resolved within the computational mesh for the elastic material but discretized independently, imposing the coupling condition via non-matching Lagrange multipliers. Exploiting the multiscale properties of the problem, the resulting Lagrange multipliers space is reduced to a lower-dimensional characteristic set. We present the details of the stability analysis of the resulting method considering a non-standard boundary condition that enforces a local deformation on the solid-fluid boundary. The method is validated with several numerical examples.

翻译：本文提出了一种用于模拟弹性固体材料与流体夹杂物耦合的数值方法。该应用源于对血管化组织的建模以及医学成像中的相关问题，其目标是在考虑微尺度动力学（例如微血管中的流体流动）影响的前提下，估算有效（即宏观尺度）材料属性。该方法基于近期提出的降阶拉格朗日乘子框架。具体而言，固体与流体域之间的界面并未在弹性材料的计算网格中解析，而是独立离散化，并通过非匹配拉格朗日乘子施加耦合条件。利用问题的多尺度特性，所得拉格朗日乘子空间被降阶为一个低维特征集。我们给出了针对该方法稳定性分析的细节，其中考虑了一种在固体-流体边界上施加局部变形的非标准边界条件。通过多个数值算例验证了该方法的有效性。