论文标题
多尺度的建模和弹性变形介质中传输过程的模拟
Multi-Scale Modeling and Simulation of Transport Processes in an Elastically Deformable Perforated Medium
论文作者
论文摘要
在本文中，我们得出了一个有效的模型，用于定期穿孔的弹性介质中的运输过程，例如，由于呼吸运动而在肺组织中发生的环状弹性变形。基本的显微镜问题将域的变形与混合\ textIt {lagrangian}/\ textit {eulerian}公式中的扩散过程相结合。在将扩散问题转化为固定结构域后，我们使用两尺度渐近扩展的形式方法来得出高尺度模型，该模型通过有效系数非线性耦合。使用应用程序启发的模型问题实现和验证了有效模型。研究和解释了针对细胞问题和宏观方程的数值解。我们使用模拟定性地确定变形对传输过程的影响。
In this paper, we derive an effective model for transport processes in periodically perforated elastic media, taking into account, e.g., cyclic elastic deformations as they occur in lung tissue due to respiratory movement. The underlying microscopic problem couples the deformation of the domain with a diffusion process within a mixed \textit{Lagrangian}/\textit{Eulerian} formulation. After a transformation of the diffusion problem onto the fixed domain, we use the formal method of two-scale asymptotic expansion to derive the upscaled model, which is nonlinearly coupled through effective coefficients. The effective model is implemented and validated using an application-inspired model problem. Numerical solutions for both, cell problems and macroscopic equations, are investigated and interpreted. We use simulations to qualitatively determine the effect of the deformation on the transport process.
