We present an adaptive isogeometric‐analysis approach to elasto‐capillary fluid‐solid interaction (FSI), based on a diffuse‐interface model for the binary fluid and an Arbitrary‐Lagrangian‐Eulerian formulation for the FSI problem. We consider approximations constructed from adaptive high‐regularity truncated hierarchical splines, as employed in the isogeometric analysis (IGA) paradigm. The considered adaptive strategy comprises a two‐level hierarchical a posteriori error estimate. The hierarchical a posteriori error estimate directs a support‐based refinement procedure. To attain robustness of the solution procedure for the aggregated binary‐fluid‐solid‐interaction problem, we apply a fully monolithic solution procedure and we introduce a continuation process in which the diffuse interface of the binary fluid is artificially enlarged on the coarsest levels of the adaptive‐refinement procedure. To assess the capability of the presented adaptive IGA method for elasto‐capillary FSI, we conduct numerical computations for a configuration pertaining to a sessile droplet on a soft solid substrate.

中文翻译：

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弹性-毛细流体-固体相互作用的自适应等几何分析方法

我们基于二元流体的扩散界面模型和FSI问题的任意拉格朗日欧拉公式，提出了一种用于弹性体-毛细流体-固体相互作用（FSI）的自适应等几何分析方法。我们考虑了根据等几何分析（IGA）范式采用的自适应高正则截断层次样条构造的近似值。所考虑的自适应策略包括两级分层后验误差估计。后验误差的分层估算指导了基于支持的改进过程。为了获得解决方案对二元流固耦合问题的鲁棒性，我们应用了一个完整的整体求解程序，并引入了一个连续过程，在该过程中，在自适应细化程序的最粗糙级别上人为地扩大了二元流体的扩散界面。为了评估所提出的自适应IGA方法用于弹性毛细管FSI的能力，我们对与软固体基质上的无滴液滴有关的构型进行了数值计算。