An adaptive isogeometric analysis approach to elasto‐capillary fluid‐solid interaction

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.