An adaptive isogeometric analysis approach to elasto‐capillary fluid‐solid interaction. (16th June 2020) - van Brummelen, E. H.; Demont, T. H. B.; van Zwieten, G. J.
Summary: 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.