Discrete embedded boundary method with smooth dependence on the evolution of a fluid‐structure interface

Embedded boundary methods (EBMs) are robust solution methods for highly nonlinear fluid‐structure interaction (FSI) problems. They suffer, however, some disadvantages because they perform their computations on embedding, nonbody‐fitted fluid meshes. In particular, they tend to generate discrete events that introduce discontinuities in the semi‐discretization process and lead to numerical solutions that are insufficiently smooth for differentiation with respect to the evolution of a discrete, fluid/structure interfaceΓ h F / S. This hinders their application to the gradient‐based solution of fluid‐structure optimization problems. Discrete events also promote spurious oscillations in the post‐processing of time‐dependent results computed atΓ h F / S.z This paper addresses these issues in the context of Finite Volume method with Exact two‐material Riemann problems (FIVER), a comprehensive framework for developing EBMs for highly nonlinear, compressible, FSI problems. It revisits the concept of the status of a node of an embedding fluid mesh and introduces that of a smoothness indicator nodal function, to eliminate discrete events and achieve smoothness in the semi‐discretization process. It also introduces a moving least squares approach in the loads evaluation algorithm, to suppress spurious oscillations from integral quantities computed onΓ h F / S. Equipped with these enhancements, FIVER is shown to deliver, for three different FSI applications, smooth results that are differentiable with respect to evolutions ofΓ h F / S.