Origin and evolution of immersed boundary methods in computational fluid dynamics

This article presents the evolutionary history of Immersed Boundary Methods (IBMs), tracing their origins to the very beginning of computational fluid dynamics in the late 1950s all the way to the present day. The article highlights the advancements in this simulation methodology over the last fifty years and explores the interplay between IBMs and body-conformal grid (BCG) methods during this time. Drawing upon the author's combined experience of over forty years in this arena, the perspective offered is personal and subjective. By employing a critical and comparative approach through the chronological lens, we hope that this article empowers the reader to understand both the capabilities and limitations of these methods, and to pursue advancements that fill the key gaps and break new ground.