On Advances of Diffuse‑Interface Immersed Boundary Method and Its Applications

The diffuse-interface immersed boundary method （IBM） possesses excellent capabilities for simulating flows around complex geometries and moving boundaries. In this method， the flow field is solved on a fixed Cartesian mesh， while the solid boundary is discretized into a series of Lagrangian points immersed in the flow field. The boundary condition is implemented by introducing a force term into the momentum equation， and the interaction between the immersed boundary and the fluid domain is achieved via an interpolation process. Over the past decades， the diffuse-interface IBM has gained popularity and spawned many variants， effectively handling a wide range of flow problems from isothermal to thermal flows， from laminar to turbulent flows， and from complex geometries to fluid-structure interaction scenarios. This paper first outlines the basic principles of the diffuse-interface IBM， then highlights recent advancements achieved by the authors’ research group， and finally shows the method’s excellent numerical performance and wide applicability through several case studies involving complex moving boundary problems.