A full-Eulerian solid level set method for simulation of fluid–structure interactions

We present a full Eulerian method, termed solid level set (SLS) method, for modeling of a class of fluid–structure interactions (FSI) problems soft solid body can deform significantly but remains nearly incompressible. The SLS method is based on the unified momentum equation framework in which the solid–fluid interactions are modeled by introducing a solid body force term and a solid–fluid interfacial force term into the Navier–Stokes equation. The key idea of the SLS method is that the deformation of the solid body is no longer tracked using a Lagrangian mesh. Instead, the solid body is tracked by introducing a reference coordinate for describing the reference state of the solid body and by introducing three dynamic level set functions on the Cartesian coordinate and one static level set functions on the reference coordinate. The SLS method is easy to implement and addresses several challenges in the simulation of FSIs in which a fixed Cartesian mesh is used for fluid flow and a Lagrangian mesh is used for tracking the solid deformation. The effectiveness of the SLS method is demonstrated by studying two FSI problems. The method is suitable for studying a wide range of problems in microfluidics, e.g., manipulation of cells in confined space and ink-jet printing of biological samples.