Impact of the discretization on the stability of an RMT based Fully Eulerian FSI approach in 1D

Numerical simulation of fluid structure interaction (FSI) plays a critical role in analyzing a wide range of engineering applications, such as aircraft or medical device design. In the Fully Eulerian "one-continuum" approach to FSI, a single set of governing equations is solved in Eulerian form with variable properties and constitutive laws to model both the solid and fluid. A fixed non-conforming grid can be used along with an interface-capturing method, such as the level set method, to easily handle complex interface geometries and motions associated with large solid deformations. In this work, we investigate the impact of the discretization on the stability of a reference map technique (RMT) based Fully Eulerian FSI method in 1D. This approach utilizes the inverse motion map to track deformation of the solid and the fluid-solid boundary. We apply several discretization choices to the RMT based FSI equations and analyze the stability properties of the methods in the context of a 1D manufactured solution example involving a weakly compressible fluid and solid.