An Eulerian approach for fluid–structure interaction problems

This paper describes a numerical method for simulating fluid–structure interaction problems on a fixed Cartesian grid. The fluid–structure interfaces are sharply represented by the aid of the level-set function and virtual flux method. The virtual flux method is one of the sharp interface Cartesian grid methods. The numerical flux across the interface is replaced with the virtual flux so that proper interface conditions must be satisfied there. For fluid and elastic structure interaction problems, the Navier–Stokes equations and unsteady evolution equations for the Eulerian strain tensor of elastic solid are simultaneously solved, so that the strain and stress tensors as well as velocities and pressures in both fluid and solid mediums can be analyzed on the fixed grid. Validity of the numerical method is demonstrated for numerical simulations about reciprocating engines, reciprocating compressors, and deformations of elastic particles in fluid flows. It is confirmed that the Eulerian approach is easily applicable to the simulation of fluid–structure interaction problems.