  The conservation laws of continuum mechanic written in an Eulerian frame make
no difference between fluids and solids except in the expression of the stress
tensors, usually with Newton's hypothesis for the fluids and Helmholtz
potentials of energy for hyperelastic solids. By taking the velocities as
unknown , monolithic methods for fluid structure interactions (FSI) are built.
In this article such a formulation is analyzed when the fluid is compressible
and the fluid is incompressible. The idea is not new but the progress of mesh
generators and numerical schemes like the Characteristics-Galerkin method
render this approach feasible and reasonably robust. In this article the method
and its discretization are presented, stability is discussed by through an
energy estimate. A numerical section discusses implementation issues and
presents a few simple tests.

Computational Engineering, Finance, and Science;Numerical Analysis;Numerical Analysis;Fluid Dynamics