  The equation of state (EOS) embodies thermodynamic properties of compressible
fluid materials and usually has very complicated forms in real engineering
applications, subject to the physical requirements of thermodynamics. The
complexity of EOS in form gives rise to the difficulty in analyzing relevant
wave patterns. Concerning the design of numerical algorithms, the complex EOS
causes the inefficiency of Riemann solvers and even the loss of robustness,
which hampers the development of Godunov-type numerical schemes.
  In this paper, a strategy of local stiffened gas approximation is proposed
for real materials. The stiffened gas EOS is used to approximate general EOS
locally at each interface of computational control volumes so that the Riemann
solver can be significantly simplified. In the meantime, the generalized
Riemann problem (GRP) solver is adopted not only for high resolution purpose
but effective reflection of the local thermodynamics as well. The resulting
scheme is demonstrated to be efficient and robust and numerical examples
display the excellent performance of such an approximation.
