  One of the fundamental differences of compressible fluid flows from
incompressible fluid flows is the involvement of thermodynamics. This
difference should be manifested in the design of numerical methods and seems
often be neglected in addition that the entropy inequality, as a conceptual
derivative, is taken into account to reflect irreversible processes and
verified for some first order schemes. In this paper, we refine the GRP solver
to illustrate how the thermodynamical variation is integrated into the design
of high resolution methods for compressible fluid flows and demonstrate
numerically the importance of thermodynamic effect in the resolution of strong
waves. As a by-product, we show that the GRP solver works for generic equations
of state, and is independent of technical arguments.
