  The nonlinear convection terms in the governing equations of compressible
fluid flows are hyperbolic in nature and are nontrivial for modelling and
numerical simulation. Many numerical methods have been developed in the last
few decades for this purpose and are typically based on Riemann solvers, which
are strongly dependent on the underlying eigen-structure of the governing
equations. Objective of the present work is to develop simple algorithms which
are not dependent on the eigen-structure and yet can tackle easily the
hyperbolic parts. Central schemes with smart diffusion mechanisms are apt for
this purpose. For fixing the numerical diffusion, the basic ideas of satisfying
the Rankine-Hugoniot (RH) conditions along with generalized Riemann invariants
are proposed. Two such interesting algorithms are presented, which capture
grid-aligned steady contact discontinuities exactly and yet have sufficient
numerical diffusion to avoid numerical shock instabilities. Both the algorithms
presented are robust in avoiding shock instabilities, apart from being accurate
in capturing contact discontinuities, do not need wave speed corrections and
are independent of eigen-strutures of the underlying hyperbolic parts of the
systems.
