A recently developed central scheme which can capture steady discontinuities exactly is the algorithm termed as MOVERS (Method of Optimal Viscosity for Enhanced Resolution of Shocks),
developed by S. Jaisankar and S.V. Raghurama Rao (J. Comp. Phy., 228, 770-798, 2009). This
simple central scheme is based on enforcing Rankine-Hugoniot jump conditions directly in the
discretization process and does not need projection of the solution on to the space of eigenvectors,
time consuming Riemann solvers or complicated flux splittings. Two recent attempts to make
this simple and accurate solver entropy stable will be presented in this talk - (i) a limiter based
switch over from a numerical diffusion for the entropy conservation equation to that satisfying
R-H condition and (ii) a polynomial dissipation based on R-H condition. Some typical bench-mark test case results will be presented for simulating hyperbolic conservation laws.