  An exact discontinuity capturing central solver developed recently, named
MOVERS (Method of Optimal Viscosity for Enhanced Resolution of Shocks, J
Computat Phys 2009;228:770-798), is analyzed and improved further to make it
entropy stable. MOVERS, which is designed to capture steady shocks and contact
discontinuities exactly by enforcing the Rankine-Hugoniot jump condition
directly in the discretization process, is a low diffusive algorithm in a
simple central discretization framework, free of complicated Riemann solvers
and flux splittings. However, this algorithm needs an entropy fix to avoid
nonsmoothness in the expansion regions. The entropy conservation equation is
used as a guideline to introduce an optimal numerical diffusion in the smooth
regions and a limiter based switchover is introduced for numerical diffusion
based on jump conditions at the large gradients. The resulting new scheme is
entropy stable, accurate and captures steady discontinuities exactly while
avoiding an entropy fix.
