  Various forms of numerical shock instabilities are known to plague many
contact and shear preserving approximate Riemann solvers, including the popular
Harten-Lax-van Leer with Contact (HLLC) scheme, during high speed flow
simulations. In this paper we propose a simple and inexpensive novel strategy
to prevent the HLLC scheme from developing such spurious solutions without
compromising on its linear wave resolution ability. The cure is primarily based
on a reinterpretation of the HLLC scheme as a combination of its well-known
diffusive counterpart, the HLL scheme, and an antidiffusive term responsible
for its accuracy on linear wavefields. In our study, a linear analysis of this
alternate form indicates that shock instability in the HLLC scheme could be
triggered due to the unwanted activation of the antidiffusive terms of its mass
and interface-normal flux components on interfaces that are not aligned with
the shock front. This inadvertent activation results in weakening of the
favourable dissipation provided by its inherent HLL scheme and causes
unphysical mass flux variations along the shock front. To mitigate this, we
propose a modified HLLC scheme that employs a simple differentiable pressure
based multidimensional shock sensor to achieve smooth control of these critical
antidiffusive terms near shocks. Using a linear perturbation analysis and a
matrix based stability analysis, we establish that the resulting scheme, called
HLLC-ADC (Anti-Diffusion Control), is shock stable over a wide range of
freestream Mach numbers. Results from standard numerical test cases demonstrate
that the HLLC-ADC scheme is indeed free from the most common manifestations of
shock instability including the Carbuncle phenomenon without significant loss
of accuracy on shear dominated viscous flows.
