  The Harten-Lax-van Leer with contact (HLLC) scheme is known to be plagued by
various forms of numerical shock instabilities. In this paper, we propose a new
framework for developing shock stable, contact and shear preserving approximate
Riemann solvers based on the HLLC scheme for the Euler system of equations. The
proposed framework termed as HLLC-SWM (\textbf{S}elective \textbf{W}ave
\textbf{M}odified) scheme identifies and increases the magnitude of the
inherent diffusive HLL component within the HLLC scheme in the vicinity of a
shock wave while leaving its antidiffusive component unmodified to retain
accuracy on linearly degenerate wavefields. We present two strategies to
compute the requisite supplementary dissipation which results in HLLC-SWM-E and
HLLC-SWM-P variants. Through a linear perturbation analysis of the HLLC-SWM
framework, we clarify how the additional dissipation introduced in this way
helps in damping of unphysical perturbations in primitive quantities under a
derived CFL constraint. A matrix based stability analysis of a steady
two-dimensional normal shock is used to show that both variants of the HLLC-SWM
scheme are shock stable over a wide range of inlet Mach numbers. Results from
standard test cases demonstrate that the HLLC-SWM schemes are capable of
computing shock stable solutions on a variety of problems while retaining
positivity and exact inviscid contact ability. On viscous flows, while the
HLLC-SWM-P variant is quite accurate, the HLLC-SWM-E variant introduces slight
inaccuracy which can be corrected through a simple Mach number based switching
function.
