  A low diffusion version of the HLL-CPS scheme for resolving the shear layers
and the flow features at low Mach numbers is presented here. The low diffusion
HLL-CPS scheme is obtained by reconstructing the velocities at the cell
interface with the face normal Mach number and a pressure function. Asymptotic
analysis of the modified scheme shows a correct scaling of the pressure at low
Mach numbers and a significant reduction in numerical dissipation. The
robustness of the HLL-CPS scheme for strong shock is improved by reducing the
contribution of the contact wave in the vicinity of the shock. The improvement
in robustness for strong shock is demonstrated analytically through linear
perturbation and matrix stability analyses. A set of numerical test cases are
solved to demonstrate the efficacy of the proposed scheme over a wide range of
Mach numbers.
