  A simple HLLE-type scheme is proposed for all Mach number flows. In the
proposed scheme, no extra wave structure is added in the HLLE scheme to resolve
the shear wave while the contact wave is resolved by adding a wave structure
similar to the HLLEM scheme. The resolution of the shear layers and the flow
features at low Mach number are achieved by a velocity reconstruction method
based on the face normal Mach number. Robustness against the numerical
instabilities is achieved by scaling the velocity reconstruction function in
the vicinity of shock with a multi-dimensional pressure sensor. The ability of
the proposed scheme to resolve low Mach flow features is demonstrated through
asymptotic analysis while stability of the proposed scheme for strong shock is
demonstrated through linear perturbation and matrix stability analyses. A set
of numerical test cases are solved to show that the proposed scheme is free
from numerical shock instability problems at high speeds and is capable of
resolving the flow features at very low Mach numbers.
