  In this paper, a unified framework to develop all-speed HLL-type schemes for
hypersonic heating computations is constructed. Such a unified construction
method combines two effective improving techniques: a shock robustness
improvement and a low-Mach number fix. It is implemented by properly modifying
the approximate solutions of the local Riemann problem in the HLL framework,
resulting in two all-speed HLL-type schemes, namely ASHLLC and ASHLLEM solvers.
Results from both numerical analysis and experiments demonstrate that the newly
proposed schemes not only preserve desirable properties of their original
versions, but are also able to provide accurate and robust solutions for
complex flows ranging from low-Mach number incompressible to hypersonic
compressible regimes. Thus, both the ASHLLC and ASHLLEM schemes can be used as
reliable methods for hypersonic heating computations.
