  A new implementation of the Roe scheme for solving two-layer shallow-water
equations is presented in this paper. The proposed A-Roe scheme is based on the
analytical solution to the characteristic quartic of the flux matrix, which is
an efficient alternative to a numerical eigensolver. Additionally, an accurate
method for maintaining the hyperbolic character of the governing system is
proposed. The efficiency of the quartic closed-form solver is examined and
compared to numerical eigensolvers. Furthermore, the accuracy and computational
speed of the A-Roe scheme is compared to the Roe, Lax-Friedrichs, GFORCE, PVM,
and IFCP schemes. Finally, numerical tests are presented to evaluate the
efficiency of the iterative treatment for the hyperbolicity loss. The proposed
A-Roe scheme is as accurate as the Roe scheme, but much faster, with
computational speeds closer to the GFORCE and IFCP scheme.
