  Within the framework of the de Saint Venant equations coupled with the Exner
equation for morphodynamic evolution, this work presents a new efficient
implementation of the Dumbser-Osher-Toro (DOT) scheme for non-conservative
problems. The DOT path-conservative scheme is a robust upwind method based on a
complete Riemann solver, but it has the drawback of requiring expensive
numerical computations. Indeed, to compute the non-linear time evolution in
each time step, the DOT scheme requires numerical computation of the flux
matrix eigenstructure (the totality of eigenvalues and eigenvectors) several
times at each cell edge. In this work, an analytical and compact formulation of
the eigenstructure for the de Saint Venant-Exner (dSVE) model is introduced and
tested in terms of numerical efficiency and stability. Using the original DOT
and PRICE-C (a very efficient FORCE-type method) as reference methods, we
present a convergence analysis (error against CPU time) to study the
performance of the DOT method with our new analytical implementation of
eigenstructure calculations (A-DOT). In particular, the numerical performance
of the three methods is tested in three test cases: a movable bed Riemann
problem with an analytical solution; a problem with smooth analytical solution;
a test in which the water flow is characterised by subcritical and
supercritical regions. For a given target error, the A-DOT method is always the
most efficient choice. Finally, two experimental data sets and different
transport formulae are considered to test the A-DOT model in more practical
case studies.
