Morphological accelerators, such as the MORFAC (MORphological acceleration FACtor) approach [24], are widely adopted techniques for the acceleration of the bed evolution, which reduces the computational cost of morphodynamic numerical simulations. In this work we apply a non-uniform acceleration to the onedimensional morphodynamic problem described by the de Saint Venant-Exner model by multiplying all the spatial derivatives by an individual constant (≥ 1) acceleration factor. The final goal is to identify the best combination of the three accelerating factors for which i) the bed responds linearly to hydrodynamic changes; ii) a consistent decrease of the computational cost is obtained. The sought combination is obtained by studying the behaviour of an approximate solution of the three eigenvalues associated with the flux matrix of the accelerated system. This approach allows to derive a new linear morphodynamic acceleration technique, the MASSPEED (MASs equations SPEEDup) approach, and the a priori determination of the highest acceleration allowed for a given simulation. In this new approach both mass conservation equations (water and sediment) are accelerated by the same factor, differently from the MORFAC approach where only the sediment mass equation is modified. The analysis shows that the MASSPEED gives a larger validity range for linear acceleration and requires smaller computational costs than that of the classical MORFAC approach. The MASSPEED approach is implemented within an example code, using an adaptive approach that applies the maximum linear acceleration similarly to the Courant-Friedrichs-Lewy stability condition.Finally, numerical simulations have been performed in order to assess accuracy and efficiency of the new approach. Results obtained in the long-term propagation of a sediment hump demonstrate the advantages of the new approach. Keywords:SWE -Exner model, Morphological accelerators, MASSPEED approach, MORFAC approach, long term morphodynamic evolution IntroductionReducing the computational costs of numerical simulations of the morphological evolution in rivers, estuaries and coastal areas is a critical issue for engineers and geomorphologists [e.g. 4, 25, 26]. Even

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 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.