Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
Formulations for Numerically Approximating Hyperbolic Systems Governing Sediment Transport
Journal of Scientific Computing
Journal of Computational Physics
High Order Extensions of Roe Schemes for Two-Dimensional Nonconservative Hyperbolic Systems
Journal of Scientific Computing
Solution of the Sediment Transport Equations Using a Finite Volume Method Based on Sign Matrix
SIAM Journal on Scientific Computing
Comparison of unstructured finite-volume morphodynamic models in contracting channel flows
Mathematics and Computers in Simulation
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Numerical simulation of morphodynamic problems is considered. The physical model is based on the shallow-water equations coupled with the Exner equation closed by the Grass model to describe the time evolution of the bed profile. The SRNH predictor-corrector scheme and a modified Roe scheme for non-conservative systems of equations are considered for space discretization. Second-order accuracy in space is achieved through variable reconstruction. These schemes were previously used in the simulation of the considered problems together with explicit time advancing. Linearized implicit time-advancing versions are generated here, in which the flux Jacobians are computed through automatic differentiation. Second-order accuracy in time is obtained through a backward differentiation formula associated with a defect-correction approach. For both the considered numerical methods, the explicit and implicit versions are compared in terms of accuracy and efficiency for one-dimensional and two-dimensional morphodynamic problems characterized by different time scales for the evolution of the bed and of the water flow.