Approximate Riemann solvers, parameter vectors, and difference schemes
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Formulations for Numerically Approximating Hyperbolic Systems Governing Sediment Transport
Journal of Scientific Computing
Numerical methods for nonconservative hyperbolic systems: a theoretical framework.
SIAM Journal on Numerical Analysis
A well-balanced approach for flows over mobile-bed with high sediment-transport
Journal of Computational Physics
Two-dimensional simulation of debris flows in erodible channels
Computers & Geosciences
Journal of Computational Physics
An Exner-based coupled model for two-dimensional transient flow over erodible bed
Journal of Computational Physics
Hyperconcentrated 1D Shallow Flows on Fixed Bed with Geometrical Source Term Due to a Bottom Step
Journal of Scientific Computing
Improved Riemann solvers for complex transport in two-dimensional unsteady shallow flow
Journal of Computational Physics
Journal of Computational Physics
A Riemann solver for unsteady computation of 2D shallow flows with variable density
Journal of Computational Physics
Hi-index | 31.48 |
The problem of two-phase, free-surface flows over a mobile bed is characterized by a hyperbolic partial differential equations system that shows nonconservative terms and highly nonlinear relations between primitive and conserved variables. Weak solutions of the present problem were obtained resorting both to the distribution theory and to the integral formulation of momentum conservation: the comparison of these two approaches allowed us to give a physical insight into the meaning of the nonconservative term across a discontinuity. Starting from this result, we derived the conditions necessary to obtain generalized, well-balanced Roe solvers without using the concept of a family of paths. Two numerical schemes based on the same set of matrices have been developed, one in terms of conserved variables and one in terms of primitive variables. The friction-source term has also been included by using an upwind approach. The capabilities and limits of the proposed schemes have been analyzed by comparison with exact solutions of Riemann problems and with numerical solutions obtained with the AWB-3SRS scheme.