In this paper, an extension of a second-order Godunov-type wave propagation algorithm is presented for modelling two-dimensional morphodynamic problems using a coupled approach. In this solution, the two-dimensional shallow water equations (SWEs) and bedload sediment mass balance laws are expressed in a coupled form. The proposed numerical solver treats the source term including the bedload variations as well as the friction terms within the flux-differencing of the finite-volume neighbouring cells. In order to solve the morphodynamic system in two-dimensions, the dimensional-splitting method is utilised. To consider the bedload sediment discharge within the Exner equation, the Smart and Meyer-Peter & Müller formulae are adopted. To verify the capability of the extended wave propagation solver in dealing with different flow regimes several numerical test cases are investigated. The numerical results show that for all examined cases, excellent agreement is achieved between the numerical results and the exact solutions and experimental data, confirming the effectiveness of the method.
- Two-dimensional morphodynamic system
- Bedload sediment transport
- Coupled solution
- Wave propagation algorithm
- Flux-wave approach