Boundary effects on wave trains in the Exner model of sedimental transport

In this work we compute the numerical solution of the Exner model of sedimentation when a train of waves is imposed at the inflow boundary (E. Macca in Shock-Capturing methods: Well-Balanced Approximate Taylor and Semi-Implicit schemes. PhD thesis, Universit‘a degli Studi di Palermo, Palermo, (2022) and Major Revision, (2023)). The numerical solver is a second order finite-volume scheme, with semi-implicit time discretization based on Implicit-Explicit (IMEX) schemes, which guarantees better stability properties than explicit ones, still at a lower cost than fully implicit schemes. We show the effect of spurious reflected waves generated at the outflow edge of the computational domain, propose two remedies, and show how such spurious effects can be reduced by suitable non-reflecting boundary conditions.