Abstract

not-yet-known not-yet-known not-yet-known unknown This article presents an algebraic method for designing an initial bed profile to ensure minimal sediment deposition in open channels. We address the hyperbolic system of partial differential equations, known as the Saint-Venant-Exner system, which describes the behavior of water flow and sediment transport. By applying a priori estimation techniques and reformulating the problem as an optimal control problem, we construct a minimizing control law, via the adjoint method. This control law ensures the stability of the system and minimizes sediment deposition. In addition, a finite volume scheme is implemented to numerically solve both the direct system (SVE) and its adjoint system. Numerical simulations are provided for illustration.