New Saint-Venant-Exner coupled finite volume solver for sediment transport in 1D: Arrakis

Summary

We propsoe a new numerical model (new 1D module named Arrakis) for the simulation of unsteady trans-critical flow with bedload transport in rivers. The approach uses second-order well-balanced finite volume methods to solve the Saint-Venant-Exner equations with rectangular cross-section in 1 dimension. The equations are treated as a non-conservative hyperbolic system with distinct wave speeds, influenced by sediment transport processes. The equations solved are as follows

\partial_t h + \partial_x hu = - hu \dfrac{B'}{B}, \partial_t hu + \partial_x \left( hu^2 + \frac{gh^2}{2} \right) = - hu^2 \dfrac{B'}{B} -gh\partial_x z_b -gh J, \partial_t z_b + \xi \partial_x q_s = - \xi q_s \dfrac{B'}{B},

where

• h : the water depth,
• u : the water velocity,
• z_b : the bottom elevation,
• B : the channel width,
• J=q|q|/(K_s^2 h^2 R_h^{4/3}) : the friction slope,
• K_s : the Strikler coefficient,
• R_h=hB/(B+2h) : the hydraulic radius,
• q_s : the solid flux.

Why is this feature useful?

Solves the SVE system with coupled numerical methods, contrary to Mascaret-Courlis which uses a splitting technique. As a consequence, the new solvers are robust for any Froude number, contrary to Mascaret-Courlis which only works for Fr<1. The new solver uses second order MUSCL scheme which offers better accuracy than Mascaret-Courlis which is only first order.