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