A multi-purpose, intra-wave, shallow water hydro-morphodynamic solver

Stochastic-deterministic modeling of bed load transport in shallow water flow over erodible slope: Linear stability analysis and numerical simulation

“…For instance, two of the three system eigenvalues vanish [60], which requires a careful treatment of critical conditions and the absence of sediment motion. Schemes used for strongly coupled or decoupled numerical schemes are also the object of intense debates [29,45,66,72]. Interestingly here, we will see that the erosiondeposition formulation for bed load transport allows us to readily extend previous finite volume methods for frictional shallow water equations similar to what has been done for computing the suspended load in dilute flows, see Bohorquez and Fernández-Feria [14].…”

A Weighted Average Flux (WAF) scheme applied to shallow water equations for real-life applications

“…It guarantees a second order of accuracy in time and space, with no need for data reconstruction. Several works using the WAF method dedicated to different applications can be found in the literature, see for instance [9,25,26]. We first present the method in the one dimensional case and later we generalize it to two dimensions.…”

Numerical error control for second-order explicit TVD scheme with limiters in advection simulation

“…air mass movement in the atmosphere [1,2], and transport of pollutant and sediment in environmental flows [3][4][5]. In numerical simulations, the advection is hard to cope with due to its hyperbolic property [6,7], and may induce numerical errors such as numerical diffusion and oscillations, especially near the discontinuous parts of the solution [8][9][10].…”