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Available online xxxxKeywords: Two-layer system Well-balanced model Nonconservative 2LSWE HLL A robust and well-balanced numerical model is developed for solving the two-layer shallow water equations based on the approximate Riemann solver in the framework of finitevolume methods. The HLL (Harten, Lax, and van Leer) solver is employed to calculate the numerical fluxes. The numerical balance between the flux gradient and the source terms is achieved by using a balance-reformulation method. To obtain exactly the lake-atrest solutions as the water depth is chosen as the conserved variable for the continuity equations, a modified HLL flux formulation is proposed for mass flux calculations. Several numerical tests used to validate the performance of the developed numerical model. The results show that the developed model is accurate, well balanced, and that it predicts no oscillations around large gradients.

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Xia et al. (2017) proposed a novel, fully implicit method for the discretization of the bed friction terms for solving the shallow‐water equations. The friction terms contain h−7∕3 (h denotes water depth), which may be extremely large, introducing machine error when h approaches zero. To address this problem, Xia et al. (2017) introduces auxiliary variables (their equations (37) and (38)) so that h−4∕3 rather than h−7∕3 is calculated and solves a transformed equation (their equation (39)). The introduced auxiliary variables require extra storage. We implemented an analysis on the magnitude of the friction terms to find that these terms on the whole do not exceed the machine floating‐point number precision, and thus we proposed a simple‐to‐implement technique by splitting h−7∕3 into different parts of the friction terms to avoid introducing machine error. This technique does not need extra storage or to solve a transformed equation and thus is more efficient for simulations. We also showed that the surface reconstruction method proposed by Xia et al. (2017) may lead to predictions with spurious wiggles because the reconstructed Riemann states may misrepresent the water gravitational effect.