Numerical modelling of free-surface shallow flows over irregular topography with complex geometry.

*(English)*Zbl 1427.76163Summary: A well-balanced Godunov-type finite volume algorithm is developed for modelling free-surface shallow flows over irregular topography with complex geometry. The algorithm is based on a new formulation of the classical shallow water equations in hyperbolic conservation form. Unstructured triangular grids are used to achieve the adaptability of the grid to the geometry of the problem and to facilitate localised refinement. The numerical fluxes are calculated using HLLC approximate Riemann solver, and the MUSCL-Hancock predictor-corrector scheme is adopted to achieve the second-order accuracy both in space and in time where the solutions are continuous, and to achieve high-resolution results where the solutions are discontinuous. The novelties of the algorithm include preserving well-balanced property without any additional correction terms and the wet/dry front treatments. The good performance of the algorithm is demonstrated by comparing numerical and theoretical results of several benchmark problems, including the preservation of still water over a two-dimensional hump, the idealised dam-break flow over a frictionless flat rectangular channel, the circular dam-break, and the shock wave from oblique wall. Besides, two laboratory dam-break cases are used for model validation. Furthermore, a practical application related to dam-break flood wave propagation over highly irregular topography with complex geometry is presented. The results show that the algorithm can correctly account for free-surface shallow flows with respect to its effectiveness and robustness thus has bright application prospects.

##### MSC:

76M12 | Finite volume methods applied to problems in fluid mechanics |

76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |

##### Keywords:

free-surface shallow flows; unstructured grids; finite volume; well-balanced; wetting and drying; dam break
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\textit{Y. Liu} et al., Appl. Math. Modelling 37, No. 23, 9482--9498 (2013; Zbl 1427.76163)

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