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The MOOD method for the non-conservative shallow-water system. (English) Zbl 1390.76415
Summary: We present an adaptation of the MOOD method, initially introduced in [the first author et al., J. Comput. Phys. 230, No. 10, 4028–4050 (2011; Zbl 1218.65091); S. Diot et al., Comput. Fluids 64, 43–63 (2012; Zbl 1365.76149)], for the two-dimensional shallow-water system with varying bathymetry, where the major novelty of the study is the non-conservative term discretization in the framework of the MOOD strategy. We derive a robust sixth-order well-balanced scheme and propose a large panel of numerical tests to assess the accuracy of the method and show that numerical solutions are free of oscillations in the vicinity of discontinuities. We also demonstrate that the MOOD method guarantees the height positivity as long as the first-order scheme does.

76M12 Finite volume methods applied to problems in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
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