[hal-01077557] The MOOD method for the non-conservative shallow-water system

We present an adaptation of the MOOD method initially introduced in 12 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 scheme and propose a large panel of numerical tests to assess the accuracy of the method and show that nu-merical 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



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