The MOOD method for the non-conservative shallow-water system

Stéphane Clain (1) , J Figueiredo (1)

1 CMAT - Centro de Matemática [Minho]

We present an adaptation of the MOOD method, initially introduced in [1,2], 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.

Mots clés: Finite volume; High-order; Non-conservative problem; Polynomial reconstruction; Unstructured mesh; Shallow-water; MOOD; Positivity-preserving

Domaines: Analyse numérique [math.NA]

Stéphane Clain, J Figueiredo. The MOOD method for the non-conservative shallow-water system. 2014. ⟨hal-01077557⟩