Details

Autor(en) / Beteiligte

• Michel-Dansac, Victor
• Berthon, Christophe
• Clain, Stéphane
• Foucher, Françoise

Titel

A two-dimensional high-order well-balanced scheme for the shallow water equations with topography and Manning friction

Ist Teil von

• Computers & fluids, 2021-11, Vol.230, p.105152, Article 105152

Ort / Verlag

Amsterdam: Elsevier Ltd

Erscheinungsjahr

2021

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We develop a two-dimensional high-order numerical scheme that exactly preserves and captures the moving steady states of the shallow water equations with topography or Manning friction. The high-order accuracy relies on a suitable polynomial reconstruction, while the well-balancedness property is based on the first-order scheme from Michel-Dansac et al. (2016, 2017), extended to two space dimensions. To get both properties, we use a convex combination between the high-order scheme and the first-order well-balanced scheme. By adequately choosing the convex combination parameter following a very simple steady state detector, we ensure that the resulting scheme is both high-order accurate and well-balanced. The method is then supplemented with a MOOD procedure to eliminate the spurious oscillations coming from the high-order polynomial reconstruction and to guarantee the physical admissibility of the solution. Numerical experiments show that the scheme indeed possesses the claimed properties. The simulation of the 2011 Tōhoku tsunami, on real data, further confirms the relevance of this technique. •Construction of a fully well-balanced 2D high-order scheme•The scheme is for the shallow water equations with topography or Manning friction•The scheme exactly preserves and captures the moving steady states•Convex combination between high-order and first-order schemes gives well-balancedness•MOOD procedure to eliminate the spurious oscillations coming from the reconstruction•Validation on several numerical experiments