Well balanced residual distribution for the ALE spherical shallow water equations on moving adaptive meshes

Luca Arpaia (1) , Mario Ricchiuto (2)

1 BRGM - Bureau de Recherches Géologiques et Minières (BRGM)
2 CARDAMOM - Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts

We consider the numerical approximation of the Shallow Water Equations (SWEs) in spherical geometry for oceanographic applications. To provide enhanced resolution of moving fronts present in the flow we consider adaptive discrete approximations on moving triangulations of the sphere. To this end, we restate all Arbitrary Lagrangian Eulerian (ALE) transport formulas, as well as the volume transformation laws, for a 2D manifold. Using these results, we write the set of ALE-SWEs on the sphere. We then propose a Residual Distribution discrete approximation of the governing equations. Classical properties as the DGCL and the C-property (well balancedness) are reformulated in this more general context. An adaptive mesh movement strategy is proposed. The discrete framework obtained is thoroughly tested on standard benchmarks in large scale oceanography to prove their potential as well as the advantage brought by the adaptive mesh movement.

Mots clés: Arbitrary Lagrangian Eulerian formulation; curvilinear coordinates; Shallow Water equations; Moving Mesh; Residual Distribution; Well-Balanced

Domaines: Modélisation et simulation; Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]; Océan, Atmosphère

Luca Arpaia, Mario Ricchiuto. Well balanced residual distribution for the ALE spherical shallow water equations on moving adaptive meshes. Journal of Computational Physics, 2020, 405, pp.109173. ⟨10.1016/j.jcp.2019.109173⟩. ⟨hal-02422335⟩