Serge Piperno

Pierre Sochala, Alexandre Ern, Serge Piperno

Robust and accurate schemes are designed to simulate the coupling between subsurface and overland flows. The coupling conditions at the interface enforce the continuity of both the normal flux and the pressure. Richards' equation governing the subsurface flow is discretized using a Backward Differentiation Formula and a symmetric interior penalty Discontinuous Galerkin method. The kinematic wave equation governing the overland flow is discretized using a Godunov scheme. Both schemes individually are mass conservative and can be used within single-step or multi-step coupling algorithms that ensure overall mass conservation owing to a specific design of the interface fluxes in the multi-step case. Numerical results are presented to illustrate the performances of the proposed algorithms.

Laurent Monasse, Virginie Daru, Christian Mariotti et al.

This paper deals with a new solid-fluid coupling algorithm between a rigid body and an unsteady compressible fluid flow, using an Embedded Boundary method. The coupling with a rigid body is a first step towards the coupling with a Discrete Element method. The flow is computed using a Finite Volume approach on a Cartesian grid. The expression of numerical fluxes does not affect the general coupling algorithm and we use a one-step high-order scheme proposed by Daru and Tenaud [Daru V,Tenaud C., J. Comput. Phys. 2004]. The Embedded Boundary method is used to integrate the presence of a solid boundary in the fluid. The coupling algorithm is totally explicit and ensures exact mass conservation and a balance of momentum and energy between the fluid and the solid. It is shown that the scheme preserves uniform movement of both fluid and solid and introduces no numerical boundary roughness. The effciency of the method is demonstrated on challenging one- and two-dimensional benchmarks.