A conservative MURD scheme on moving domains: Application to three-dimensional free surface flows

We introduce a monotonic and conservative numerical scheme for the resolution of the linear advection problem set on a moving domain. The scheme is based on an extension to moving domains of the Multidimensional Upwind Residual Distributive (MURD) approach. The properties ensured by the residual distribution schemes set on fixed domains are not altered by the domain movement, except for the conservation of the advected quantity. We introduce in this paper an additional condition which ensures the conservation properties of the MURD scheme on amoving domain. Several numerical tests have been performed, providing satisfying results in terms of conservation of the advected quantity

Partitioned FSI strategy for simulations of a thin elastic valve

We present a Fictitious Domain (FD)/Lagrange multiplier method to approximate a thin valve movement immersed in an incompressible fluid. We developed a partitioned FSI algorithm that is able to keep the fluid and structure codes independent and which involve only minor modifications to each one . We propose a quantitative comparison between FD and ALE, when the displacement is moderated. We show that the two approaches give results in good agreement. We also illustrate FD in a simulation involving very large displacements

Linear versus nonlinear approaches for the stability analysis of aluminium production cells

The modelling of magnetohydrodynamics (MHD) phenomena in aluminium electrolysis cells is a challenging problem. The basic equations are the MHD equations in parabolic form, for two immiscible fluids. Among the various nonlinearities in the model, one is due to the moving interface between the two fluids. The basic question that numerical simulations contribute to solve is the study of the stability of the cell. In previous works, we have developed and implemented a fully nonlinear approach to solve the two-fluid MHD system. On the other hand, many approaches rely on a simplified version of the equations, and linear stability analysis. The present study compares and discusses the results obtained in the two approaches