Abstract

In this paper we analyze a stabilized finite element method to approximate the convection diffusion equation on moving domains using an ALE framework. As basic numerical strategy, we discretize the equation in time using first and second order backward differencing (BDF) schemes, whereas space is discretized using a stabilized finite element method (the orthogonal subgrid scale formulation) to deal with convection dominated flows. The semi-discrete problem (continuous in space) is first analyzed. In this situation it is easy to identify the error introduced by the ALE approach. After that, the fully discrete method is considered. We obtain optimal error estimates in both space and time in a mesh dependent norm. The analysis reveals that the ALE approach introduces an upper bound for the time step size for the results to hold. The results obtained for the fully discretized second order scheme (in time) are associated to a weaker norm than the one used for the first order method. Nevertheless, optimal convergence results have been proved. For fixed domains, we recover stability and convergence results with the strong norm for the second order scheme, stressing the aspects that make the analysis of this method much more involved.

Abstract

In this paper we propose a method to approximate flow problems in moving domains using always a given grid for the spatial discretization, and therefore the formulation to be presented falls within the category of fixed-grid methods. Even though the imposition of boundary conditions is a key ingredient that is very often used to classify the fixed-grid method, our approach can be applied together with any technique to impose approximately boundary conditions, although we also describe the one we actually favor. Our main concern is to properly account for the advection of information as the domain boundary evolves. To achieve this, we use an arbitrary Lagrangian–Eulerian framework, the distinctive feature being that at each time step results are projected onto a fixed, background mesh, that is where the problem is actually solved.

Abstract

In order to enhance safety assessments of Sodium Fast Reactors (SFR), some scenarios involving transient Fluid-Structure Interactions (FSI) are investigated using numerical simulation tools. SFRs are indeed quite sensible to mechanical deformations regarding their nuclear power (see [1] for more details). The originality of the scenario presented in the paper is to consider sufficient large mechanical interactions involving a large pressure decrease in the fluid domain. This decrease leads to vaporization of the fluid and then to a different impact on the structures. By means of the open-source software Code Saturne developed by EDF [2], this scenario is investigated in 2D using a 3-equation model derived from the Navier-Stokes equations while an harmonic model is applied for the mechanical structures. The code coupling is managed using the Newmark algorithm for the mechanical part and a damped fixed point algorithm in order to get a converged coupled FSI problem.

Abstract