Comparison of several interpolation methods to reconstruct field data in the vicinity of a finite element immersed boundary

Abstract

Thermal-hydraulics safety requirements for the second and third generation of nuclear reactors led to the development of innovative passive safety systems. In particular, new devices must be developed involving numerical simulations for turbulent two-phase flows around complex geometries. To reduce the time-consuming mesh generation phase when testing various geometries, we use a fictitious domain approach. More specifically, we choose the Penalized Direct Forcing Method to take into account inflow obstacles. Following a recent work, involving the resolution of the one-phase incompressible Navier-Stokes equations using a projection scheme and the Finite Element Method, this paper focuses on different techniques to recover data from the discrete immersed boundary and different ways to achieve order 2 in space via linear interpolation. Indeed, we investigate two data reconstruction approaches (one based on various weighted averaging, the other based on optimization) and compare their results for cylindrical and NACA0012 airfoil shapes: they provide similar accuracy but the weighting is much faster in terms of execution time. We also investigate three different interpolation types: unidirectional, multi-directional and a new hybrid between the two. The Taylor-Couette flow and the flow around a circular cylinder are used to carry out mesh convergence studies. Globally, order 2 in space is numerically assessed in both L 2 and L ∞ norms for all the interpolation types, which is consistent with theoretical expectations – even if the space convergence order is a bit higher for the multi-directional approach. For the flow around a circular cylinder, the values of aerodynamic coefficients and Strouhal number are in good agreement with the literature, especially when using directional interpolation. Finally, an industrial case, representative of passive safety systems, is presented to assess the robustness and capability of the method. The simulations tend to show that, here again, the directional interpolation offers the best behavior when dealing with complex geometries and relatively coarse meshes.