A Finite Elements Penalized Direct Forcing Method to Take Into Account Infinitely Thin Immersed Boundaries in a Dilatable Flow

Abstract

In the framework of the new passive safety systems developed by the French Atomic Energy Commission (CEA) for the second and third generations of nuclear reactors, a numerical simulation tool capable of modeling thin inflow obstacles is needed [1]. Considering its future use in shape optimization and thermalhydraulics safety studies, the tool must be the fastest, the most accurate and the most robust possible. The aforementioned context has lead to the Computational Fluid Dynamics (CFD) modeling we are currently developing. For now, it involves a projection scheme to solve the dilatable Navier-Stokes equations and, to take into account obstacles, an adaptation of the Penalized Direct Forcing (PDF) method [2] ­ a technique whose characteristics inherit from both penalty [3] and Immersed Boundary Method (IBM) [4] ­ to a Finite Element (FE) formulation. This first modeling offers two variants : one in which the velocity imposed at the vicinity of an obstacle is constant and another in which it is linearly interpolated using properties of the considered immersed boundary (normal vector, barycenter, characteristic function) and the FE basis functions. The results obtained via those two variants, for laminar flow, are in good agreement with analytical and experimental data. However, when compared to each other, it appears that the interpolation of the velocity imposed at the vicinity of the immersed boundary increases the mesh convergence order ­ which is very interesting, in term of accuracy/computation time ratio. Some enhancements of the tool are also considered, mainly related to turbulence modeling. Indeed, the interpolating process, instead of being linear, could follow a turbulent wall law.

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