A Finite Element Penalized Direct Forcing Immersed Boundary Method for infinitely thin obstacles in a dilatable flow

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

“…The numerical methods involved in this paper are directly taken from [2] and references within. A brief summary is given in the following section.…”

“…The chosen Immersed Boundary Method is called Penalized Direct Forcing and was initially developed by M. BELLIARD et al in a Finite Difference framework [3,4]. In this paper, we consider the adaptation of this method to a Finite Element formulation, proposed in [2]. To make a brief reminder, the idea is to add a specific (penalized) Direct Forcing term to the momentum balance equation and to split it between the prediction and projection steps of the fractional-step algorithm (based on the work of [21] and references within):…”

“…PESKIN [1], in which the geometry of the obstacle is independent from the computational domain mesh -for a more extensive history of fictitious domain methods, the interested reader can refer to [2]. In this paper, we are interested in the Penalized Direct Forc-In a recent work [2], we presented a Finite Element version of the PDF method, inspired from [4], in the context of the incompressible laminar Navier-Stokes equations, using an implicit fractional step algorithm (or projection scheme) [11] and a directional linear interpolation technique of the velocity near the immersed boundaries. In this present paper, we focus on different techniques to recover data from the discrete immersed boundary and different ways to achieve order 2 in space via linear interpolation.…”

“…In this present paper, we focus on different techniques to recover data from the discrete immersed boundary and different ways to achieve order 2 in space via linear interpolation. In particular, we are motivated by the comparison of the data reconstruction and interpolation techniques proposed in [2] with the more global ones proposed in [4].…”

Penalized direct-dorcing method and power-law-based wall model for immersed-boundary numerical simulations of obstacles in turbulent flow

“…Using an in-house industrial software, we face the constraint to not being able to modify the physical-problem governing equations in the code. Taking into account this fact, we choose the Penalized Direct Forcing method, a merge of the Penalty and Direct-Forcing (DF) methods [2]. It consists in a penalized forcing term, written in a DF formulation, added to the governing equations for taking into account the immersed boundaries.…”