A partition of unity approach to fluid mechanics and fluid-structure interaction

For problems involving large deformations of thin structures, simulating fluid-structure interaction (FSI) remains challenging largely due to the need to balance computational feasibility, efficiency, and solution accuracy. Overlapping domain techniques have been introduced as a way to combine the fluid-solid mesh conformity, seen in moving-mesh methods, without the need for mesh smoothing or re-meshing, which is a core characteristic of fixed mesh approaches. In this work, we introduce a novel overlapping domain method based on a partition of unity approach. Unified function spaces are defined as a weighted sum of fields given on two overlapping meshes. The method is shown to achieve optimal convergence rates and to be stable for steady-state Stokes, Navier-Stokes, and ALE Navier-Stokes problems. Finally, we present results for FSI in the case of a 2D mock aortic valve simulation. These initial results point to the potential applicability of the method to a wide range of FSI applications, enabling boundary layer refinement and large deformations without the need for re-meshing or user-defined stabilization.Comment: 34 pages, 15 figur

On dynamic computational subgrid modeling

In this paper we study a subgrid model based on extrapolation of a corrective force, in the case of a linear convection-diffusion problem $Lu=f$ in one dimension. The running average $u^{h}$ of the exact solution $u$ on the finest computational scale $h$ satisfies an equation $L_{h}u^{h}=[f]^{h}+F_{h}$, where $L_{h}$ is the operator used in the computation on the scale $h$, $[f]^{h}$ is the approximation of $f$ on the scale $h$, and $F_{h}$ acts as a corrective force, which needs to be modeled. The subgrid modeling problem is to compute approximations of $F_{h}$ without using finer scales than $h$. In this study we model $F_{h}$ by extrapolation from coarser scales than $h$ where the corrective force is directly computed with the finest scale $h$ as reference. We show in experiments that a corrected solution with subgrid model on scale $h$ corresponds to a non-corrected solution on less than $h/4$

Adjoint Based Mesh Adaptation Techniques for Simulation of Turbulent Flow

In this paper we address the challenges of adjoint based mesh adaptation in the setting of industrial CFD, characterized by complex geometry and high Reynolds numbers. We use a space-time finite element discretization of the NS equations, and we focus on the challenges of massively parallel algorithms and the mathematical formulation of the NS equations

Adaptive simulation of unsteady flow past the submerged part of a floating wind turbine platform

Offshore floating platforms for wind turbines represent challenging concepts for design- ers trying to combine an optimal compromise between cost effectiveness and performance. Modelling of the hydrodynamic behaviour of the structure is still the subject of wide de- bate in the technical communities. The assessment of the hydrodynamics of the support structure is not an easy task as the floaters consist of an assembly of columns, braces and pontoons, commonly also with heave plates: each of these components corresponds to a different hydrodynamic model and it further interacts with the other elements. This results in very complex non-linear modeling, which makes it necessary to resort to computational fluid dynamics (CFD) methods for the evaluation of the combined hydrodynamics. In the framework of the collaboration between the Basque Centre for Applied Mathe- matics (BCAM) and Tecnalia R&I, the interaction of the sea flow with a semisubmersible floating offshore wind platform have been calculated by using the open source solver Uni- corn in the FEniCS-HPC framework when subject to a steady inflow. The prototype of the platform consists in a semi-submersible 4-columns column stabilized platform - NAUTILUS Floating Solutions concept-; columns are connected by a rigid ring pontoon provided with heave damping plates at the bottom. The novelty of the approach in FEniCS-HPC hinges upon an implicit formulation for the turbulence, a cheap free slip model of the boundary layer and goal-oriented mesh adaptivity [8, 6, 9, 20, 1]. We find that the results are consistent with experimental results for cylinders at high Reynolds number

Computational Modeling of Dynamical Systems

In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be very costly. By resolving the fast time scales in a short time simulation, a model for the effect of the small time scale variation on large time scales can be determined, making solution possible on a long time interval. This process of computational modeling can be completely automated. Two examples are presented, including a simple model problem oscillating at a time scale of 1e-9 computed over the time interval [0,100], and a lattice consisting of large and small point masses

Exoplanet detection in metal-poor stars

The game meat industry is continuing to grow in South Africa. Several stakeholders are involved in the game meat supply chain and a high level of knowledge is necessary to ensure compliance with legislation and standards. It was therefore necessary to determine the level of knowledge of the stakeholders since this has not been determined before. Information regarding the extent ofstakeholders' knowledge and the possible impact on compliance to standards was obtained through a desk-top study and an analysis of questionnaire responsesfrom industry, consumers and relevant authorities. Results have shown that consumers have a specific expectation regarding the safe production of game meat. Limitations in the knowledge of the stakeholders have been identified. Understanding these limitations can assist policy-makers, law enforcers and the game meat industry in developing strategies to alleviate the problem. The result of this study may assist in providing consumers with game meat that is safe for human consumption