Turbulence modeling for flows around convex features giving rapid eddy distortion

Reynolds averaged Navier-Stokes model performances in the stagnation and wake regions for turbulent flows with relatively large Lagrangian length scales (generally larger than the scale of geometrical features) approaching small cylinders (both square and circular) is explored. The effective cylinder (or wire) diameter based Reynolds number, ReW ≤ 2.5 × 103. The following turbulence models are considered: a mixing-length; standard Spalart and Allmaras (SA) and streamline curvature (and rotation) corrected SA (SARC); Secundov's νt-92; Secundov et al.'s two equation νt-L; Wolfshtein's k-l model; the Explicit Algebraic Stress Model (EASM) of Abid et al.; the cubic model of Craft et al.; various linear k-ε models including those with wall distance based damping functions; Menter SST, k-ω and Spalding's LVEL model. The use of differential equation distance functions (Poisson and Hamilton-Jacobi equation based) for palliative turbulence modeling purposes is explored. The performance of SA with these distance functions is also considered in the sharp convex geometry region of an airfoil trailing edge. For the cylinder, with ReW ≈ 2.5 × 103 the mixing length and k-l models give strong turbulence production in the wake region. However, in agreement with eddy viscosity estimates, the LVEL and Secundov νt-92 models show relatively little cylinder influence on turbulence. On the other hand, two equation models (as does the one equation SA) suggest the cylinder gives a strong turbulence deficit in the wake region. Also, for SA, an order or magnitude cylinder diameter decrease from ReW = 2500 to 250 surprisingly strengthens the cylinder's disruptive influence. Importantly, results for ReW ≪ 250 are virtually identical to those for ReW = 250 i.e. no matter how small the cylinder/wire its influence does not, as it should, vanish. Similar tests for the Launder-Sharma k-ε, Menter SST and k-ω show, in accordance with physical reality, the cylinder's influence diminishing albeit slowly with size. Results suggest distance functions palliate the SA model's erroneous trait and improve its predictive performance in wire wake regions. Also, results suggest that, along the stagnation line, such functions improve the SA, mixing length, k-l and LVEL results. For the airfoil, with SA, the larger Poisson distance function increases the wake region turbulence levels by just under 5%. © 2007 Elsevier Inc. All rights reserved.

Novel applications of BEM based Poisson level set approach

Accurate and efficient computation of the distance function d for a given domain is important for many areas of numerical modeling. Partial differential (e.g. HamiltonJacobi type) equation based distance function algorithms have desirable computational efficiency and accuracy. In this study, as an alternative, a Poisson equation based level set (distance function) is considered and solved using the meshless boundary element method (BEM). The application of this for shape topology analysis, including the medial axis for domain decomposition, geometric de-featuring and other aspects of numerical modeling is assessed. © 2011 Elsevier Ltd. All rights reserved.

Regression on fixed-rank positive semidefinite matrices: A Riemannian approach

The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The mathematical developments rely on the theory of gradient descent algorithms adapted to the Riemannian geometry that underlies the set of fixedrank positive semidefinite matrices. In contrast with previous contributions in the literature, no restrictions are imposed on the range space of the learned matrix. The resulting algorithms maintain a linear complexity in the problem size and enjoy important invariance properties. We apply the proposed algorithms to the problem of learning a distance function parameterized by a positive semidefinite matrix. Good performance is observed on classical benchmarks. © 2011 Gilles Meyer, Silvere Bonnabel and Rodolphe Sepulchre.

Directional algebraic reconstruction technique for electrical impedance tomography

We assume that the resistance matrix can be found in electrical impedance tomography from the assumption of linear dependence between the voltages and the currents and with the help of the resistance matrix and the transfer impedance between the electrodes, a directional algebraic reconstruction technique is proposed. The goal is to reconstruct the resistivity distribution by weighting the matrices that are obtained by calculating the orthogonal distance of the underlying mesh elements from the neighbouring port resistivity lines. These weighting matrices, which only depend on the topology of the underlying mesh, can be calculated offline and result in a computationally efficient online procedure with a reasonable image reconstruction performance. Simulation results are provided to validate this approach.

Numerical modelling of chirality-Induced bi-Directional swimming of artificial flagella

Biomimetic micro-swimmers can be used for various medical applications, such as targeted drug delivery and micro-object (e.g. biological cells) manipulation, in lab-on-a-chip devices. Bacteria swim using a bundle of flagella (flexible hair-like structures) that form a rotating cork-screw of chiral shape. To mimic bacterial swimming, we employ a computational approach to design a bacterial (chirality-induced) swimmer whose chiral shape and rotational velocity can be controlled by an external magnetic field. In our model, we numerically solve the coupled governing equations that describe the system dynamics (i.e. solid mechanics, fluid dynamics and magnetostatics). We explore the swimming response as a function of the characteristic dimensionless parameters and put special emphasis on controlling the swimming direction. Our results provide fundamental physical insight on the chirality-induced propulsion, and it provides guidelines for the design of magnetic bi-directional micro-swimmers. © 2013 The Author(s) Published by the Royal Society. All rights reserved.