Instability and equilibration of centrifugally stable stratified Taylor-Couette flow

The flow between two concentric cylinders, V(r), is studied analytically and computationally for a fluid with stable axial density stratification. A sufficient condition for linear, inviscid instability is d(V/r)(2)/dr<0 (i.e., all anticyclonically sheared flows) rather than the Rayleigh condition for centrifugal instability, d(Vr)(2)/dr<0. This implies a far wider range of instability than previously identified. The instability persists with finite viscosity and nonlinearity, leading to chaos and fully developed turbulence through a sequence of bifurcations. Laboratory tests are feasible and desirable.     

Speed limit quasi splines and their application to interpolation with bounded first order derivative

The problem of computing spline‐like functions for ideal data, subject to two‐sided inequality constraints on the first‐order derivative, are considered, focusing primarily on constant constraints and then generalizing. Using a variational approach, in which the inequality constraints are not explicitly imposed, a special type of exponential splines we call speed limit quasi splines is introduced. A simple, non‐parametric, efficient, and robust iterative solver is suggested, which is suitable for a wide range of inequality constraints. Analysis of the convergence factor of this algorithm is provided and supported by extensive numerical tests. Copyright © 2014 John Wiley & Sons, Ltd.     

A robust implicit multigrid method for RANS equations with two-equation turbulence models

The design of a new, truly robust multigrid framework for the solution of steady-state Reynolds-Averaged Navier–Stokes (RANS) equations with two-equation turbulence models is presented. While the mean-flow equations and the turbulence model equations are advanced in time in a loosely-coupled manner, their multigrid cycling is strongly coupled (FC-MG). Thanks to the loosely-coupled approach, the unconditionally positive-convergent implicit time-integration scheme for two-equation turbulence models (UPC) is used. An improvement to the basic UPC scheme convergence characteristics is developed and its extension within the multigrid method is proposed. The resulting novel FC-MG-UPC algorithm is nearly free of artificial stabilizing techniques, leading to increased multigrid efficiency. To demonstrate the robustness of the proposed algorithm, it is applied to linear and non-linear two-equation turbulence models. Numerical experiments are conducted, simulating separated flow about the NACA4412 airfoil, transonic flow about the RAE2822 airfoil and internal flow through a plane asymmetric diffuser. Results obtained from numerical simulations demonstrate the strong consistency and case-independence of the method.     

Preconditioning systems arising from the KKR Green function method using block-circulant matrices

Recently, a linearly scaling method for the calculation of the electronic structure based on the Korringa–Kohn–Rostoker Green function method has been proposed. The method uses the transpose free quasi minimal residual method (TFQMR) to solve linear systems with multiple right hand sides. These linear systems depend on the energy-level under consideration and the convergence rate deteriorates for some of these energy points. While traditional preconditioners like ILU are fairly useful for the problem, the computation of the preconditioner itself is often relatively hard to parallelize. To overcome these difficulties, we develop a new preconditioner that exploits the strong structure of the underlying systems. The resulting preconditioner is block-circulant and thus easy to compute, invert and parallelize. The resulting method yields a dramatic speedup of the computation compared to the unpreconditioned solver, especially for critical energy levels.     

Using a VOM model for reconstructing potential coding regions in EST sequences

This paper presents a method for annotating coding and noncoding DNA regions by using variable order Markov (VOM) models. A main advantage in using VOM models is that their order may vary for different sequences, depending on the sequences’ statistics. As a result, VOM models are more flexible with respect to model parameterization and can be trained on relatively short sequences and on low-quality datasets, such as expressed sequence tags (ESTs). The paper presents a modified VOM model for detecting and correcting insertion and deletion sequencing errors that are commonly found in ESTs. In a series of experiments the proposed method is found to be robust to random errors in these sequences.     

Review of Methods Inspired by Algebraic-Multigrid for Data and Image Analysis Applications

Algebraic Multigrid (AMG) methods were developed originally for numerically solving Partial Differential Equations (PDE), not necessarily on structured grids. In the last two decades solvers inspired by the AMG approach, were developed for non PDE problems, including data and image analysis problems, such as clustering, segmentation, quantization and others. These solvers share a common principle that there is a crosstalk between fine and coarse representations of the problems, with flow of information in both directions, fine-to-coarse and coarse-to-fine. This paper surveys some of these problems and the AMG-inspired algorithms for their solution.