56,143 research outputs found
A matrix-less and parallel interpolation–extrapolation algorithm for computing the eigenvalues of preconditioned banded symmetric Toeplitz matrices
No full textIn the past few years, Bogoya, Boettcher, Grudsky, and Maximenko obtained the precise asymptotic expansion for the eigenvalues of a Toeplitz matrix
T_n(f), under suitable assumptions on the generating function f , as the matrix size n goes to infinity. On the basis of several numerical experiments, it was conjectured by Serra-Capizzano that a completely analogous expansion also holds for the eigenvalues of the preconditioned Toeplitz matrix T_n(u)^{-1}*T_n(v), provided f = v/u is monotone and further conditions on u and v are satisfied. Based on this expansion, we here propose and analyze an interpolation–extrapolation algorithm for computing the eigenvalues of T_n(u)^{−1}*T_n(v). The algorithm is suited for parallel implementation and it may be called “matrix-less” as it does not need to store the entries of the matrix. We illustrate the performance of the algorithm through numerical experiments and
we also present its generalization to the case where f = v/u is non-monotone
The molecular electric quadrupole moment and electric-field-gradient induced birefringence (Buckingham effect) of Cl2
No full textAn ab initio investigation of the molecular properties rationalizing the electric-field-gradient induced birefringence
(Buckingham effect) for Cl2 is presented. The quadrupole moment is determined using hierarchies of basis sets and wavefunction
models. The electric dipole polarizability, the dipole – dipole – quadrupole and dipole – dipole – magnetic dipole
hyperpolarizabilities are determined exploiting a Coupled Cluster Singles and Doubles (CCSD) response approach. The properties
are zero-point vibrationally averaged, and the contribution of excited ro-vibrational states accounted for. To this end, the
interatomic 1Σ+g ground state potential has been computed at CCSD plus perturbative triples – CCSD(T) – level employing a
large augmented correlation consistent basis set. The effect of relativity is estimated at the Dirac-Hartree-Fock level. Our best
value for the quadrupole moment of Cl2 is (2.327 ± 0.010) au and it is in excellent agreement with experiment which, after
revision and dependent on the procedure employed for correcting the original estimate of (2.24 ± 0.04) au of Graham et al.,
[Mol. Phys., 93, 49, (1998)], ranges from (2.31 ± 0.04) au to (2.36 ± 0.04) au
The molecular electric quadrupole moment and electric-field-gradientinduced birefringence (Buckingham effect) of Cl2
No full textEigenvalue Isogeometric Approximations Based on B-Splines: Tools and Results
No full textIn this note, we focus on the spectral analysis of large matrices coming from isogeometric approximations based on B-splines of the eigenvalue problem (Formula Presented) where u(0) and u(1) are given. When considering the collocation case, global distribution results for the eigenvalues are available in the literature, despite the nonsymmetry of the related matrices. Here we complement such results by providing precise estimates for the extremal eigenvalues and hence for the spectral conditioning of the resulting matrices. In the Galerkin setting, the matrices are symmetric and positive definite and a more complete analysis has been conducted in the literature. In the latter case we furnish a further procedure that gives a highly accurate estimate of all the eigenvalues, starting from the knowledge of the spectral distribution symbol. The techniques involve dyadic decomposition arguments, tools from the theory of generalized locally Toeplitz sequences, and basic extrapolation methods
A Dynamic Subfilter-scale Stress Model for Large Eddy Simulations Based on Physical Flow Scales
No full textWe propose a new definition of the length scale in an eddy-viscosity model for large-eddy simulations (LES). This formulation extends and generalizes a previous proposal [Piomelli, Rouhi and Geurts, Proc. ETMM10, 2014], in which the LES length scale was expressed in terms of the integral length-scale of turbulence determined by the flow characteristics and explicitly decoupled from the simulation grid; this approach was named Integral Length-Scale Approximation (ILSA). As in the original ILSA, the model coefficient was determined by the user, and required to maintain a desired contribution of the unresolved, subfilter scales (SFS) to the global transport. We propose a local formulation (local ILSA) in which the model coefficient is local in space, allowing a precise control over SFS activity as a function of location. This new formulation preserves the properties of the global model; application to channel flow and backward-facing step verifies its features and accuracy
Large-eddy simulation of a separated flow with a sub-filter scale model based on the integral length-scale
No full textA new sub-filter scale model for large-eddy simulations, which uses a length-scale proportional to the integral scale of the turbulence instead of the grid resolution to parametrize the modelled stresses, will be assessed in the prediction of the flow of a boundary-layer over a rough surface, which includes separation and reattachment
Near Wall PIV-Measurements on the Windward Slope of a Hill
No full textThe turbulent flow over periodic hills was measured near to the wall, using planar Particle-Image-Velocimetry (PIV) at high spatial resolution. Our focus is on the near wall turbulence structure on the windward slope of the hill. For large-eddy simulation (LES) we suspect that, if this was not predicted accurately, it affects the prediction of the velocity profiles over the hill crest which in turn will affect the recirculation length downstream of the hill. Regarding the time averaged velocities, we were able to resolve the linear viscous region of the boundary layer. The velocity distribution and also the Reynolds stress does not comply with the law of the wall as it is valid for a turbulent boundary layer at equilibrium
Energy dissipation and flux laws for unsteady turbulence
No full textDirect Numerical Simulations of spatially periodic unsteady turbulence show that the high Reynolds number scalings of the instantaneous energy dissipation rate and interscale energy flux at intermediate wavenumbers are qualitatively different from the well-known cornerstone scalings of equilibrium turbulence where and are time-dependent rms velocity and integral length-scales. Instead, they both scale as where and are length and velocity scales characterizing initial/overall unsteady turbulence conditions
Direct numerical simulation of turbulent Couette-Poiseuille flow with zero skin friction
No full textThe near-wall scaling of mean velocity U(y) is addressed for the case of zero skin friction on one wall of a fully turbulent channel flow. The present DNS results can be added to the evidence in support of the conjecture that U is proportional to √yw in the region just above the wall at which the mean shear dU/dy = 0
Real-space Manifestations of Bottlenecks in Turbulence Spectra
No full textAn energy-spectrum bottleneck, a bump in the turbulence spectrum between the inertial and dissipation ranges, is shown to occur in the non-turbulent, one-dimensional, hyperviscous Burgers equation and found to be the Fourier-space signature of oscillations in the real-space velocity, which are explained by boundary-layer-expansion techniques. Pseudospectral simulations are used to show that such oscillations occur in velocity correlation functions in one- and three-dimensional hyperviscous hydrodynamical equations that display genuine turbulence
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