Random field sampling for a simplified model of melt-blowing considering turbulent velocity fluctuations

In melt-blowing very thin liquid fiber jets are spun due to high-velocity air streams. In literature there is a clear, unsolved discrepancy between the measured and computed jet attenuation. In this paper we will verify numerically that the turbulent velocity fluctuations causing a random aerodynamic drag on the fiber jets -- that has been neglected so far -- are the crucial effect to close this gap. For this purpose, we model the velocity fluctuations as vector Gaussian random fields on top of a k-epsilon turbulence description and develop an efficient sampling procedure. Taking advantage of the special covariance structure the effort of the sampling is linear in the discretization and makes the realization possible

An error indicator-based adaptive reduced order model for nonlinear structural mechanics -- application to high-pressure turbine blades

The industrial application motivating this work is the fatigue computation of aircraft engines' high-pressure turbine blades. The material model involves nonlinear elastoviscoplastic behavior laws, for which the parameters depend on the temperature. For this application, the temperature loading is not accurately known and can reach values relatively close to the creep temperature: important nonlinear effects occur and the solution strongly depends on the used thermal loading. We consider a nonlinear reduced order model able to compute, in the exploitation phase, the behavior of the blade for a new temperature field loading. The sensitivity of the solution to the temperature makes {the classical unenriched proper orthogonal decomposition method} fail. In this work, we propose a new error indicator, quantifying the error made by the reduced order model in computational complexity independent of the size of the high-fidelity reference model. In our framework, when the {error indicator} becomes larger than a given tolerance, the reduced order model is updated using one time step solution of the high-fidelity reference model. The approach is illustrated on a series of academic test cases and applied on a setting of industrial complexity involving 5 million degrees of freedom, where the whole procedure is computed in parallel with distributed memory

High-resolution distributed sampling of bandlimited fields with low-precision sensors

The problem of sampling a discrete-time sequence of spatially bandlimited fields with a bounded dynamic range, in a distributed, communication-constrained, processing environment is addressed. A central unit, having access to the data gathered by a dense network of fixed-precision sensors, operating under stringent inter-node communication constraints, is required to reconstruct the field snapshots to maximum accuracy. Both deterministic and stochastic field models are considered. For stochastic fields, results are established in the almost-sure sense. The feasibility of having a flexible tradeoff between the oversampling rate (sensor density) and the analog-to-digital converter (ADC) precision, while achieving an exponential accuracy in the number of bits per Nyquist-interval per snapshot is demonstrated. This exposes an underlying ``conservation of bits'' principle: the bit-budget per Nyquist-interval per snapshot (the rate) can be distributed along the amplitude axis (sensor-precision) and space (sensor density) in an almost arbitrary discrete-valued manner, while retaining the same (exponential) distortion-rate characteristics. Achievable information scaling laws for field reconstruction over a bounded region are also derived: With N one-bit sensors per Nyquist-interval, $\Theta(\log N)$ Nyquist-intervals, and total network bitrate $R_{net} = \Theta((\log N)^2)$ (per-sensor bitrate $\Theta((\log N)/N)$), the maximum pointwise distortion goes to zero as $D = O((\log N)^2/N)$ or $D = O(R_{net} 2^{-\beta \sqrt{R_{net}}})$. This is shown to be possible with only nearest-neighbor communication, distributed coding, and appropriate interpolation algorithms. For a fixed, nonzero target distortion, the number of fixed-precision sensors and the network rate needed is always finite.Comment: 17 pages, 6 figures; paper withdrawn from IEEE Transactions on Signal Processing and re-submitted to the IEEE Transactions on Information Theor