Explicit Filtering Research Articles

Model based on the reinitialised partial moments for initialising output-error identification methods

The present study addresses the initialisation problem of output-error (OE) identification methods. The challenge is to find a suitable initialization, which brings about a convergence towards the global optimum. A common way to initialise OE methods is to use the ARX model, but it must be used cautiously. The purpose of this study is to describe an alternative method based on the reinitialised partial moment (the RPM model) and to compare this approach with the ARX model by analysing the bias. The RPM model property is an implicit embedded filter that substitutes the explicit data filter required by the ARX model.

New explicit two-dimensional higher order filters

In the present work, a new class of explicit two-dimensional filter is proposed that is significantly different from the conventional one-dimensional Padè type filters. Comparison of performance between one- and two-dimensional filters are made in studying propagation problems and actual viscous flow problems. In this preliminary work, the focus is kept solely on developing central filters with its real transfer function. Many applications related to Navier–Stokes equation have been shown to demonstrate that these two-dimensional filters help in numerical stabilization; control aliasing and control over spurious upstream propagating disturbances. Furthermore, its potential for large eddy simulation (LES) is suggested by band-limiting the solution via filters in post-processing mode.

Fully explicit implementation of direct numerical simulation for a transient near-field methane/air diffusion jet flame

Direct numerical simulation (DNS) is a kind of ultimate numerical simulation tool for studying fundamental turbulent flows, mixing, chemical reactions and interactions among them. In the present work, a fully explicit method of implementing DNS is presented for investigating transient multi-component methane/air jet flame in the near field. The detailed methodology, enclosing non-dimensional governing equations, inlet velocity disturbance, chemical scheme and fluid property, was discussed. An explicit eighth-order finite-difference scheme was used combined with an explicit tenth-order filter. Conservative variables are temporally advanced in two segmented stages that handle Euler terms and viscous terms respectively. A modified non-reflecting boundary condition was used, which has better performance about the characteristic waves on boundary planes. The developed code was firstly tested with an air jet and evaluated in terms of accuracy and parallel efficiency. Then a methane/air combusting jet was simulated to study the characteristics of the chemical heat-release in turbulence.

Evaluation of Turbulence Closure Models for Large-Eddy Simulation over Complex Terrain: Flow over Askervein Hill

Abstract The evaluation of turbulence closure models for large-eddy simulation (LES) has primarily been performed over flat terrain, where comparisons with theory and observations are simplified. The authors have previously developed improved closure models using explicit filtering and reconstruction, together with a dynamic eddy-viscosity model and a near-wall stress term. This dynamic reconstruction model (DRM) is a mixed model, combining scale-similarity and eddy-viscosity components. The DRM gave improved results over standard eddy-viscosity models for neutral boundary layer flow over flat but rough terrain, yielding the expected logarithmic velocity profiles near the wall. The results from the studies over flat terrain are now extended to flow over full-scale topography. The test case is flow over Askervein Hill, an isolated hill in western Scotland, where a field campaign was conducted in 1983 with the purpose of capturing wind data representing atmospheric episodes under near-neutral stratification and steady wind conditions. This widely studied flow provides a more challenging test case for the new turbulence models because of the sloping terrain and separation in the lee of the hill. Since an LES formulation is used, a number of simulation features are different than those typically used in the Askervein literature. The simulations are inherently unsteady, the inflow conditions are provided by a separate turbulent flow database, and (uniquely herein) ensemble averages of the turbulent flow results are used in comparisons with field data. Results indicate that the DRM can improve the predictions of flow speedup and especially turbulent kinetic energy (TKE) over the hill when compared with the standard TKE-1.5 model. This is the first study, to the authors’ knowledge, in which explicit filtering and reconstruction (scale similarity) and dynamic turbulence models have been applied to full-scale simulations of the atmospheric boundary layer over terrain. Simulations with the lowest level of reconstruction are straightforward. Increased levels of reconstruction, however, present difficulties when used with a dynamic eddy-viscosity model. An alternative mixed model is proposed to avoid the complexities associated with the dynamic procedure and to allow higher levels of reconstruction; this mixed model combines a standard TKE-1.5 eddy-viscosity closure with velocity reconstruction to form a simple and efficient turbulence model that gives good results for both mean flow and turbulence over Askervein Hill. The results indicate that significant improvements in LES over complex terrain can be obtained by the use of mixed models that combine scale-similarity and eddy-viscosity components.

Lattice Boltzmann method with selective viscosity filter

For high-Reynolds number flows, the lattice Boltzmann method suffers from numerical instabilities that can induce local blowup of the computation. The von Neumann stability analysis applied to the LBE-BGK and LBE-MRT models shows that numerical instabilities occur in the high wavenumber range and are due to the interplay between acoustic modes and some other modes. As it is done in the LBE-MRT model, an increase of the bulk viscosity is an efficient way of damping spurious oscillations. However, this stabilization method induces an over-damping of acoustic waves. Some selective spatial filters can be used in order to eliminate the spurious small spatial scales without affecting the large scale physical modes. Three different lattice Boltzmann algorithms based on filtering step are proposed: the fully filtered LBE, the LBE with filtered macroscopic quantities and the LBE with filtered collision operator. The behavior of several explicit filter stencils is studied in the Fourier space. For a given filter stencil, the filtered collision operator approach leads to the highest cut-off wavenumber. In this case, the theoretical wavenumber-dependent viscosity is ν ( k ) = c s 2 ( τ / [ 1 - σ f ( k ) ] - 1 / 2 ) where f ( k ) is the filter shape and σ the filter strength. Under-resolved simulations (high Reynolds number) are performed on the case of the doubly periodic shear layers. The performance of the three filtered LBE is found to be the same as the MRT model for stability control. Propagation of acoustic plane waves is also simulated with the three filtering algorithms. The measured dissipation of acoustic wave compares well with the theoretical results.

Spatial antialias filtering in the slowness-frequency domain

A rigorous, explicit spatial antialias filter is designed and applied to spatially coarsely sampled seismic data by removing all energy above the first Nyquist wavenumber, and aliased energy that is folded back across the Nyquist, in the horizontal slowness-frequency domain. The spatial filtering in the slowness-frequency domain is explicit, free from any event linearity assumption, and does not require any interpolation. The spatially aliased energy is dispersive, and present at small and large slownesses. Comparison of the output data after antialias spatial filtering, with output data after conventional antialias frequency filtering, shows that the filter removes the spatially aliased frequencies selectively at each slowness; antialias low-pass frequency filtering under- or overcorrects for spatial aliasing at all slownesses. A seismic gather can be spatially dealiased only at the expense of wavelet spectral changes; dealiasing and preservation of amplitude variations with offset are not simultaneously possible.

Initialization of output-error identification methods – Comparison between ARX and RPM models

The main disadvantage of the Output-Error (OE) identification methods is that they may converge to a secondary optimum. A good initialization converges to the global optimum. The ARX model is often selected as initialization step to OE algorithms. However, the ARX model may be too biased and may not lead to a good initialization. This paper presents an approach based on the Reinitialized Partial Moment (RPM) to obtain a good initialization for OE methods. The RPM model presents an implicit filter that replaces the necessary explicit filter required by the ARX model. The result are encouraging and they have shown that the RPM based approach has to lead to a better initialization than the conventional techniques.

Nonlinear Complementary Filters on the Special Orthogonal Group

This paper considers the problem of obtaining good attitude estimates from measurements obtained from typical low cost inertial measurement units. The outputs of such systems are characterized by high noise levels and time varying additive biases. We formulate the filtering problem as deterministic observer kinematics posed directly on the special orthogonal group SO (3) driven by reconstructed attitude and angular velocity measurements. Lyapunov analysis results for the proposed observers are derived that ensure almost global stability of the observer error. The approach taken leads to an observer that we term the direct complementary filter. By exploiting the geometry of the special orthogonal group a related observer, termed the passive complementary filter, is derived that decouples the gyro measurements from the reconstructed attitude in the observer inputs. Both the direct and passive filters can be extended to estimate gyro bias online. The passive filter is further developed to provide a formulation in terms of the measurement error that avoids any algebraic reconstruction of the attitude. This leads to an observer on SO(3), termed the explicit complementary filter, that requires only accelerometer and gyro outputs; is suitable for implementation on embedded hardware; and provides good attitude estimates as well as estimating the gyro biases online. The performance of the observers are demonstrated with a set of experiments performed on a robotic test-bed and a radio controlled unmanned aerial vehicle.

Comparative survey on nonlinear filtering methods: the quantization and the particle filtering approaches

We provide a comparative study between two different approaches to construct nonlinear filter estimators: on the one hand grid methods using zero-order and first-order quantization schemes, and on the other hand particle filtering algorithms using sequential importance sampling or resampling. For each method, numerical implementation is explicited in addition to convergence arguments and algorithmic complexity. Numerical examples are then given over three state space models: the Kalman filter case, the canonical stochastic volatility model and the infinite dimension explicit filter introduced in [Genon-Catalot, V., 2003, A non linear explicit filter. Statistics and Probability Letters, 61, 145–154]

Large-Eddy Simulation of High Reynolds Number Cannel Flow applying Explicit Filtering

Correct representation of the effects of the turbulence structure near solid boundaries is very important for successful large-eddy simulation (LES). In the present work, this so-called wall-layer modeling is done on commutation error terms near solid boundaries obtained by explicit filtering. These terms are ignored in conventional LES, but in the present work, these error terms are modeled using a dynamic procedure, making use of the scale-similarity of the modeled terms. It is found, by applying the procedure in LES of a high Reynolds number channel flow, that the dynamic modeling of these error terms makes it possible to gain the roughly same velocity profile as DNS results statistically, and moreover, to simulate the features of large-scale structures instantaneously.

Effect of grid discontinuities on large-eddy simulation statistics and flow fields

We have performed large-eddy simulations of spatially developing homogeneous isotropic turbulence advected past an interface where the grid is suddenly coarsened or refined by a factor of two in each direction. We have compared simulations in which the filter width is proportional to the grid size and is discontinuous at the coarse–fine grid interface, to others in which the filter width varies gradually between the values corresponding to the coarse and fine grids. The Smagorinsky and Lagrangian-dynamic eddy viscosity (LDEV) models were used to parameterize the unresolved subgrid scales. A sudden refinement of the grid does not result in significant flow perturbation: small scales are gradually generated and the flow is generally quite smooth across the interface. When the grid is suddenly coarsened, on the other hand, a considerable energy pileup at small scales is observed near the interface. At lower resolutions, the extent of this high-energy zone grows. Increasing the eddy viscosity upstream of the interface by smoothly increasing the filter width is beneficial. For fine-to-coarse interfaces, the LDEV model with a smoothly varying filter width yields more accurate results than other models. Explicit filtering of the advective term is also beneficial: by increasing the length scale of the turbulence upstream of the grid discontinuity, interpolation and aliasing errors are reduced and better agreement with single-grid results is obtained.

Reconstruction of a grounded object in an electrostatic halfspace with an indicator function

This article explores the use of capacitance measurements made between electrodes embedded in or around a display surface, to detect the position, orientation and shape of hands and fingers. This is of interest for unobtrusive 3D gesture input for interactive displays, so called touch-less interaction. The hand is assumed to be grounded and formally the problem is a Cauchy problem for the Laplace equation in which Cauchy data on the boundary ∂H (the display surface) is used to reconstruct the zero potential contour of the unknown object D (the hand). The problem is solved with the so-called factorisation method developed for acoustic scattering and electrostatic problems. In the factorisation method, a test function gz is used to characterise points , in which is the Dirichlet to Neumann map on the display surface. We demonstrate a suitable test function gz appropriate to the boundary conditions present here. In the application, ΛD is obtained from measurements at finite precision as a finite matrix and the calculation of is implicitly regularised. The resulting level set P(z) is finite and differentiable everywhere. The level representing the object ∂D is found through minimising the cost function. Numerical simulations demonstrate that for realistic electrode layouts and noise levels the method provides good reconstruction. The application of explicit regularisation filters can be beneficial and allows a trade-off between resolution and stability.

Large-eddy simulation of the flow in a lid-driven cubical cavity

Large-eddy simulations of the turbulent flow in a lid-driven cubical cavity have been carried out at a Reynolds number of 12000 using spectral element methods. Two distinct subgrid-scales models, namely a dynamic Smagorinsky model and a dynamic mixed model, have been both implemented and used to perform long-lasting simulations required by the relevant time scales of the flow. All filtering levels make use of explicit filters applied in the physical space (on an element-by-element approach) and spectral (modal) spaces. The two subgrid-scales models are validated and compared to available experimental and numerical reference results, showing very good agreement. Specific features of lid-driven cavity flow in the turbulent regime, such as inhomogeneity of turbulence, turbulence production near the downstream corner eddy, small-scales localization and helical properties are investigated and discussed in the large-eddy simulation framework. Time histories of quantities such as the total energy, total turbulent kinetic energy or helicity exhibit different evolutions but only after a relatively long transient period. However, the average values remain extremely close.

On the application of explicit spatial filtering to the variables or fluxes of linear equations

The need for filtering high-frequency waves is a recurrent issue in numerical simulations. These waves might indeed lead to instability, and they are in general not calculated accurately by the discretization algorithms. Selective filters have therefore been designed in order to damp high-frequency waves without affecting significantly low-frequency disturbances [1–6]. These filters are particularly used in computational aeroacoustics, but they appear also suitable for Large-Eddy Simulations (LES), in which only the scales larger than the grid size are computed, and whose equations are derived formally by applying a filter operator to the Navier– Stokes equations [7]. Moreover LES based specially on explicit filtering have been also developed [8–10]. In practice, the flow variables are usually filtered explicitly after each time step. Consider for example the time integration of the following differential equation:

Retrieval of Moisture from Simulated GPS Slant-Path Water Vapor Observations Using 3DVAR with Anisotropic Recursive Filters

Abstract Anisotropic recursive filters are implemented within a three-dimensional variational data assimilation (3DVAR) framework to efficiently model the effect of flow-dependent background error covariance. The background error covariance is based on an estimated error field and on the idea of Riishøjgaard. In the anisotropic case, the background error pattern can be stretched or flattened in directions oblique to the alignment of the grid coordinates and is constructed by applying, at each point, six recursive filters along six directions corresponding, in general, to a special configuration of oblique lines of the grid. The recursive filters are much more efficient than corresponding explicit filters used in an earlier study and are therefore more suitable for real-time numerical weather prediction. A set of analysis experiments are conducted at a mesoscale resolution to examine the effectiveness of the 3DVAR system in analyzing simulated global positioning system (GPS) slant-path water vapor observations from ground-based GPS receivers and observations from collocated surface stations. It is shown that the analyses produced with recursive filters are at least as good as those with corresponding explicit filters. In some cases, the recursive filters actually perform better. The impact of flow-dependent background errors modeled using the anisotropic recursive filters is also examined. The use of anisotropic filters improves the analysis, especially in terms of finescale structures. The analysis system is found to be effective in the presence of typical observational errors. The sensitivity of isotropic and anisotropic recursive-filter analyses to the decorrelation scales is also examined systematically.

Explicit parameterization of sleep EEG transients

Adaptive time-frequency approximations, implemented via the matching pursuit algorithm, offer description of local signals structures in terms of their time occurrence and width, frequency and amplitude. This allows to construct explicit filters for finding EEG waveforms, known from the visual analysis, in the matching pursuit decomposition of signals. In such a way detectors of relevant structures of both transient and oscillatory nature can be constructed in the space of physically meaningful parameters. This study presents evaluation of changes of power and frequency of sleep spindles and delta waves, related to the depth of the sleep, which were previously assessed in a qualitative way. We confirm quantitatively the decrease of frequencies of sleep spindles and delta waves with the depth of the sleep.

Investigation of Nonreflective Boundary Conditions for Computational Aeroacoustics

Direct aeroacoustic computations require nonreflective boundary conditions that allow disturbances to leave the domain freely without anomalous reflections. In the present paper we analyze a series of nonreflective boundary conditions already published in the literature and propose an improved outflow nonreflective boundary condition with reflection characteristic that is reduced greatly. For the solution of the linearized Euler equations, a sixth-order compact finite-difference algorithm is used together with a sixth-order explicit digital filter that suppresses the high-frequency spurious oscillations in the solution. A number of representative test cases are presented. The new outflow boundary condition is recommended for the simulation of sound produced by turbulence.

Large eddy simulations of transitional round jets: Influence of the Reynolds number on flow development and energy dissipation

Transitional round jets at Mach number M=0.9, with identical initial conditions except for the diameter, yielding Reynolds numbers over the range 1.7×103⩽ReD⩽4×105, are computed by large eddy simulation (LES) using explicit selective/high-order filtering. The effects of the Reynolds number on the jet flows are first presented. As the Reynolds number decreases, the jets develop more slowly upstream from the end of the potential core, but more rapidly downstream. At lower Reynolds numbers, the decay of the centerline velocity and the jet spreading are indeed faster, and the turbulence intensities are higher after the potential core, in agreement with data of the literature. The integral length scales are also significantly larger. The results suggest moreover that the jet self-similar region is reached at shorter axial distances at lower Reynolds numbers. The influence of the Reynolds number on the energy-dissipation mechanisms involved in the LES, namely molecular viscosity and explicit filtering, is secondly investigated. At high Reynolds number, energy dissipation is mainly ensured by the explicit filtering, through the smaller scales discretized. As the Reynolds number decreases, the contribution of molecular viscosity increases and becomes predominant. Molecular viscosity is also shown to affect a large range of turbulent scales with a dissipation peak observed around the Taylor length scale.

Retrieval of Moisture from Slant-Path Water Vapor Observations of a Hypothetical GPS Network Using a Three-Dimensional Variational Scheme with Anisotropic Background Error

Abstract A three-dimensional variational (3DVAR) scheme is developed for retrieving three-dimensional moisture in the atmosphere from slant-path measurements of a hypothetical ground-based global positioning system (GPS) observation network. It is assumed that the observed data are in the form of slant-path water vapor (SWV), which is the integrated water vapor along the slant path between the ground receiver and the GPS satellite. The inclusion of a background in the analysis overcomes the under-determinedness problem. An explicit Gaussian-type spatial filter is used to model the background error covariances that can be anisotropic. As a unique aspect of this study, an anisotropic spatial filter based on flow-dependent background error structures is implemented and tested and the filter coefficients are derived from either true background error field or from the increment of an intermediate analysis that is obtained using an isotropic filter. In the latter case, an iterative procedure is involved. A set of experiments is conducted to test the new scheme with hypothetical GPS observations for a dryline case that occurred during the 2002 International H2O Project (IHOP_2002) field experiment. Results illustrate that this system is robust and can properly recover three-dimensional mesoscale moisture structures from GPS SWV data and surface moisture observations. The analysis captures major features in water vapor associated with the dryline even when an isotropic spatial filter is used. The analysis is further improved significantly by the use of flow-dependent background error covariances modeled by an anisotropic spatial filter. Sensitivity tests show that surface moisture observations are important for the analysis near ground, and more so when flow-dependent background error covariances are not used. Vertical filtering is necessary for obtaining accurate analysis increments. The retrieved moisture field remains reasonably accurate when the surface moisture observations and GPS SWV data contain errors of typical magnitudes. The positive impact of flow-dependent background error covariances increases when the density of ground-based GPS receiver stations decreases.

Design of fixed-structure controllers with frequency-domain criteria: a multiobjective optimisation approach

An optimisation-based iterative design of fixed-structure controllers with frequency-domain criteria is presented. An interactive multiobjective optimisation procedure is presented, which is based on a direct shaping of the frequency responses, without the need to construct explicit weighting filters. At each iteration, a constrained optimisation problem is formulated in such a way that successive improvements of the design to meet the designer's specifications are achieved. For computational efficiency, time-domain expressions consisting of linear matrix equations are used to characterise the frequency responses.