Explicit Filtering Research Articles

Wavelet-based adaptive large-eddy simulation with explicit filtering

Stochastic coherent adaptive large-eddy simulation is a novel approach to the numerical simulation of turbulence, where the coherent energetic eddies are solved for, while modeling the influence of the less energetic coherent/incoherent background flow. The formal separation between resolved and unresolved field is obtained by wavelet threshold filtering that is inherent to the adaptive wavelet collocation numerical method. A new explicit wavelet filtering strategy is introduced and tested, by considering two different filtering levels: the physical level, which controls the turbulence model, and the numerical level that is responsible for the accuracy of numerical simulations. The theoretical basis for wavelet-based adaptive large-eddy simulation with explicit filtering and consistent dynamic modeling is given. Numerical experiments are presented for unsteady homogeneous turbulence, demonstrating the existence of grid-independent solutions.

Direct Numerical Simulation of Pulverized Coal Combustion in a Hot Vitiated Co-flow

A compressible direct numerical simulation (DNS) solver for pulverized coal combustion has been developed and used to study a pulverized coal jet flame with a Reynolds number of 28 284 based on the nozzle diameter. An eighth-order center differential scheme combined with an explicit tenth-order filter is used for spatial discretization. The classical fourth-order Runge–Kutta method is used for time integration. The characteristic non-reflecting boundary conditions are used to describe the boundary conditions. A comprehensive model for coal combustion is applied, and the reaction mechanism of CH4 with five species and two-step reactions is adopted for gas-phase combustion. The grid system has been carefully designed to make sure that turbulent scales and chemical reaction scales are reasonably resolved and the point-source assumptions of particles are valid. The simulation is partially validated against the experiment, and the particle behavior is investigated. It is found that, in the upstream region, the reaction rate is quite scattered and a single particle is found inside the burning flame to form an individual particle combustion mode. While in the downstream region, the reaction zone is more continuous, with a large number of particles enclosed, which characterizes the group combustion mode. Conditional statistics with respect to the mixture fraction are also obtained to provide insights into coal combustion and the related models.

LLSURE: Local Linear SURE-Based Edge-Preserving Image Filtering

In this paper, we propose a novel approach for performing high-quality edge-preserving image filtering. Based on a local linear model and using the principle of Stein's unbiased risk estimate as an estimator for the mean squared error from the noisy image only, we derive a simple explicit image filter which can filter out noise while preserving edges and fine-scale details. Moreover, this filter has a fast and exact linear-time algorithm whose computational complexity is independent of the filtering kernel size; thus, it can be applied to real time image processing tasks. The experimental results demonstrate the effectiveness of the new filter for various computer vision applications, including noise reduction, detail smoothing and enhancement, high dynamic range compression, and flash/no-flash denoising.

Large-eddy simulation of turbulent channel flow using explicit filtering and dynamic mixed models

Large-eddy simulations of turbulent channel flow at Reτ = 395 are performed using explicit filtering. Two different subfilter-scale models, the dynamic Smagorinsky mixed model and the dynamic global-coefficient mixed model, are formulated in accordance with the explicitly filtered governing equations. The use of explicit filtering separates the filtering operation from discretization, thereby producing a grid-independent solution. In explicit-filter large-eddy simulations, both the dynamic Smagorinsky mixed and the dynamic global-coefficient mixed subfilter-scale models are found to produce solutions close to the non-filtered direct numerical simulation data when explicit-filter widths in the streamwise and spanwise directions and at the center of the channel in the wall normal direction are about four times the grid spacings for direct numerical simulation. Solutions obtained using explicit-filter large-eddy simulation are compared with solutions obtained using implicit-filter large-eddy simulation in a range of filter and grid resolution. Explicit-filter large-eddy simulations performed on gradually refined grids with a fixed set of explicit-filter widths are found to produce grid-converged solutions for both models. Similarly in implicit-filter large-eddy simulation, predictive capabilities of subfilter-scale models in explicit-filter large-eddy simulation are found to be interfered with truncation errors when the ratio of the explicit-filter width to the grid spacing is small.

High-Order Noise Filtering in Nontrivial Quantum Logic Gates

Treating the effects of a time-dependent classical dephasing environment during quantum logic operations poses a theoretical challenge, as the application of noncommuting control operations gives rise to both dephasing and depolarization errors that must be accounted for in order to understand total average error rates. We develop a treatment based on effective Hamiltonian theory that allows us to efficiently model the effect of classical noise on nontrivial single-bit quantum logic operations composed of arbitrary control sequences. We present a general method to calculate the ensemble-averaged entanglement fidelity to arbitrary order in terms of noise filter functions, and provide explicit expressions to fourth order in the noise strength. In the weak noise limit we derive explicit filter functions for a broad class of piecewise-constant control sequences, and use them to study the performance of dynamically corrected gates, yielding good agreement with brute-force numerics.

Narrow line width and polarization independent multi-channel filter based on one-dimensional photonic crystal containing negative index materials

Narrow line width and polarization independent multichannel filter based on one-dimensional photonic crystal (1D PC) containing negative index materials (NIMs) is proposed and theoretically studied. It is found that narrow transmission bands for 1D PC containing NIMs are merely centered at frequencies (wavelengths) satisfying Fabry–Perot resonating condition due to the existence of n¯-zero gap. Besides, we disclose that this PC is simultaneously characterized by polarization independence at normal incidence and that transfer characteristics of this 1D PC such as frequency spacing and line width could be adjusted by changing structure parameters of it. Finally, we devise an explicit multi-channel filter based on such 1D PC for DWDM system with 50GHz channel spacing for verification.

Detail‐feature‐preserving surface reconstruction

ABSTRACTIn this paper, we propose a feature‐preserving surface reconstruction method from sparse noisy 3D measurements such as range scanning or passive multiview stereo. In contrast to earlier methods, we define a novel type of explicit 3D filter—regularized weighted least squares filter—to characterize the detail features such as surface wrinkles and sharp features. To account for noise, we rasterize input‐oriented points into a probabilistic volume (base volume) and then create a guidance volume by Gaussian filtering. Both the base volume and the guidance volume are further filtered by regularized weighted least squares filter to detect and recover detail features. After the two‐stage filtering, a global minimal surface is computed by graph cut and meshed as a geometric model. Experimental results on various datasets show that our method is robust to noise, outliers, and missing parts, which makes it more suitable to fit indoor/outdoor multiview stereo data. Unlike other methods, our method can completely recover scene structures and preserve detail features from noisy point samples. Copyright © 2012 John Wiley & Sons, Ltd.

Frequency‐space wavefield extrapolation using infinite impulse response digital filters: is it feasible?

ABSTRACTThe purpose of this paper is to study the possibility of performing practically stable and efficient frequency‐space (f−x) wavefield extrapolation for the application of seismic imaging and datuming via infinite impulse response (IIR) filters. The model reduction control theory was adopted to design such IIR f−x extrapolation filters. The model reduction theory reduces the order of a given order system which, in this case, involves reducing a finite impulse response (FIR) f−x extrapolation filter system into an IIR f−x extrapolation filter system. This theory relies on decomposing the states of the given filter system into strong and weakly coupled sub‐systems, and then eliminating the weakly coupled states via singular value decomposition of the Hankel and the impulse response Gramian matrices. Simulation results indicate that IIR f−x filters can be obtained, which are stable from an IIR filter design point of view. Simulations also indicate that stable seismic impulse responses and synthetics can be obtained with a reduced system model order and, hence, less computational efforts with respect to the number of complex multiplications and additions per output sample. It is hoped that this study will open new possibilities for researchers to reconsider designing IIR f−x explicit depth extrapolation filters due to their expected computational savings and wavenumber response accuracy, when compared to the FIR f−x explicit depth extrapolation filters.

Explicit filtering to obtain grid-spacing-independent and discretization-order-independent large-eddy simulation of compressible single-phase flow

AbstractIn large-eddy simulation (LES), it is often assumed that the filter width is equal to the grid spacing. Predictions from such LES are grid-spacing dependent since any subgrid-scale (SGS) model used in the LES equations is dependent on the resolved flow field which itself varies with grid spacing. Moreover, numerical errors affect the flow field, especially the smallest resolved scales. Thus, predictions using this approach are affected by both modelling and numerical choices. However, grid-spacing-independent LES predictions unaffected by numerical choices are necessary to validate LES models through comparison with a trusted template. First, such a template is created here through direct numerical simulation (DNS). Then, simulations are conducted using the conventional LES equations and also LES equations which are here reformulated so that the small-scale-producing nonlinear terms in these equations are explicitly filtered (EF) to remove scales smaller than a fixed filter width; this formulation is called EFLES. First, LES is conducted with four SGS models, then EFLES is performed with two of the SGS models used in LES; the results from all these simulations are compared to those from DNS and from the filtered DNS (FDNS). The conventional LES solution is both grid-spacing and spatial discretization-order dependent, thus showing that both of these numerical aspects affect the flow prediction. The solution from the EFLES equations is grid independent for a high-order spatial discretization on all meshes tested. However, low-order discretizations require a finer mesh to reach grid independence. With an eighth-order discretization, a filter-width to grid-spacing ratio of two is sufficient to reach grid independence, while a filter-width to grid-spacing ratio of four is needed to reach grid independence when a fourth- or a sixth-order discretization is employed. On a grid fine enough to be utilized in a DNS, the EFLES solution exhibits grid independence and does not converge to the DNS solution. The velocity-fluctuation spectra of EFLES follow those of FDNS independent of the grid spacing used, in concert with the original concept of LES. The reasons for the different predictions of conventional LES or EFLES according to the SGS model used, and the different characteristics of the EFLES predictions compared to those from conventional LES are analysed.

Investigation of the explicit cutoff filtering in Large Eddy Simulation

Implicit filtering is a common procedure in Large Eddy Simulation (LES). Problems with implicit filtering have led to the development of an alternate method called explicit filtering. Most explicit filtering methods are expensive, but filtering the entire flow field is one of the least expensive methods. Closeness of the filter shape to the sharp cut-off is a significant parameter in this kind of filtering. The aim of this paper is to study the effects of the closeness of filter shape to the sharp cut-off on flow statistics and to compare the Pade-type filter with different discrete filters that have shapes close to the sharp cut-off. Turbulent channel flow was chosen for the simulations. The finite-volume method was used along with the PISO algorithm. Moreover, the second-order central difference scheme was applied for spatial derivations and the Crank-Nicolson method for time integration. The problem was solved by three different types of discrete filters, all of which had shapes close to the cut-off filter. The results suggest that the use of explicit filtering by sharp cut-off filters improves the specific statistics of the wall-bounded turbulent channel flow. Pade-type filters produced the most desirable results.

A high-order finite-difference algorithm for direct computation of aerodynamic sound

A high-order finite-difference algorithm is proposed in the aim of performing LES calculations for CAA applications. The subgrid scale dissipation is performed by the explicit high-order numerical filter used for numerical stability purpose. A shock-capturing non-linear filter is also used to deal with compressible discontinuous flows. In order to tackle complex geometries, an overset-grid approach is used. High-order interpolations make possible the communication between overlapping domains. The whole algorithm is first validated on canonical flow problems to illustrate both its properties for shock-capturing as well as for accurate wave propagation. Then, the influence of the multi-domain approach on the high-order spatial accuracy is assessed. Finally, a rod-airfoil configuration is studied to highlight the potential of the proposed algorithm to deal with multi-scale aeroacoustic applications.

Large-Eddy Simulation of the Stable Boundary Layer with Explicit Filtering and Reconstruction Turbulence Modeling

AbstractLarge-eddy simulation (LES) of the stably stratified atmospheric boundary layer is performed using an explicit filtering and reconstruction approach with a finite difference method. Turbulent stresses are split into the resolvable subfilter-scale and subgrid-scale stresses. The former are recovered from a reconstruction approach, and the latter are represented by a dynamic eddy-viscosity model. The resulting dynamic reconstruction model (DRM) can sustain resolved turbulence with less stringent resolution requirements than conventional closure models, even under strong atmospheric stability. This is achieved by proper representation of subfilter-scale (SFS) backscatter of turbulent kinetic energy (TKE). The flow structure and turbulence statistics for the moderately stable boundary layer (SBL) are analyzed with high-resolution simulations. The DRM simulations show good agreement with established empirical formulations such as flux and gradient-based surface similarity, even at relatively coarse resolution. Similar results can be obtained with traditional closure models at the cost of higher resolution. SBL turbulence under strong stability is also explored. Simulations show an intermittent presence of elevated TKE below the low-level jet. Overall, the explicit filtering and reconstruction approach is advantageous for simulations of the SBL. At coarse resolution, it can extend the working range of LES to stronger stability, while maintaining agreement to similarity theory; at fine resolution, good agreement with theoretical formulations provides confidence in the results and allows for detailed investigation of the flow structure under moderate to strong stability conditions.

Large Eddy Simulation of Supersonic Jet Noise from a Circular Nozzle

An imperfectly expanded supersonic jet is simulated with large eddy simulation (LES) method. The full 3D filtered Navier-Stokes equations in cylindrical coordinates coupled with the standard Smagorinsky model are solved by a computational aeroacoustic method. The Dispersion-Relation-Preserving scheme is used for spatial discretization and the low dissipation low dispersion Runge-Kutta method in 2N storage form is utilized for time marching. A high order explicit spatial filter is applied to remove the grid oscillations. An adaptive artificial selective damping is used for shock capturing. The supersonic jet with Mach number 1.19 is simulated. The simultaneous and time average flow field is analyzed. The near filed noise spectra are presented and compared with the experimental data of Ponton et al. and with the numerical results of the present authors by unsteady Reynolds averaged Navier-Stokes (URANS) method. It is shown that the numerical results by LES method agree better with the experimental data than the results by URANS method.

Turbulence Modeling for the Stable Atmospheric Boundary Layer and Implications for Wind Energy

The near-surface structure of atmospheric turbulence affects the design and operation of wind turbines and is especially difficult to predict under stably-stratified conditions. This study uses large-eddy simulation (LES) to explore properties of the stable boundary layer (SBL) using an explicit filtering and reconstruction turbulence modeling approach. Simulations of the atmospheric boundary layer over flat terrain, under both moderately and strongly stable conditions are performed. Results from high-resolution simulations are used to investigate SBL flow structures including mean profiles and turbulence statistics, which are relevant to wind energy applications. The applicability of power-law relations and empirical similarity formulations for predicting wind speed depend on the strength of stratification and are shown to be inadequate. Low-level jets form in the simulations. Under strong stability, vertical wind shear below the jet triggers intermittent turbulence. The associated sporadic “bursting” events are extremely energetic and last longer than the time scale of the largest eddies. Such phenomena can have adverse effects on turbine lifetime and performance.

Comparison between explicit filterings with smooth and cutoff filters in the large eddy simulation of turbulent channel flows

The Large Eddy Simulation (LES) equations are obtained by applying a low-pass filter to the Navier–Stokes equations. The turbulence modeling in the LES method is affected by the shape of the applied filter. In this paper, two explicit filtering methods are compared during the simulation of fully developed turbulent channel flows. First, a fully developed turbulent channel flow is simulated by explicit filtering, using a smooth Laplace filter. In this case, the subfilter stress term is added to the subgrid model. Good agreement is observed between the calculated results and the available direct numerical simulation results. Second, to evaluate the effects of the explicit filter shape as it relates to the cutoff filter, three kinds of filters are used for the flow simulation. Finally, the ability of each approach to predict turbulence statistics is investigated. Moreover, the boundary layer regions that have the highest effect on each approach are specified.

Globally conservative high-order filters for large-eddy simulation and computational aero-acoustics

In computational aero-acoustics, large-eddy simulations (LES) or direct numerical simulations (DNS) are often employed for flow computations in the source region. As part of the numerical implementation or required modeling, explicit spatial filters are frequently employed. For instance, in LES spatial filters are employed in the formulation of various subgrid-scale (SGS) models such as the dynamic model or the variational multi-scale (VMS) Smagorinsky model; both in LES or DNS, spatial high-pass filters are often used to remove undesired grid-to-grid oscillations. Though these type of spatial filters adhere to local accuracy requirements, in practice, they often destroy global conservation properties in the presence of non-periodic boundaries conditions. This leads to the incorrect prediction of the flow properties near hard boundaries, such as walls. In the current work, we present globally conservative high-order accurate filters, which combine traditional filters at the internal points with one-sided conservative filters near the wall boundary. We test these filters to remove grid-to-grid oscillations both in a channel-flow case and in 2D cavity flow. We find that the use of a non-conservative filter leads to erroneous predictions of the skin friction in channel flows up to 30%. In the cavity-flow simulations, the use of non-conservative filters to remove grid-to-grid oscillations leads to important shifts in the Strouhal number of the dominant mode, and a change of the flow pattern inside the cavity. In all cases, the use of conservative high-order filter formulations to remove grid-to-grid oscillations lead to very satisfactory results. Finally, in our channel-flow test case, we also illustrate the importance of using conservative filters for the formulation of the VMS Smagorinsky model.

Two stable methods with numerical experiments for solving the backward heat equation

This paper presents results of some numerical experiments on the backward heat equation. Two quasi-reversibility techniques, explicit filtering and structural perturbation, to regularize the ill-posed backward heat equation have been used. In each of these techniques, two numerical methods, namely Euler and Crank–Nicolson (CN), have been used to advance the solution in time. Crank–Nicolson method is very counter-intuitive for solving the backward heat equation because the dispersion relation of the scheme for the backward heat equation has a singularity (unbounded growth) for a particular wave whose finite wave number depends on the numerical parameters. In comparison, the Euler method shows only catastrophic growth of relatively much shorter waves. Strikingly we find that use of smart filtering techniques with the CN method can give as good a result, if not better, as with the Euler method which is discussed in the main text. Performance of these regularization methods using these numerical schemes have been exemplified.

Grid-independent large-eddy simulation using explicit filtering

The governing equations for large-eddy simulation are derived from the application of a low-pass filter to the Navier–Stokes equations. It is often assumed that discrete operations performed on a particular grid act as an implicit filter, causing results to be sensitive to the mesh resolution. Alternatively, explicit filtering separates the filtering operation, and hence the resolved turbulence, from the underlying mesh distribution alleviating some of the grid sensitivities. We investigate the use of explicit filtering in large-eddy simulation in order to obtain numerical solutions that are grid independent. The convergence of simulations using a fixed filter width with varying mesh resolutions to a true large-eddy simulation solution is analyzed for a turbulent channel flow at Reτ=180, 395, and 640. By using explicit filtering, turbulent statistics and energy spectra are shown to be independent of the mesh resolution used.

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.