Spurious Waves Research Articles

Voronoi‐based peridynamics and cracking analysis with adaptive refinement

SummaryThe most common technique for the numerical implementation of peridynamic theory is the uniform discretization together with constant horizon. However, unlike the nonuniform discretization and varying horizons, it is not a natural and intrinsic component of the adaptive refinement analysis and multiscale modeling. Besides, it encounters discretization difficulty in analyzing irregular structures. Therefore, to analyze problems with nonuniform discretization and varying horizons and solve the resulting problems of ghost forces and spurious wave reflection, the dual‐horizon peridynamics based on uniform discretization is extended to the nonuniform discretization based on Voronoi diagrams, for which we call it Voronoi‐based peridynamics. We redefine the damage definition as well. Next, an adaptive refinement analysis method based on the proposed Voronoi‐based peridynamics and its numerical implementation is introduced. Finally, the traditional bond‐based peridynamics and the Voronoi‐based peridynamics with or without refinement are used to simulate 4 benchmark problems. The examples of 2‐D quasi‐static elastic deformation, 2‐D wave propagation, 2‐D dynamic crack growth, and 3‐D simulation of the Kalthoff‐Winkler experiment demonstrate the efficiency and effectivity of the proposed Voronoi‐based peridynamics. Further, the adaptive refinement analysis can be used to obtain reasonable crack path and crack propagation speed with reduced computational burden.

A balanced Kalman filter ocean data assimilation system with application to the South Australian Sea

In this paper, an Ensemble Kalman Filter (EnKF) based regional ocean data assimilation system has been developed and applied to the South Australian Sea. This system consists of the data assimilation algorithm provided by the NCAR Data Assimilation Research Testbed (DART) and the Regional Ocean Modelling System (ROMS). We describe the first implementation of the physical balance operator (temperature-salinity, hydrostatic and geostrophic balance) to DART, to reduce the spurious waves which may be introduced during the data assimilation process. The effect of the balance operator is validated in both an idealised shallow water model and the ROMS model real case study. In the shallow water model, the geostrophic balance operator eliminates spurious ageostrophic waves and produces a better sea surface height (SSH) and velocity analysis and forecast. Its impact increases as the sea surface height and wind stress increase. In the real case, satellite-observed sea surface temperature (SST) and SSH are assimilated in the South Australian Sea with 50 ensembles using the Ensemble Adjustment Kalman Filter (EAKF). Assimilating SSH and SST enhances the estimation of SSH and SST in the entire domain, respectively. Assimilation with the balance operator produces a more realistic simulation of surface currents and subsurface temperature profile. The best improvement is obtained when only SSH is assimilated with the balance operator. A case study with a storm suggests that the benefit of the balance operator is of particular importance under high wind stress conditions. Implementing the balance operator could be a general benefit to ocean data assimilation systems.

Application of Physical Filter Initialization in 4DVar

Abstract Generally, the results of data assimilation are not well balanced dynamically due to errors in background, observations, or the model itself. So, initialization methods have been introduced to remove spurious gravity waves from the analysis. One of the initialization methods is digital filter initialization (DFI), which has been used in operational forecast systems, though its physical meaning is not well understood. Other methods eliminate high-frequency noise in optimized initial conditions by introducing physical constraints, such as the model constraint scheme, which minimizes the time tendency of model variables. In this study, a physical filter initialization (PFI) scheme, based on the model constraint scheme, is implemented in the four-dimensional variational data assimilation (4DVar) system of the Weather Research and Forecasting (WRF) Model. The impacts of the PFI scheme are examined by both single-observation and real-data experiments. The results indicate that the PFI scheme can eliminate high-frequency noise effectively, obtain flow-dependent analysis increments, and shorten forecast spinup time. Consequently, the precipitation forecast is improved to a certain extent, especially during the first few hours thanks to the shorter spinup time.

A sound extrapolation method for aeroacoustics far-field prediction in presence of vortical waves

Off-surface integral solutions to an inhomogeneous wave equation based on acoustic analogy could suffer from spurious wave contamination when volume integrals are ignored for computation efficiency and vortical/turbulent gusts are convected across the integration surfaces, leading to erroneous far-field directivity predictions. Vortical gusts often exist in aerodynamic flows and it is inevitable their effects are present on the integration surface. In this work, we propose a new sound extrapolation method for acoustic far-field directivity prediction in the presence of vortical gusts, which overcomes the deficiencies in the existing methods. The Euler equations are rearranged to an alternative form in terms of fluctuation variables that contains the possible acoustical and vortical waves. Then the equations are manipulated to an inhomogeneous wave equation with source terms corresponding to surface and volume integrals. With the new formulation, spurious monopole and dipole noise produced by vortical gusts can be suppressed on account of the solenoidal property of the vortical waves and a simple convection process. It is therefore valid to ignore the volume integrals and preserve the sound properties. The resulting new acoustic inhomogeneous convected wave equations could be solved by means of the Green’s function method. Validation and verification cases are investigated, and the proposed method shows a capacity of accurate sound prediction for these cases. The new method is also applied to the challenging airfoil leading edge noise problems by injecting vortical waves into the computational domain and performing aeroacoustic studies at both subsonic and transonic speeds. In the case of a transonic airfoil leading edge noise problem, shocks are present on the airfoil surface. Good agreements of the directivity patterns are obtained compared with direct computation results.

An Approach to Obtain the Correct Shock Speed for Euler Equations with Stiff Detonation

AbstractIncorrect propagation speed of discontinuities may occur by straightforward application of standard dissipative schemes for problems that contain stiff source terms for underresolved grids even for time steps within the CFL condition. By examining the dissipative discretized counterpart of the Euler equations for a detonation problem that consists of a single reaction, detailed analysis on the spurious wave pattern is presented employing the fractional step method, which utilizes the Strang splitting. With the help of physical arguments, a threshold values method (TVM), which can be extended to more complicated stiff problems, is developed to eliminate the wrong shock speed phenomena. Several single reaction detonations as well as multispecies and multi-reaction detonation test cases with strong stiffness are examined to illustrate the performance of the TVM approach.

A damping boundary condition for atomistic-continuum coupling

The minimization of spurious wave reflection is a challenge in multiscale coupling due to the difference of spatial resolution between atomistic and continuum regions. In this study, a new damping condition is presented for eliminating spurious wave reflection at the interface between atomistic and continuum regions. This damping method starts by a coarse–fine decomposition of the atomic velocity based on the bridging scale method. The fine scale velocity of the atoms in the damping region is reduced by applying nonlinear damping coefficients. The effectiveness of this damping method is verified by one- and two- dimensional simulations.

Dual-horizon peridynamics: A stable solution to varying horizons

In this paper, we present a dual-horizon peridynamics formulation which allows for simulations with dual-horizon with minimal spurious wave reflection. We prove the general dual property for dual-horizon peridynamics, based on which the balance of momentum and angular momentum in PD are naturally satisfied. We also analyze the crack pattern of random point distribution and the multiple materials issue in peridynamics. For selected benchmark problems, we show that DH-PD is less sensitive to the spatial than the original PD formulation.

Relativistic Second-Harmonic Gyrotron With a Selective Quasi-Regular Cavity

A typical problem of gyrotrons operating at the second harmonic of the electron cyclotron frequency is the suppression of parasitic near-cutoff waves excited at the fundamental harmonic. In this paper, we discuss the possibility for the selective excitation of two different second-harmonic waves in a relativistic millimeter-wavelength gyrotron by means of the use of a method for a significant improvement of the selectivity of this system. This method is based on the use of a quasi-regular cavity with a short irregularity providing different effects on the interaction of the electron beam with the operating second-harmonic wave and the spurious fundamental-harmonic wave.

Improvement of Circularly Polarized Slot-Patch Antenna Parameters by Using Electromagnetic Band Gap Structures

This paper is devoted to the design of a novel Electromagnetic Band Gap (EBG) circularly polarized slot-patch antenna in multilayered configuration. The operating frequency band can be controlled via the disk radius and adjusting the slit lengths. An arrangement combining the circular slot-patch antenna design and feeding sources included are considered is necessary. Due to the exisiting of two feeding points, Position of both feeding points will permit Right-hand and Left-hand circular polarization operations. Thickness of substrate is chosen to reduce the spurious surface wave and width. The same technique will be used for the EBG cirlcularly polarized circular slot-patch antenna network and carry two benefits (such as improvement of bandwidth, beamforming, creating zero radiation beams) and filtering characteristics of the resonator (spatial filtering, increased directivity, misalignment) due to the resonant structure itself. The analysis provided will confirm successfully the various proposed structures and interest occupied by these types of antenna. Two approaches, one introduced by one layered Circularly-Polarized Patch-Slot antenna design with some changes in material configuration and the other produced by multilayered structures with different dielectric constants in the EBG resonator, are simultaneously used as key controllers of directivity enhancement.

Artificial viscosity model to mitigate numerical artefacts at fluid interfaces with surface tension

Abstract The numerical onset of parasitic and spurious artefacts in the vicinity of fluid interfaces with surface tension is an important and well-recognised problem with respect to the accuracy and numerical stability of interfacial flow simulations. Issues of particular interest are spurious capillary waves, which are spatially underresolved by the computational mesh yet impose very restrictive time-step requirements, as well as parasitic currents, typically the result of a numerically unbalanced curvature evaluation. We present an artificial viscosity model to mitigate numerical artefacts at surface-tension-dominated interfaces without adversely affecting the accuracy of the physical solution. The proposed methodology computes an additional interfacial shear stress term, including an interface viscosity, based on the local flow data and fluid properties that reduces the impact of numerical artefacts and dissipates underresolved small scale interface movements. Furthermore, the presented methodology can be readily applied to model surface shear viscosity, for instance to simulate the dissipative effect of surface-active substances adsorbed at the interface. The presented analysis of numerical test cases demonstrates the efficacy of the proposed methodology in diminishing the adverse impact of parasitic and spurious interfacial artefacts on the convergence and stability of the numerical solution algorithm as well as on the overall accuracy of the simulation results.

Reducing ocean model imbalances in the equatorial region caused by data assimilation

The equatorial region is a particularly challenging area for ocean data assimilation. In this region the dominant balance near the surface is between the ocean pressure gradients and the applied wind stress. When increments are applied to an ocean model near the Equator, the pressure gradients are modified and this can cause an imbalance with the unchanged wind stress. This can lead to an initialization shock where spurious equatorial waves and vertical velocities are triggered. The equatorial waves can degrade the performance of the ocean model while the increased vertical velocities have a significant negative impact on biogeochemical models forced by these physical ocean fields. Previous studies have proposed a scheme to reduce the ocean biases associated with slowly varying errors in the applied wind stress by applying a pressure correction calculated from accumulated temperature and salinity increments. This scheme has previously been shown to reduce the mean vertical velocities and improve modelled circulation. However, when applying this scheme, we still see equatorial imbalances from data assimilation on shorter time‐scales.We consider a new method which is an extension of the pressure correction and aims to act as a balance to the equatorial increments and reduce intialization shock. We refer to this as an incremental pressure correction. We provide a description of this method and an analysis of its energetics. In initial experiments with a global ocean data assimilation system, this new method is shown to suppress the generation of equatorial waves in a single observation experiment and to significantly reduce the standard deviation of vertical velocities in a re‐analysis experiment.

Wave filtering through a selective perfectly matched layer in multiscale couplings with dynamically incompatible models

SummaryIn this paper, we develop a strategy that enables a consistent wave transfer when coupling mechanical models exhibiting various description scales under dynamic loading. Incompatibilities between concurrent models are addressed by a selective filtering based on the perfectly matched layer framework and involving a dedicated projection operator. This filtering, performed in the vicinity of the coupling interface, aims at avoiding spurious wave reflections by automatically killing part of the signal with wavelength range not compatible with the downstream (coarser scale) model while the relevant complementary part is transferred. Performances of the proposed approach are evaluated in details by conducting one‐dimensional and two‐dimensional numerical experiments. The definition of the projection operator, which is a key point of the method, is particularly tackled by analyzing and comparing several possible choices. Copyright © 2016 John Wiley & Sons, Ltd.

An efficient shock-capturing scheme for simulating compressible homogeneous mixture flow

This work is devoted to the development of a procedure for the numerical solution of Navier-Stokes equations for cavitating flows with and without ventilation based on a compressible, multiphase, homogeneous mixture model. The governing equations are discretized on a general structured grid using a high-resolution shock-capturing scheme in conjunction with appropriate limiters to prevent the generation of spurious solutions near shock waves or discontinuities. Two well-known limiters are examined, and a new limiter is proposed to enhance the accuracy and stability of the numerical scheme. A sensitivity analysis is first conducted to determine the relative influences of various model parameters on the solution. These parameters are adopted for the computation of water flows over a hemispherical body, conical body and a divergent/convergent nozzle. Finally, numerical calculations of ventilated supercavitating flows over a hemispherical cylinder body with a hot propulsive jet are conducted to verify the capabilities of the numerical scheme.

GHz spurious mode free AlN lamb wave resonator with high figure of merit using one dimensional phononic crystal tethers

This letter reports a spurious mode free GHz aluminum nitride (AlN) lamb wave resonator (LWR) towards high figure of merit (FOM). One dimensional gourd-shape phononic crystal (PnC) tether with large phononic bandgaps is employed to reduce the acoustic energy dissipation into the substrate. The periodic PnC tethers are based on a 1 μm-thick AlN layer with 0.26 μm-thick Mo layer on top. A clean spectrum over a wide frequency range is obtained from the measurement, which indicates a wide-band suppression of spurious modes. Experimental results demonstrate that the fabricated AlN LWR has an insertion loss of 5.2 dB and a loaded quality factor (Q) of 1893 at 1.02 GHz measured in air. An impressive ratio of the resistance at parallel resonance (Rp) to the resistance at series resonance (Rs) of 49.8 dB is obtained, which is an indication of high FOM for LWR. The high Rp to Rs ratio is one of the most important parameters to design a radio frequency filter with steep roll-off.

Space-time characteristics of wall-pressure and wall shear-stress fluctuations in wall-modeled large eddy simulation.

We report the space-time characteristics of the wall-pressure fluctuations and wall shear-stress fluctuations from wall-modeled large eddy simulation (WMLES) of a turbulent channel flow at Re τ = 2000. Two standard zonal wall models (equilibrium stress model and nonequilibrium model based on unsteady RANS) are employed, and it is shown that they yield similar results in predicting these quantities. The wall-pressure and wall shear-stress fields from WMLES are analyzed in terms of their r.m.s. fluctuations, spectra, two-point correlations, and convection velocities. It is demonstrated that the resolution requirement for predicting the wall-pressure fluctuations is more stringent than that for predicting the velocity. At least δ/Δx > 20 and δ/Δz > 30 are required to marginally resolve the integral length scales of the pressure-producing eddies near the wall. Otherwise, the pressure field is potentially aliased. Spurious high wave number modes dominate in the streamwise direction, and they contaminate the pressure spectra leading to significant overprediction of the second-order pressure statistics. When these conditions are met, the pressure statistics and spectra at low wave number or low frequency agree well with the DNS and experimental data. On the contrary, the wall shear-stress fluctuations, modeled entirely through the RANS-based wall models, are largely underpredicted and relatively insensitive to the grid resolution. The short-time, small-scale near-wall eddies, which are neither resolved nor modeled adequately in the wall models, seem to be important for accurate prediction of the wall shear-stress fluctuations.

Multiscale coupling of molecular dynamics and peridynamics

We propose a multiscale computational model to couple molecular dynamics and peridynamics. The multiscale coupling model is based on a previously developed multiscale micromorphic molecular dynamics (MMMD) theory, which has three dynamics equations at three different scales, namely, microscale, mesoscale, and macroscale. In the proposed multiscale coupling approach, we divide the simulation domain into atomistic region and macroscale region. Molecular dynamics is used to simulate atom motions in atomistic region, and peridynamics is used to simulate macroscale material point motions in macroscale region, and both methods are nonlocal particle methods. A transition zone is introduced as a messenger to pass the information between the two regions or scales. We employ the “supercell” developed in the MMMD theory as the transition element, which is named as the adaptive multiscale element due to its ability of passing information from different scales, because the adaptive multiscale element can realize both top-down and bottom-up communications. We introduce the Cauchy–Born rule based stress evaluation into state-based peridynamics formulation to formulate atomistic-enriched constitutive relations. To mitigate the issue of wave reflection on the interface, a filter is constructed by switching on and off the MMMD dynamic equations at different scales. Benchmark tests of one-dimensional (1-D) and two-dimensional (2-D) wave propagations from atomistic region to macro region are presented. The mechanical wave can transit through the interface smoothly without spurious wave deflections, and the filtering process is proven to be efficient.

A method for suppression of spurious fundamental-harmonic waves in gyrotrons operating at the second cyclotron harmonic

A typical problem of gyrotrons operating at high harmonics of the electron cyclotron frequency is the suppression of parasitic near-cutoff waves excited at lower harmonics. In this paper, a method for a significant improvement of the selectivity of the second-harmonic gyrotrons is proposed. This method is based on the use of quasi-regular cavities with short irregularities, which provide different effects on the process of excitation of the operating second-harmonic wave and the spurious fundamental-harmonic wave by the electron beam.

Three-dimensional detonation simulations with the mapped WENO-Z finite difference scheme

Abstract We perform a very long time numerical simulation to capture the three-dimensional detonation structures in a rectangular duct by solving the reactive Euler equations using the high order/resolution WENO-Z conservative finite difference scheme (Gao et al. J. Sci. Comput. 55 : 351–371, 2013). In the algorithm, the perfectly matched layer (PML) absorbing boundary condition (ABC) for the reactive Euler equations is used to reduce the spurious wave reflection from the open left boundary which allows one to use a significant smaller truncated physical domain. Moreover, a tangent grid mapping is used to enhance the grid resolution within the half reaction zone that greatly reduces the memory usage and computational time compared with solving the problem with a uniform grid. The initial Zeldovich-von Neumann-Doring (ZND) profile of two classical stable and slightly unstable detonation waves is perturbed to generate the rectangular in-phase, diagonal in-phase and spinning detonation structures. Depending on the initial perturbation, the stable case shows the presence of a rectangular mode and a diagonal mode of the detonation front, which are suggested to be geometrically similar. The slightly unstable case, as expected, generates the spinning detonations instead in a narrow duct. The results show that a short time simulation is insufficient to capture the cellular detonation structures. The width-to-length ratio of the cellular patterns depends on the gas properties only, but independent of the perturbation of the initial conditions.

The emergence of spurious arrivals in Green’s function extraction and passive imaging

Cross-correlations of ambient noise at two receivers can extract the two-point Green’s function, given that the wave-field is spatially uniform. The presence of scatterers that act as uncorrelated secondary sources can destroy this condition. We retrieve the Green’s function in one-sided noise with a scatterer in an aeroacoustic experiment, using a pair of microphones (separation 1 m) parallel to the beach which generate one-sided surf noise. The scatterer is a 20-cm-radius polyvinyl chloride pipe 2.5 m to the landside of the microphone pair. We cross correlate 400–2000 Hz noise to retrieve the Green’s function. The results show that spurious scattered arrival emerges in the cross-correlation functions when the source distribution is limited. This causes the generalized optical theorem to break down, and thus, there is no guarantee that the spurious scattered arrival cancels. However, the spurious waves have a geometric interpretation, which are useful for inversion. By combining the travel times of the spurious and physical scattered waves, only a pair of receivers is sufficient to locate the scatterer passively.

Reducing numerical dispersion and reflections in finite element and finite difference simulation of acoustic wave propagation and scattering

Discretization methods such as the finite element method (FEM) and the finite difference method (FDM) suffer from two types of accuracy problems: spurious wave dispersion for long-range propagation and artificial reflections from discretization of perfectly matched layers that are often used to represent the unbounded exterior. In this talk, we focus on lower-order FEM and compact FDM stencils, and show that these errors can be significantly reduced using simple measures: using modified integration rules for FEM, and modified compact stencils for FDM. It turns out that these needed corrections for reducing dispersion and reflections are in opposite directions, indicating that reducing one error results in increasing the other, which is not desirable. In this talk, we introduce a special technique that leads to reduction of both dispersion and reflection errors, and illustrate its effectiveness through theoretical analysis and numerical experiments.