Nonlinear Wave Propagation Model Research Articles

2DH numerical model of nonlinear wave propagation based on a hybrid finite-volume and finite-difference scheme

A two-dimensional hybrid (2DH) numerical model suitable for nonlinear wave propagation from deep to shallow waters is developed based on a hybrid finite-volume and finite-difference scheme. To utilize this method conveniently, the selected governing equations are derived again in a conservative form. The fourth-order monotonic upstream-centered scheme for conservation laws–total variation diminishing scheme with a Riemann solver is employed to calculate the numerical flux. The finite-difference scheme is employed to discretize the other spatial derivatives, and the third-order strong stability-preserving (SSP) Runge–Kutta scheme is used for time-stepping. Wave breaking is simulated by locally switching the governing equations to nonlinear shallow-water equations when the Froude number exceeds a certain threshold. A comparison of the numerical results and analytical or experimental data showed that the numerical model performs well in simulating nearshore wave propagation.

Modeling of a lattice model for nonlinear wave propagation in phononic crystals

We construct a nonlinear lattice model to investigate the dynamics of nonlinear behavior in phononic crystals (PnCs). Two types of mass points and springs are introduced in the model to reproduce the difference in material properties between the scatterers and background in PnCs. The nonlinearity is introduced to the model by changing the mass of each mass point depending on the displacement gradient at the mass point. We numerically confirm that both the 1D and 2D models have the bandgap in the linear dispersion relation. Moreover, in both model, switching behavior of wave propagation is found.

Strong near band-edge excited second-harmonic generation from multilayer 2H Tin diselenide

We report strong second-harmonic generation (SHG) from 2H polytype of multilayer Tin diselenide (SnSe2) for fundamental excitation close to the indirect band-edge in the absence of excitonic resonances. Comparison of SHG and Raman spectra from exfoliated SnSe2 flakes of different polytypes shows strong (negligible) SHG and Raman Eg mode at 109 cm−1 (119 cm−1), consistent with 2H (1T) polytypes. The difference between the A1g–Eg Raman peak positions is found to exhibit significant thickness dependent for the 1T form, which is found to be absent for the 2H form. The observed thickness dependence of SHG with rapid oscillations in signal strength for small changes in flake thickness are in good agreement with a nonlinear wave propagation model considering nonlinear polarization with alternating sign from each monolayer. The nonlinear optical susceptibility extracted from SHG signal comparison with standard quartz samples for 1040 nm excitation is found to be more than 4-times higher than that at 1550 nm. This enhanced nonlinear response at 1040 nm is attributed to the enhanced nonlinear optical response for fundamental excitation close to the indirect band-edge. We also study SHG from heterostructures of monolayer MoS2/multilayer SnSe2 which allows us to unambiguously compare the nonlinear optical response of SnSe2 with MoS2. We find the SHG signal and any interference effect in the overlap region to be dominated by the SnSe2 layer for the excitation wavelengths considered. The comparison of SHG from SnSe2 and MoS2 underscores that the choice of the 2D material for a particular nonlinear optical application is contextual on the wavelength range of interest and its optical properties at those wavelengths. The present works further highlights the usefulness of near band-edge enhancement of nonlinear processes in emerging 2D materials towards realizing useful nanophotonic devices.

Nonlinear model predictive control of ultra-high-purity air separation units using transient wave propagation model

Model reduction techniques can be used to reduce the computational burden associated with nonlinear model predictive control (NMPC). In our recent work, we introduced the transient nonlinear wave propagation model (TWPM) for reduced dynamic modeling of multi-component distillation columns with variable holdup, and demonstrated its suitability for optimization and control of single-section distillation columns and simple air separation units [Caspari et al., J. Process Control, 2020]. We show here that the TWPM is well-suited for reduced modeling of multi-sectional ultra-high-purity distillation columns and enables real-time capable NMPC of complex process flowsheets with tight operational constraints. To demonstrate its performance and accuracy, we apply the TWPM for NMPC of an ultra-high-purity nitrogen air separation unit. We perform an in-silico closed-loop case study comprising a series of load changes. Our approach reduces CPU time by 84%, enabling NMPC in real time.

High-Intensity Focused Ultrasound Ablation by the Dual-Frequency Excitation.

High-intensity focused ultrasound (HIFU) has emerged as an effective and noninvasive therapeutic modality for cancer and solid tumor. Despite its promising clinical outcomes and the approval of the Food and Drug Administration of many countries, the ablation time of a large target is long, so enhancement of the lesion production is highly desired. In this study, dual-frequency (or amplitude modulation) excitation was evaluated both numerically and experimentally, and its performance was compared with that using single-frequency excitation at the same power output. The nonlinear wave propagation model was used to simulate the acoustic field of HIFU exposure, the Gilmore model was used to determine the induced bubble dynamics, and then absorbed acoustic energy and bubble-enhanced heating were put into the BioHeat equation to calculate the temperature elevation. HIFU-produced lesion in the bovine serum albumin-embedded polyacrylamide was recorded photographically. It is found that dual-frequency excitation (3.16 + 3.20MHz) can increase the lesion area by 35%-65% compared to single-frequency excitation (3.18 MHz) at the same power output. The lesion enhancement increases with the pulse repetition frequency, duty cycle, and modulation depth and decreases with the frequency difference. In summary, dual-frequency excitation can increase the bubble cavitation and the associated heating for HIFU ablation for large lesion production.

Coupling methodology for smoothed particle hydrodynamics modelling of non-linear wave-structure interactions

A two-way coupling methodology for wave propagation and wave-structure interaction with SPH is hereby presented. The methodology consists of combining a fast, fully non-linear wave propagation model, OceanWave3D, with an accurate Smoothed Particle Hydrodynamics (SPH) solver, DualSPHysics. At the coupling interface in the SPH zone, moving dynamic boundary particles are applied, which move according to the horizontal velocity calculated in the wave propagation model. The surface elevation is registered in the SPH zone and transferred back to the wave propagation model. Using this coupling methodology, a large domain can be simulated with the wave propagation model, with small, discrete SPH zones embedded to locally obtain higher accuracies. The communication between the solvers is implemented using OpenMPI. Three connected processes are run: OceanWave3D, DualSPHysics and Python. The latter is used to monitor the data transfer and manipulate the data in an efficient manner. The coupling methodology is validated by simulating wave propagation of linear and non-linear waves, and comparing the surface elevations and orbital velocities to a theoretical solution. Comparison with two experimental datasets is performed as well. The coupling methodology proofs that it is able to accurately propagate waves and shows a good agreement with theoretical and experimental results.

An algorithm for continuum modeling of rocks with multiple embedded nonlinearly-compliant joints

We present a numerical method for modeling the mechanical effects of nonlinearly-compliant joints in elasto-plastic media. The method uses a series of strain-rate and stress update algorithms to determine joint closure, slip, and solid stress within computational cells containing multiple “embedded” joints. This work facilitates efficient modeling of nonlinear wave propagation in large spatial domains containing a large number of joints that affect bulk mechanical properties. We implement the method within the massively parallel Lagrangian code GEODYN-L and provide verification and examples. We highlight the ability of our algorithms to capture joint interactions and multiple weakness planes within individual computational cells, as well as its computational efficiency. We also discuss the motivation for developing the proposed technique: to simulate large-scale wave propagation during the Source Physics Experiments (SPE), a series of underground explosions conducted at the Nevada National Security Site (NNSS).

Applicable sloping range and bottom smoothing treatment for σ-based modeling of wave propagation over rapidly varying topography

Accurate modeling of nonlinear wave propagation over mildly or rapidly varying topography is an important topic in costal/ocean engineering. This study examines the applicable sloping ranges and proposes a bottom smoothing treatment for the σ-based modeling framework. An efficient non-hydrostatic σ model is chosen to be validated against a series of experiments with various slopes from 1:20 to 1:∞. The measured and simulated free surface time series are compared and analyzed using both one- and two-dimensional short-time Fourier transform. The reflection rate and high harmonic generation including a recurrence behavior are characterized and discussed. Overall, the excellent agreement reveals the applicability of the σ-based model along with an appropriate 1:0.5 virtual slope to the wave problems with vertical (or extremely steep) bottom topography.

Passive time-domain numerical models of viscothermal wave propagation in acoustic tubes of variable cross section.

Numerical modeling of wave propagation in acoustic tubes is a subject of longstanding interest, particularly for enclosures of varying cross section, and especially when viscothermal losses due to boundary layer effects are taken into consideration. Though steady-state, or frequency domain methods, are a common avenue of approach, recursive time domain methods are an alternative, allowing for the generation of wideband responses, and offer a point of departure for more general modeling of nonlinear wave propagation. The design of time-domain methods is complicated by numerical stability considerations, and to this end, a passive representation is a useful design principle leading to simple stable and explicit numerical schemes, particularly in the case of viscothermal loss modeling. Such schemes and the accompanying energy and stability analysis are presented here. Numerical examples are presented for a variety of duct profiles, illustrating strict energy dissipation, and for comparison of computed input impedances against frequency-domain results.

HEATING OF THE PARTIALLY IONIZED SOLAR CHROMOSPHERE BY WAVES IN MAGNETIC STRUCTURES

ABSTRACT In this paper, we show a “proof of concept” of the heating mechanism of the solar chromosphere due to wave dissipation caused by the effects of partial ionization. Numerical modeling of non-linear wave propagation in a magnetic flux tube, embedded in the solar atmosphere, is performed by solving a system of single-fluid quasi-MHD equations, which take into account the ambipolar term from the generalized Ohm’s law. It is shown that perturbations caused by magnetic waves can be effectively dissipated due to ambipolar diffusion. The energy input by this mechanism is continuous and shown to be more efficient than dissipation of static currents, ultimately leading to chromospheric temperature increase in magnetic structures.

Numerical simulation of the nonlinear ultrasonic pressure wave propagation in a cavitating bubbly liquid inside a sonochemical reactor

We investigate the acoustic wave propagation in bubbly liquid inside a pilot sonochemical reactor which aims to produce antibacterial medical textile fabrics by coating the textile with ZnO or CuO nanoparticles. Computational models on acoustic propagation are developed in order to aid the design procedures. The acoustic pressure wave propagation in the sonoreactor is simulated by solving the Helmholtz equation using a meshless numerical method. The paper implements both the state-of-the-art linear model and a nonlinear wave propagation model recently introduced by Louisnard (2012), and presents a novel iterative solution procedure for the nonlinear propagation model which can be implemented using any numerical method and/or programming tool. Comparative results regarding both the linear and the nonlinear wave propagation are shown. Effects of bubble size distribution and bubble volume fraction on the acoustic wave propagation are discussed in detail. The simulations demonstrate that the nonlinear model successfully captures the realistic spatial distribution of the cavitation zones and the associated acoustic pressure amplitudes.

Modeling of Nonlinear Wave Attenuation due to Vegetation

ABSTRACT Karambas, T.; Koftis, T., and Prinos, P., 2016. Modeling of nonlinear wave attenuation due to vegetation. In the present work, a nonlinear wave propagation model is developed and is applied for the simulation of the wave dissipation over vegetation. The free-surface flow over the vegetation is simulated using a Boussinesq model, while the flow within the canopy is simulated by solving simultaneously a canopy flow model. The parameters of the canopy flow model are related to the geometric characteristics of the vegetation, while the drag coefficient is taken from existing formulas found in literature and is related to the Reynolds number. The coupling between the Boussinesq and the canopy flow model is simulated by adding two extra terms, due to vegetation, in the continuity and momentum equations of the Boussinesq model. The numerical results are found to be in good agreement with several experimental measurements found in the relevant literature. The advantage of the proposed methodology is base...

Predictive modeling of nonlinear wave propagation for structural health monitoring with piezoelectric wafer active sensors

This article presents predictive modeling of nonlinear guided wave propagation for structural health monitoring using both finite element method and analytical approach. In our study, the nonlinearity of the guided waves is generated by interaction with a nonlinear breathing crack. Two nonlinear finite element method techniques are used to simulate the breathing crack: (a) element activation/deactivation method and (b) contact analysis. Both techniques are available in ANSYS software package. The solutions obtained by these two finite element method techniques compare quite well. A parametric analytical predictive model is built to simulate guided waves interacting with linear/nonlinear structural damage. This model is coded into MATLAB, and the WaveFormRevealer graphical user interface is developed to obtain fast predictive waveform solutions for arbitrary combinations of sensor, structural properties, and damage. The predictive model is found capable of describing the nonlinear wave propagation phenomenon. This article finishes with summary and conclusions followed by recommendations for further work.

Surfactant shedding and gas diffusion during pulsed ultrasound through a microbubble contrast agent suspension

Interest in coated microbubbles as agents for therapeutic and quantitative imaging applications in biomedical ultrasound has increased the need for their accurate theoretical characterization. Effects such as gas diffusion, variation in the properties of the coating and the resulting changes in bubble behavior under repeated exposure to ultrasound pulses are, however, still not well understood. In this study, a revised equation for microbubble motion is proposed that includes the effects of gas diffusion, as well as adsorption, desorption and shedding of a surfactant from the bubble surface. This is incorporated into a nonlinear wave propagation model to account for these additional time dependent effects in the response of microbubble populations. The results from the model indicate there can be significant changes in both bubble behavior and the propagated pulse over time. This is in agreement with existing experimental data but is not predicted by existing propagation models. The analysis indicates that changes in bubble dynamics are dominated by surfactant shedding on the timescale of a diagnostic ultrasound pulse and gas diffusion over the timescale of the pulse repetition frequency. The implications of these results for the development of more accurate algorithms for quantitative imaging and for therapeutic applications are discussed.

The effect of surfactant shedding and gas diffusion on pressure wave propagation through an ultrasound contrast agent suspension

Interest in microbubbles as agents for therapeutic and quantitative imaging applications in biomedical ultrasound has increased the need for their accurate modeling. However, effects such as gas diffusion, the properties of the shell, and changes in bubble behavior under repeated exposure to ultrasound pulses are still not well understood. A revised equation for microbubble motion is proposed that includes the effects of gas diffusion as well as a nonlinear surface tension, which depends on a non-constant surfactant surface concentration. This is incorporated into a nonlinear wave propagation model to account for these additional time-dependent effects in the response of microbubble contrast agent populations. The results from the model indicate significant changes in both bubble behavior and the propagated pulse compared with those predicted by existing propagation models; and show better agreement with experimental data. Our analysis indicates that changes in bubble dynamics are dominated both by surfactant shedding on ultrasonic timescales and gas diffusion over longer timescales between pulses. Therefore, incorporating such time-dependent phenomena in ultrasound imaging algorithms should lead to better quantitative agreement with experiments.

Performance Assessment of HIFU Lesion Detection by Harmonic Motion Imaging for Focused Ultrasound (HMIFU): A 3-D Finite-Element-Based Framework with Experimental Validation

Harmonic motion imaging for focused ultrasound (HMIFU) is a novel high-intensity focused ultrasound (HIFU) therapy monitoring method with feasibilities demonstrated in vitro, ex vivo and in vivo. Its principle is based on amplitude-modulated (AM) - harmonic motion imaging (HMI), an oscillatory radiation force used for imaging the tissue mechanical response during thermal ablation. In this study, a theoretical framework of HMIFU is presented, comprising a customized nonlinear wave propagation model, a finite-element (FE) analysis module and an image-formation model. The objective of this study is to develop such a framework to (1) assess the fundamental performance of HMIFU in detecting HIFU lesions based on the change in tissue apparent elasticity, i.e., the increasing Young’s modulus, and the HIFU lesion size with respect to the HIFU exposure time and (2) validate the simulation findings ex vivo. The same HMI and HMIFU parameters as in the experimental studies were used, i.e., 4.5-MHz HIFU frequency and 25 Hz AM frequency. For a lesion-to-background Young’s modulus ratio of 3, 6 and 9, the FE and estimated HMI displacement ratios were equal to 1.83, 3.69 and 5.39 and 1.65, 3.19 and 4.59, respectively. In experiments, the HMI displacement followed a similar increasing trend of 1.19, 1.28 and 1.78 at 10-s, 20-s and 30-s HIFU exposure, respectively. In addition, moderate agreement in lesion size growth was found in both simulations (16.2, 73.1 and 334.7 mm 2) and experiments (26.2, 94.2 and 206.2 mm 2). Therefore, the feasibility of HMIFU for HIFU lesion detection based on the underlying tissue elasticity changes was verified through the developed theoretical framework, i.e., validation of the fundamental performance of the HMIFU system for lesion detection, localization and quantification, was demonstrated both theoretically and ex vivo.

Numerical Investigation of Superharmonic Imaging Using Chirp Excitation

At present, along with the fundamental method of ultrasound imaging, tissue harmonic imaging based on imprinting of the second harmonic component is established as the standard method of ultrasound imaging. Recently introduced superharmonic imaging (SHI) has an edge over this standard method and has improved spatial resolution. To explore further advancement in ultrasound imaging for enhanced resolution and penetration depth. SHI is the summation of higher harmonics generated due to nonlinear tissue propagation of ultrasound. Here, the addition of third, fourth and fifth harmonics has been done for the superharmonic field. The modeling of nonlinear wave propagation is done in frequency domain on the basis of the second order operator splitting approach. The higher harmonic components are picked up using the inverse filters. The standard evaluation parameters were significantly improved with linear frequency modulation (FM) chirp. The axial level was 2.8 times higher with linear FM chirp as compared to conventional short pulse. Minor benefits such as a 5% increase in beam width and suppression of side lobes were also recorded. This numerical investigation confirms that linear FM chirp in SHI provides better resolution and penetration depth. State of the art fundamental and second harmonic ultrasound imaging techniques were also improved with linear FM chirp as compared with conventional excitation. SHI is superior to the existing diagnostic ultrasound techniques.

Modeling of nonlinear wave propagation over fringing reefs

The applicability of existing nonlinear (triad) spectral models for steep slopes (0.1–0.2) characteristic of reef environments was investigated, using both deterministic (phase-resolving) and stochastic (phased-averaged) formulations. Model performance was tested using laboratory observations of unidirectional wave transformation over steep and smooth bathymetry profiles. The models, developed for mild slopes, were implemented with minimal modifications (the inclusion of breaking parametrizations and linear steep-slope corrections) required by laboratory data. The deterministic model produced typically more accurate predictions than the stochastic one, but the phase averaged formulation proved fast enough to allow for an inverse modeling search for the optimal breaking parametrization. The effects of the additional assumptions of the stochastic approach resulted in a slower than observed evolution of the infragravity band. Despite the challenge posed by the fast wave evolution and energetic breaking characteristic to the steep reef slopes, both formulations performed overall well, and should be considered as good provisional candidates for use in numerical investigation of wave–current interaction processes on steep reefs.

The homotopy analysis method for solving nonlinear wave propagation model in inhomogeneous cylindrical shells

The investigation of nonlinear wave propagation in cylindrical shells is of theoretical and realistic significance. In this work, using homotopy analysis method, we study a new model of nonlinear wave propagation in inhomogeneous cylindrical shells, and obtain approximate solitary wave solution and periodic wave solution with high accuracy. It shows that homotopy analysis method is one of the most effective methods for research into the problems of nonlinear wave propagation.

The Korteweg-de Vries equation in a cylindrical pipe

A mathematical model of nonlinear wave propagation in a pipeline is constructed. The Korteweg-de Vries equation is derived by determining asymptotic solutions and changing variables. A particular solution to the model equations is found that has the fluid velocity function in the form of a solitary wave. Thus, the class of nonlinear fluid dynamics problems described by the KdV equation is expanded.