Model Wave Research Articles

Two‐dimensional anisotropic acoustic wave modelling using the support operator method

AbstractWe developed an algorithm to simulate two‐dimensional frequency domain acoustic‐wave response in a transversely isotropic medium with a tilted symmetry axis. The algorithm employs a support operator finite‐difference method for modelling. This method constructs a nine‐point stencil finite‐difference scheme for second‐order elliptic equations for generalized anisotropic physical properties. The medium's properties are described as P‐wave velocity on the symmetric axis, density, Thomsen's anisotropic parameters (epsilon and delta) and the tilt angle. The benchmarking analysis of the modelled amplitude is illustrated using an isotropic whole‐space model. Several synthetic experiments are conducted to evaluate the accuracy of the scheme for anisotropic models. The results suggest that the developed algorithm simulates the P‐wave solution and the fictitious S‐wave mode as reported in the literature. Simulation for a heterogeneous model with a spatially varying tilt angle of the medium symmetry axis is performed to ascertain the algorithm's robustness. The outcomes of the numerical experiments demonstrate that the developed algorithm can accurately simulate the frequency domain response of acoustic waves in the tilted anisotropic media.

Novel approach for modeling and attenuation of power waves in large – scale power systems

In this paper modeling and attenuation of electromechanical power waves in large – scale power systems are discussed. Mathematical model of power wave is derived using Euler – Lagrange equation. The proposed modeling procedure is based on kinetic and potential energies of the system, as well as system’s dissipation power. A novel method for incorporation of spatially dependent power losses into Euler – Lagrange equation is defined as well. The obtained mathematical model is simple for derivation, straightforward and practical for use, so it can easily be applied to derive wave equation of other technical systems or natural phenomena as well, which is an additional advantage compared to the existing models. Based on the developed model, an appropriate control system is proposed. The main idea for control system synthesis is to reduce transmitted waves inside the system. It is shown that the series power line impedance and voltage amplitude have the greatest impact on the wave transmission coefficient. Since unified power flow controller (UPFC) is capable of simultaneously modulating both these parameters, this device is chosen to perform control tasks in proposed operation mode. The effectiveness of the proposed solution has been verified by thorough computer simulations on artificial generator array and IEEE benchmark simplified Australian system. The results show significant power wave reduction. Some future works such as derivation of the mathematical model of inverter array or incorporation of artificial intelligence algorithms in UPFC control system based on transmission coefficient reduction might rely on this work.

Statistical assessment of the wave loads at walls through two-phase CFD modeling of the effects of air compressibility

The modeling of wave impacts against coastal structures requires the analysis of hundreds or thousands of waves to be statistically meaningful. Long irregular wave attacks, when affordable, can be performed experimentally, but may be inadequate to track the air entrapment and account for air compressibility, which, instead, plays a key role in the wave impacts. On the other hand, long simulations are generally avoided in numerical modeling for computational effort and numerical stability reasons, even more so when two-phase flows and air compressibility are involved. In such a context, this paper presents, for the first time, the application of a plug-in suite developed in the OpenFOAM® environment to the representation of long time series of irregular waves impacting against coastal defenses while solving two compressible fluids. To this purpose, such a plug-in compressible suite was applied to reproduce recent 2D experiments of wave overtopping and wave impacts at smooth dikes with crown walls. The numerical stability of the compressible solver and its adequacy to accurately reproduce the wave reflection and the wave overtopping are first verified by comparing the numerical results with the laboratory tests. Second, the improved representation of the wave pressures and wave forces at the walls obtained with the plug-in compressible suite is shown by comparing its results with the corresponding ones obtained with the incompressible solver. Specifically, the plug-in suite—accounting for the effects of the air compressibility during the impact events—outperforms the incompressible native solver in the capture of the pressure peaks, in the reproduction of the time–pressure trace, and in the statistical analysis of the pressure distribution along the crown wall.

SeismicNet: Physics-informed neural networks for seismic wave modeling in semi-infinite domain

Recently, there has been an increasing interest in leveraging physics-informed neural networks (PINNs) for modeling dynamical systems. However, limited studies have been conducted along this horizon on seismic wave modeling tasks. A critical challenge is that these geophysical problems are typically defined in large domains (i.e., semi-infinite), which leads to high computational costs. We present a new PINN model for seismic wave modeling in semi-infinite domain without the need for labeled data. Specifically, the absorbing boundary condition is introduced into the network as a soft regularizer for handling truncated boundaries. To scale up, we consider a sequential training strategy via temporal domain decomposition to improve the scalability of the network and solution accuracy. Moreover, we design a novel surrogate modeling strategy to account for parametric loading, which estimates the wave propagation in semi-infinite domain given the seismic loading at different locations. Various numerical experiments are implemented to evaluate the performance of the proposed PINN model in the context of forward modeling of seismic wave propagation. In particular, we use diverse material distributions to test the versatility of this approach. The results demonstrate excellent solution accuracy under distinctive scenarios.

On the assessment of the wave modeling uncertainty in wave climate projections

Abstract This study investigates the epistemic uncertainty associated with the wave propagation modeling in wave climate projections. A single-forcing, single-scenario, seven-member global wave climate projection ensemble is used, developed using three wave models with a consistent numerical domain. The uncertainty is assessed through projected changes in wave height, wave period, and wave direction. The relative importance of the wave model used and its internal parameterization are examined. The former is the dominant source of uncertainty in approximately two-thirds of the global ocean. The study reveals divergences in projected changes from runs of different models and runs of the same model with different parameterizations over 75% of the ensemble mean change in several ocean regions. Projected changes in the wave period shows the most significant uncertainties, particularly in the Pacific Ocean basin, while the wave height shows the least. Over 30% of global coastlines exhibit significant uncertainties in at least two out of the three wave climate variables analyzed. The coasts of western North America, the Maritime Continent and the Arabian Sea show the most significant wave modeling uncertainties.

Design and evaluation of an efficient high-precision ocean surface wave model with a multiscale grid system (MSG_Wav1.0)

Abstract. Ocean surface waves induced by wind forcing and topographic effects are a crucial physical process at the air–sea interface, which significantly affect typhoon development, ocean mixing, etc. Higher-resolution wave modeling can simulate more accurate wave states but requires a huge number of computational resources, making it difficult for Earth system models to include ocean waves as a fast-response physical process. Given that high-resolution Earth system models are in demand, efficient high-precision wave simulation is necessary and urgent. Based on the wave dispersion relation, we design a new wave modeling framework using a multiscale grid system. It has the fewest number of fine grids and reasonable grid spacing in deep-water areas. We compare the performance of wave simulation using different spatial propagation schemes, reveal the different reasons for wave simulation differences in the westerly zone and the active tropical cyclone region, and quantify the matching of spatial resolutions between wave models and wind forcing. A series of numerical experiments show that this new modeling framework can more precisely simulate wave states in shallow-water areas without losing accuracy in the deep ocean while costing a fraction of the price of traditional simulations with uniform fine-gridding space. With affordable computational expenses, the new ocean surface wave modeling can be implemented into high-resolution Earth system models, which may significantly improve the simulation of the atmospheric planetary boundary layer and upper-ocean mixing.

Geometric modeling of blast waves reflected from the cylindrical surface of a sineusidal profile

A method is proposed for geometric modeling of a family of blast wave fronts reflected from a cylindrical surface of a sinusoidal profile. The model of “optical” reflection is adopted as a basis, when for each incident virtual explosive “ray” the angle of reflection is equal to the angle of incidence. To illustrate the graphic-analytical approach, a test model of the formation of a family of reflected wave fronts for a cylindrical parabolic surface has been developed. A cylindrical surface of a sinusoidal profile obtained by bending a rectangular metal sheet by longitudinal forces is considered. Geometric models of a family of blast wave fronts reflected from a cylindrical surface of a sinusoidal profile are described. Maple has been compiled – programs for visualizing models of a family of blast wave fronts reflected from a cylindrical surface. Conducted studies of sinusoidal cylindrical reflectors designed to demonstrate the effect of multiplying the effects of shock blast waves directed towards the fire zone. For their practical use, it is necessary to find the bending parameters of the cylinder such that the virtual beams of the “point” explosive are transformed into a system of beams that are close to parallel in the fire zone. As a result of the research, the parameters of bending of a metal rectangular sheet by longitudinal forces were calculated, and the coordinates of the location of the “point” explosive substance were determined. It is taken into account that cylindrical reflectors with a sinusoidal profile can be manufactured at the site of their use. To do this, a rectangular sheet of metal must be bent by longitudinal forces and the bend must be fixed by welding reinforcement rods. The research carried out is aimed at developing the technology of extinguishing forest fires with directed explosions.

Modeling of shock wave produced by collapse of cavitation bubble using a fully conservative multiphase model

In this study, we extensively validated the applicability of the fully conservative compressible multiphase flow model to simulate the collapse of cavitation bubbles. The mathematical model is fully conservative, which is crucial for accurately modeling the strong shock phenomena induced via bubble collapse. The numerical method accounts for compressibility and mass transfer with phase-change transitions. A high-resolution shock-capturing finite-volume method and an accurate Riemann solver were employed to capture the strong shocks produced by bubble collapse. A grid-resolution study and validation were performed to ensure the convergence and consistency of the numerical method. This study focused on analyzing the shock waves generated during the collapse as well as the dynamics of bubble collapse and rebound. Quantitative comparisons between the simulation results and experimental data as well as the reference results revealed a high level of agreement. The investigation focused on the impact of various factors, including the bubble radius, phase change, and liquid pressure, on the collapse and rebound of the cavitation bubble, as well as the resulting shock waves. These analyses yielded valuable insight into the complex behavior of cavitation bubbles that collapse in a free field.

Forecast of the Dynamics of a Sandy Beach in Complexed Hydrodynamic Conditions

Changes in the coastal zone under the influence of currents of different nature and wind waves are being investigated. A sandy beach located in the water area of the “Park of the 300th Anniversary of St. Petersburg”, the Neva Bay of the Gulf of Finland of the Baltic Sea, is considered as an object. The beach is actively affected by wind waves and eventually washes away with the intensity of the retreat of the shore of about 4 m per year. For numerical modeling, a set of models is used: SWAN–wind-wave model and COASTOX-UN–a two-dimensional model of currents, sediment transport and bottom reformation. It was developed a model of the Neva Bay and the mouth of the Neva River from the Flood Prevention Facility Complex in the west to the river Neva near the Liteiny Bridge in the east. Based on the reanalysis of wind data, 36 strong storms were selected for a five-year period from 2014 to 2018, for the sequence of which numerical modeling of waves, currents and lithodynamic processes was carried out. It was obtained balances of alluvial and washouts after a ten-years simulated period for beach sectors. To verify the results, satellite images of the modeling area are used, it was found that the model adequately describes the main observed trends in the development of the beach.

Reducing Numerical Dispersion with High-Order Finite Difference to Increase Seismic Wave Energy

The numerical dispersion of 2D acoustic wave modeling has become an interesting subject in wave modeling in producing better subsurface images. Numerical dispersion is often caused by error accumulation with increased grid size in wave modeling. Wave modeling with high-order finite differences was carried out to reduce the numerical error. This study focused on variations in the numerical order to suppress the dispersion due to numerical errors. The wave equation used in modeling was discretized to higher orders for the spatial term, while the time term was discretized up to the second order, with every layer unabsorbed. The results showed that high-order FD was effective in reducing numerical dispersion. Thus, subsurface layers could be distinguished and observed clearly. However, from the modeling results, the wave energy decreased with increasing distance, so the layer interfaces were unclear. To increase the wave energy, we propose a new source in modeling. Furthermore, to reduce the computational time we propose a proportional grid after numerical dispersion has disappeared. This method can effectively increase the energy of reflected and transmitted waves at a certain depth. The results also showed that the computational time of high-order FD is relatively low, so this method can be used in solving dispersion problems.

A Spectral Wave Model for Inhomogeneous Water Wave Fields Using the Quasi-Coherent Theory

A numerical stochastic wave model was developed in this study based on the quasi-coherent theoretical framework proposed by Smit and Janssen in 2013. Subsequently, the model was implemented to reproduce and cross-confirm the findings of the quasi-coherent (QC) spectral wave modeling approach. The process included simulations of experiments conducted by Vincent and Briggs regarding waves propagating over a submerged shoal. The results of the simulations agree with the expected results of the QC theory, which can account for the spatial coherence of inhomogeneous wave fields and capture wave interference more accurately than conventional spectral wave models. In addition, extra insight was gained about aspects of the overall numerical implementation of the QC theory.

Physics-constrained neural networks for half-space seismic wave modeling

Forward modeling of seismic waves using physics-informed neural networks (PINNs) has attracted much attention. However, a notable challenge arises when modeling seismic wave propagation in large domains (i.e., a half-space), PINNs may encounter the issue of "soft constraint failure". To address this problem, we propose a novel framework called physics-constrained neural networks (PCNNs) specifically designed for modeling seismic wave propagation in a half-space. The method of images is incorporated to effectively implement the free stress boundary conditions of the Earth's surface, leading to the successful propagation of plane waves and cylindrical waves in a half-space. We analyze the training dynamics of neural networks when solving two-dimensional (2D) wave equations from the neural tangent kernel (NTK) perspective. An adaptive training algorithm is introduced to mitigate the unbalanced gradient flow dynamics of the different components of the loss function of PINNs/PCNNs. Furthermore, to tackle the complex behavior of seismic waves in layered media, a sequential training strategy is considered to enhance network scalability and solution accuracy. The results of numerical experiments demonstrate the accuracy and effectiveness of our approach.

High frequency attenuation of elastic waves transmitted at an angle through a randomly-fluctuating horizontally-layered slab

This paper is concerned with the modeling of elastic waves traveling at small incidence angles through a randomly-fluctuating horizontally-layered slab, in regimes where the wavelength is small compared to the thickness of the slab. The wave propagation problem is reset in a frame following the coherent front, which propagates in a homogenized medium. This homogenized medium is anisotropic because of the layering, and the equations obtained account explicitly for the coupling of quasi-P and quasi-S waves. The resulting model is governed by a set of coupled stochastic ordinary differential equations that can be approximated numerically very efficiently, and yields in particular estimates of the transmission and reflections coefficients of the slab. The latter compare favorably to the coefficients obtained in a full scale numerical simulation of the (micro-scale) wave equation, for a fraction of the cost.

Experimental and numerical modelling of water waves in sewer networks during sewer/surface flow interaction using a coupled ODE‐SWE solver

AbstractFlooding in urban areas is expected to increase its magnitude and frequency in the future. Therefore, there is a strong need to better model sewer–surface flow interactions. Existing numerical methods are commonly based on simplified representations of sewer/surface mass exchange, and mainly validated in steady flow conditions. Current methodologies describing the propagation of transient conditions/waves through interaction nodes are simplified, rely on empirical coefficients and/or lack detailed validation. In this paper, an integrated numerical approach for modelling the propagation of water waves through interaction nodes (e.g., manholes) is presented. In this solution, the shallow water equations are used to simulate the free‐surface propagation inside the sewer network, and an ordinary differential equation is employed for modelling flow regimes through pipes and manholes. The model proposed is validated against the well‐known STAR‐CD modelling software for a number of test cases. Finally, further validation is performed against experimental data describing the evolution of water depth around a manhole in unsteady surcharging conditions.

Eccentric catastrophes & what to do with them

Analytic modeling of gravitational waves (GWs) from inspiraling eccentric binaries poses an interesting mathematical challenge. When constructing analytic waveforms in the frequency domain, one has to contend with the fact that the phase of the Fourier integral in non-monotonic, resulting in a breakdown of the standard stationary phase approximation (SPA). In this work, we study this breakdown within the context of catastrophe theory. We find that the SPA holds in the context of eccentric Keplerian orbits when the Fourier frequency satisfies , where are integer multiples of the apocenter/pericenter frequencies, respectively. For values outside of this interval, the phase undergoes a fold catastrophe, giving rise to an Airy function approximation of the Fourier integral. Using these two different approximations, we generate a matched asymptotic expansion that approximates generic Fourier integrals of Keplerian motion for bound orbits across all frequency values. This asymptotic expansion is purely analytic and closed-form. We discuss several applications of this investigation and the resulting approximation, specifically: (1) the development and improvement of effective fly-by waveforms for binary black holes, (2) the transition from burst emission in the high eccentricity limit to wave-like emission in the quasi-circular limit, which results in an analogy between eccentric GW bursts and Bose–Einstein condensates, and (3) the calculation of f-mode amplitudes in eccentric binary neutron stars and black hole-neutron star binaries in terms of complex Hansen coefficients. The techniques and approximations developed herein are generic, and will be useful for future studies of GWs from eccentric binaries within the context of post-Newtonian theory.

Wave Transformation Pattern in Submerged Breakwater Planning with 2D Wave Model at Mengening Beach, Badung Regency, Bali, Indonesia

Mengening Beach is located in Badung Regency, Bali, Indonesia. The average erosion rate in Badung Regency is 1.96 m/year, so the right plan is a submerged breakwater to reduce wave energy coming to the beach, which causes erosion. This building artistically does not lessen the beauty of the beach and sea because it’s below the sea mean sea water level (MSL). Because the beach is a tourist area, it is essential to maintain the beauty of the beach. Two-dimensional wave modeling uses the CMS Wave model on SMS software version 10.1 with two modeling scenarios: before and after there is a submerged breakwater. The two-dimensional wave results show that the submerged breakwater plan can dampen waves in the building placement area, which was initially 1.3 m-1.4 m high to 0.9 m-1.3 m, so this submerged breakwater plan can reduce waves by 10%-40%. From this research, readers can learn how to plan a submerged breakwater and know the performance of the planned breakwater function at Mengening Beach.

A seismic investigation of lithospheric velocities beneath the Chhotanagpur Plateau (India) using waveform modeling of shear-coupled PL waves and other phases

A seismic investigation of lithospheric velocities beneath the Chhotanagpur Plateau (India) using waveform modeling of shear-coupled PL waves and other phases

Numerical Modelling of tsunami wave to assess the possible impacts along western coasts of India

Numerical modelling of tsunami waves has been made for the western coasts of India using TUNAMI N2 code. In this study the fault parameters are considered from earlier published literatures. Bathymetry data and possible tsunami generation locations have been obtained from the ETOPO2 (Global Relief Model) and General Bathymetric Chart of the Oceans (GEBCO) satellite data. For tsunami run-up the land topography data Shuttle Radar Topographic Mission (SRTM) is used. The present simulation consists of a duration of 6 hours (360 min). Possible arrival time with amplitude at various locations have been estimated. The paper also analyses the changes in the directivity of the generated tsunami waves towards western coasts of India by changing the dip and strike angles as different scenarios. Time series and height along the different parts of Gujarat coast and hourly travel-time chart of the tsunami wave are also discussed. After the earthquake and initial tsunami wave generation, it reaches at all the locations along the Gulf of Kachchh (Gujarat) in nearly 2 hrs to 5.30 hrs with amplitudes from 1 to 2.5 m, Mumbai in around 4.45 hrs with amplitude 2 m, Goa in around 3.08 hrs with amplitude 1 m, Karwar (Karnataka) in around 3.12 hrs and Mangalore in around 3.36 hrs with amplitudes 1 m each. The authenticity of the estimated tsunami phases of the 1945 tsunamigenic earthquake along the MSZ are corroborated with the available reports and published literatures.

A Posterior h/p Adaptive Refinement Algorithm for 3-D Goal-Oriented Electromagnetic Problems

We propose a posterior h/p adaptive mesh refinement algorithm for 3-D goal-oriented electromagnetic wave modeling in complex media. This new algorithm allows both <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$h$</tex-math> </inline-formula> -version refinement—mesh size adjustment—and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$</tex-math> </inline-formula> -version refinement—polynomial order adjustment—simultaneously. To be specific, we use the adjoint system on the dual space of the forward solver; as a result, error generation, propagation, and accumulation can be evaluated, even without the analytical solutions. In particular, the posterior error is explicitly indicated by postprocessing of original forward solver. Compared with conventional mesh adaptation strategies, such an algorithm is goal-oriented and auxiliary-system-free; as a result, it does not require pay extensive attention to entire computational domain and is complimentary in solving adjoint state equation. Numerical examples demonstrate the superior performance of the proposed mesh refinement algorithms for real-world applications, compared to uniform refinement, nongoal-oriented adaptation, and other goal-oriented adaptation.

Prediction of Long-Term Offshore Structural Responses Based on Nonlinear Wave Modeling

Wind-generated random wave loads are the dominant loads to consider for maintaining the reliability of fixed offshore structures. Based on probabilistic techniques, the inherent randomness of the wave loading can be used to predict extreme offshore structural response, which is Gaussian in nature. However, researchers have found that the hydrodynamic component and structural dynamics substantially impact the frequency spectrum, leading to a non-Gaussian stochastic offshore structural response. A finite-memory non-linear system (FMNSNL) has been proven to be an efficient approach to evaluate the non-Gaussian stochastic offshore structural response compared to the conventional method, Monte Carlo time simulation. However, the analysis has been conducted based on short-term distribution only. The most satisfactory analysis is based on long-term distribution. Hence, further investigation in this paper will evaluate the long-term probability distribution of extreme offshore structural responses. As a result, a 100-year extreme offshore structural response prediction achieves 80% to 96% accuracy compared to the Monte Carlo time simulation. The probability distribution has been evaluated using the Gumbel distribution function throughout this investigation. Still, there is a little deviation at the tail end of the distribution between the simulated response values and the fitted line. A different distribution function, such as the Generalised Extreme Value (GEV) distribution, is advised for future work.