Numerical Studies on the Generation and Propagation of Tsunami Waves Based on the High-Order Spectral Method

An effective numerical model for wave propagation over three-dimensional(3D)bathymetry was developed based on the High-Order Spectral(HOS)method and combined with a moving bottom boundary.Based on this model,tsunami waves caused by various mechanisms were simulated and analyzed.Two-dimensional bed upthrust and the effect of the uplift velocity of the bathymetry on the wave profiles of tsunami waves were studied.Next,tsunami waves caused by 3D submarine slides were generated and the effects of the slide velocity,slide dimension and water depth on the tsunami waves were analyzed.Based on wavelet analysis,the properties of the tsunami wave propagation were investigated.The results show that the bottom movement can significantly affect the generation and propagation of tsunami waves and the studies could help understand the mechanisms of tsunamis caused by a moving bottom boundary.

Re-study on Recurrence Period of Stokes Wave Train with High Order Spectral Method

Owing to the Benjamin-Feir instability, the Stokes wave train experiences a modulation-demodulation process, and presents a recurrence characteristics. Stiassnie and Shemer researched the unstable evolution process and provided a theoretical formulation for the recurrence period in 1985 on the basis of the nonlinear cubic Schrodinger equation （NLS）. However, NLS has limitations on the narrow band and the weak nonlinearity. The recurrence period is re-investigated in this paper by using a highly efficient High Order Spectral （HOS） method, which can be applied for the direct phase- resolved simulation of the nonlinear wave train evolution. It is found that the Stiassnie and Shemer＇s formula should be modified in the cases with most unstable initial conditions, which is important for such topics as the generation mechanisms of freak waves. A new recurrence period formula is presented and some new evolution characteristics of the Stokes wave train are also discussed in details.

Arbitrary High-Order Fully-Decoupled Numerical Schemes for Phase-Field Models of Two-Phase Incompressible Flows

Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.

Review:Recent Development of High⁃Order⁃Spectral Method Combined with Computational Fluid Dynamics Method for Wave⁃Structure Interactions

The present paper reviews the recent developments of a high⁃order⁃spectral method(HOS)and the combination with computational fluid dynamics(CFD)method for wave⁃structure interactions.As the numerical simulations of wave⁃structure interaction require efficiency and accuracy,as well as the ability in calculating in open sea states,the HOS method has its strength in both generating extreme waves in open seas and fast convergence in simulations,while computational fluid dynamics(CFD)method has its advantages in simulating violent wave⁃structure interactions.This paper provides the new thoughts for fast and accurate simulations,as well as the future work on innovations in fine fluid field of numerical simulations.

A Semi-Lagrangian Spectral Method for the Vlasov-Poisson System Based on Fourier, Legendre and Hermite Polynomials

In this work, we apply a semi-Lagrangian spectral method for the Vlasov-Poisson system, previously designed for periodic Fourier discretizations, by implementing Legendre polynomials and Hermite functions in the approximation of the distribution function with respect to the velocity variable. We discuss second-order accurate-in-time schemes, obtained by coupling spectral techniques in the space-velocity domain with a BDF timestepping scheme. The resulting method possesses good conservation properties, which have been assessed by a series of numerical tests conducted on some standard benchmark problems including the two-stream instability and the Landau damping test cases. In the Hermite case, we also investigate the numerical behavior in dependence of a scaling parameter in the Gaussian weight. Confirming previous results from the literature, our experiments for different representative values of this parameter, indicate that a proper choice may significantly impact on accuracy, thus suggesting that suitable strategies should be developed to automatically update the parameter during the time-advancing procedure.

High-Order Spectral Stochastic Finite Element Analysis of Stochastic Elliptical Partial Differential Equations

This study presents an experiment of improving the performance of spectral stochastic finite element method using high-order elements. This experiment is implemented through a two-dimensional spectral stochastic finite element formulation of an elliptic partial differential equation having stochastic coefficients. Deriving this spectral stochastic finite element formulation couples a two-dimensional deterministic finite element formulation of an elliptic partial differential equation with generalized polynomial chaos expansions of stochastic coefficients. Further inspection of the performance of resulting spectral stochastic finite element formulation with adopting linear and quadratic (9-node or 8-node) quadrilateral elements finds that more accurate standard deviations of unknowns are surprisingly predicted using quadratic quadrilateral elements, especially under high autocorrelation function values of stochastic coefficients. In addition, creating spectral stochastic finite element results using quadratic quadrilateral elements is not unacceptably time-consuming. Therefore, this study concludes that adopting high-order elements can be a lower-cost method to improve the performance of spectral stochastic finite element method.

A Sub-element Adaptive Shock Capturing Approach for Discontinuous Galerkin Methods

In this paper,a new strategy for a sub-element-based shock capturing for discontinuous Galerkin(DG)approximations is presented.The idea is to interpret a DG element as a col-lection of data and construct a hierarchy of low-to-high-order discretizations on this set of data,including a first-order finite volume scheme up to the full-order DG scheme.The dif-ferent DG discretizations are then blended according to sub-element troubled cell indicators,resulting in a final discretization that adaptively blends from low to high order within a single DG element.The goal is to retain as much high-order accuracy as possible,even in simula-tions with very strong shocks,as,e.g.,presented in the Sedov test.The framework retains the locality of the standard DG scheme and is hence well suited for a combination with adaptive mesh refinement and parallel computing.The numerical tests demonstrate the sub-element adaptive behavior of the new shock capturing approach and its high accuracy.

Yb,Ho∶YAG晶体的生长及光谱性能

采用中频感应提拉法成功生长出Yb(15 at%),Ho(1 at%)∶YAG激光晶体,研究了室温下晶体的吸收光谱,发射光谱特性和荧光寿命。吸收光谱中在938 nm处存在Yb3+的吸收带,能与InGaAs激光二极管(LD)有效耦合,适合激光管二极抽运。荧光光谱中存在两个荧光主峰,分别位于1907 nm和2091 nm附近。研究表明:Yb,Ho∶YAG晶体是一种有发展前景的激光增益介质。

Rogue waves during Typhoon Trami in the East China Sea

As concluded from physical theory and laboratory experiment,it is widely accepted that nonlinearities of sea state play an important role in the formation of rogue waves;however,the sea states and corresponding nonlinearities of real-world rogue wave events remain poorly understood.Three rogue waves were recorded by a directional buoy located in the East China Sea during Typhoon Trami in August 2013.This study used the WAVEWATCHⅢmodel to simulate the sea state conditions pertaining to when and where those rogue waves were observed,based on which a comprehensive and full-scale analysis was performed.From the perspectives of wind and wave fields,wave system tracking,High-Order Spectral method simulation,and some characteristic sea state parameters,we concluded that the rogue waves occurred in sea states dominated by second-order nonlinearities.Moreover,third-order modulational instabilities were suppressed in these events because of the developed or fully developed sea state determined by the typhoon wave system.The method adopted in this study can provide comprehensive and full-scale analysis of rogue waves in the real world.The case studied in this paper is not considered unique,and rules could be found and confirmed in relation to other typhoon sea states through the application of our proposed method.

Parametric study of a new HOS-CFD coupling method

This paper presents a developed new coupled method which combined our in-house CFD solver naoe-FOAM-SJTU and naoe-FOAM-os with a potential theory High Order Spectral method(HOS).A parametric study of nonlinear wave propagation in computational fluid dynamics(CFD)zone is considered.Mesh convergence,time step convergence,time discretization scheme and length of relaxation zone are all carried out.Those parametric studies verify the steady of this new combined method and give better choice for wave propagation.The dissipation in propagation of nonlinear regular wave can be lower than 3%in static mesh,and less than 2%in overset grid mesh.Meanwhile,a LNG FPSO is put into the viscous wave tank to study the suitable size of CFD zone.To achieve a better solution with least calculating resources and best numerical results,the length of CFD zone is discussed.These parametric studies can give reference upon employment of the potential-viscous coupled method and validation of the coupled method.

An Implicit LU-SGS Scheme for the Spectral Volume Method on Unstructured Tetrahedral Grids

An efficient implicit lower-upper symmetric Gauss-Seidel(LU-SGS)solution approach has been applied to a high order spectral volume(SV)method for unstructured tetrahedral grids.The LU-SGS solver is preconditioned by the block element matrix,and the system of equations is then solved with a LU decomposition.The compact feature of SV reconstruction facilitates the efficient solution algorithm even for high order discretizations.The developed implicit solver has shown more than an order of magnitude of speed-up relative to the Runge-Kutta explicit scheme for typical inviscid and viscous problems.A convergence to a high order solution for high Reynolds number transonic flow over a 3D wing with a one equation turbulence model is also indicated.

V形布局起伏地形上布拉格共振引起的波能聚焦特性研究

基于高阶谱(HOS)方法,文章建立了考虑起伏地形上三维布拉格共振的数值模型。基于该模型探讨了地形为V形空间布局时的波能聚焦特性,对比分析了地形不同夹角(α)下波能聚焦点处的聚焦效果。试验结果表明:V形布局中不同的α有着不同的聚波特性,通过优化α,可以很大程度上提高波能聚焦效果;当145°<α<180°时,波能聚焦效果较好,波能聚焦点处的振幅可达到初始入射波振幅的1.70倍以上,其中α=162.24°时,波能聚焦效果最优,最大振幅增大2.87倍。

Numerical Study of Two-Dimensional Focusing Waves

Two-dimensional focusing waves are generated and investigated by numerical method. The numerical model is developed by introducing the wave maker boundary on the high-order spectral （HOS） method proposed by Dommermuth and Yue in 1987 and verified by theoretical and experimental data. Some cases of focusing waves considering different parameters such as assumed focusing amplitudes, frequency bandwidth, central frequency and frequency spectrum are generated. Characteristics of the focusing wave including surface elevations, the maximum crest, shift of focusing points and frequency spectra are discussed. The results show that the focusing wave characteristics are strongly affected by focusing amplitudes, frequency bandwidth, central frequency and frequency spectrum.

V形布局地形上不同频率入射波的布拉格共振特性研究

文章基于高阶谱方法建立了三维布拉格共振数值模型,研究了V形布局地形的夹角对不同频率入射波布拉格共振聚焦特性的影响。通过对比各组次波能聚焦点在20个周期内有效波高较初始波高的大小,发现不同频率入射波对应的最优V形布局地形夹角α均相等,且α=162.24°。在最优V形布局地形夹角下,发生布拉格共振后的波能聚焦区域对称分布,且对称轴上的波能聚焦区计算点的有效波高增幅最大,波能聚焦点均在对称轴上。当2k_(x)/k_(b)偏离1较大时,反射能量较少,波能聚焦点在地形上方;当2k_(x)/k_(b)接近1时,反射能量较多,波能聚焦点在地形前方x=10 m附近。

Estimating the evolution of sea state non-Gaussianity based on a phase-resolving model

The occurrence of rogue waves is closely related to the non-Gaussianity of sea states,and this non-Gaussianity can be estimated using corresponding two-dimensional wave spectra.This paper presents an approach to non-Gaussianity estimation based on a phase-resolving model called the high-order spectral method(HOSM).Based on numerous HOSM simulations,a set of precalculated non-Gaussianity indicators was established that could be applied to real sea states without any calibration of spectral shapes.With a newly developed extraction approach,the indicators for given two-dimensional wave spectra could then be conveniently extracted from the precalculated dataset.The feasibility of the newly developed approach in a real wave environment is verified.Using the estimation approach,phase-resolved non-Gaussianity can now be illustrated throughout the evolution of sea states of interest,not just at a few specific times;and the level of non-Gaussianity at any time in a duration can be identified according to the statistics(e.g.,quantities)of the phase-resolved indicators,that are obtained throughout the duration concerned.

Three-dimensional dynamic sea surface modeling based on ocean wave spectrum

In conventional marine seismic exploration data processing,the sea surface is usually treated as a horizontal free boundary.However,the sea surface is affected by wind and waves and there often exists dynamic small-range fluctuations.These dynamic fluctuations will change the energy propagation path and affect the final imaging results.In theoretical research,different sea surface conditions need to be described,so it is necessary to study the modeling method of dynamic undulating sea surface.Starting from the commonly used sea surface mathematical simulation methods,this paper mainly studies the realization process of simple harmonic wave and Gerstner wave sea surface simulation methods based on ocean wave spectrum,and compares their advantages and disadvantages.Aiming at the shortcomings of the simple harmonic method and Gerstner method in calculational speed and sea surface simulation effect,a method based on wave equation and using dynamic boundary conditions for sea surface simulation is proposed.The calculational speed of this method is much faster than the commonly used simple harmonic method and Gerstner wave method.In addition,this paper also compares the new method with the more commonly used higher-order spectral methods to show the characteristics of the improved wave equation method.

Numerical Simulation of Water Wave Propagation and Transformation

A numerical approach was performed to predict the propagation and transformation of nonlinear water waves. A numerical wave flume was developed based on the non-periodic high-order spectral (HOS) method. The flume was applied to analyze the effect of wave steepness and wavelength on the propagation of nonlinear waves. The results show that for waves of low steepness, the wave profile and the wave energy spectrum are stable, and that the propagation can be predicted by the linear wave theory. For waves of moderate steepness and steep waves, the effects associated with the interactions between waves in a wave group become significant and a train of initially sinusoidal waves may drastically change its form within a short distance from its original position.

基于高阶谱方法求解波浪在不规则地形上传播的完全非线性数值模型

该文基于高阶谱方法,通过引入造波边界和水底边界条件,建立了能够模拟波浪在不规则地形上传播的完全非线性数值计算模型。对典型的二维波浪bragg反射和波浪在潜堤上传播进行了数值模拟,数值计算结果表明该模型能够很好地模拟波浪的产生、传播及与不规则地形的作用,验证了所建立的数值计算模型模拟波浪在不规则地形上传播的有效性。

基于高阶谱方法与CFD计算的耦合模型在不规则波模拟中的应用

基于高阶谱(HOS)方法的势流造波模型可进行波浪的高效率非线性演化模拟,但由于忽略了黏性影响,在研究波浪与物体相互作用中,对于波浪破碎和边界层流场细节模拟等方面很难实现,而黏性波浪水池则有计算量大的局限性。该文建立了基于高阶谱(HOS)方法与CFD计算的耦合模型,外域波浪场依靠势流模型计算,而内域波浪场演化则通过求解Navier-Stokes方程获得,通过松弛区将二者结合,可以避免求解大范围的黏性波浪场而带来的巨大计算量,并且能在波浪与物体相互作用中考虑黏性影响。在对多种波浪类型的模拟以及网格尺度影响讨论中,黏势流耦合模型的适用性得到验证。并在多向不规则波的聚焦波模拟,以及基于势流基础上的大范围长时间演化下得到的极端海浪在CFD域内重构中,黏势流耦合模型都有其成功应用。

Numerical Simulation of a Weakly Nonlinear Model for Internal Waves

Internal waves arise in a wide array of oceanographic problems of both theoretical and engineering interest.In this contribution we present a newmodel,valid in the weakly nonlinear regime,for the propagation of disturbances along the interface between two ideal fluid layers of infinite extent and different densities.Additionally,we present a novel high-order/spectral algorithm for its accurate and stable simulation.Numerical validation results and simulations of wave-packet evolution are provided.