BOUSSINESQ MODELLING OF NEARSHORE WAVES UNDER BODY FITTED COORDINATE

A set of nonlinear Boussinesq equations with fully nonlinearity property is solved numerically in generalized coordinates,to develop a Boussinesq-type wave model in dealing with irregular computation boundaries in complex nearshore regions and to facilitate the grid refinements in simulations.The governing equations expressed in contravariant components of velocity vectors under curvilinear coordinates are derived and a high order finite difference scheme on a staggered grid is employed for the numerical implementation.The developed model is used to simulate nearshore wave propagations under curvilinear coordinates,the numerical results are compared against analytical or experimental data with a good agreement.     

基于有限体积法的三维波生近岸流数值模型

波浪破碎产生近岸流是近岸浅水区域一个重要的水动力现象。该文利用辐射应力的概念,并考虑辐射应力沿水深的变化、波浪破碎引起的水滚以及波流共同作用下的水底剪应力,建立了基于有限体积法的三维波生近岸流数值模型。运用建立的数值模型模拟了两个实验室实验,并同实验的实测结果进行了对比。结果表明,建立的数值模型能够较好地模拟波浪破碎产生的近岸流。     

A TVD-WAF-based hybrid finite volume and finite difference scheme for nonlinearly dispersive wave equations

A total variation diminishing-weighted average flux(TVD-WAF)-based hybrid numerical scheme for the enhanced version of nonlinearly dispersive Boussinesq-type equations was developed. The one-dimensional governing equations were rewritten in the conservative form and then discretized on a uniform grid. The finite volume method was used to discretize the flux term while the remaining terms were approximated with the finite difference method. The second-order TVD-WAF method was employed in conjunction with the Harten-Lax-van Leer(HLL) Riemann solver to calculate the numerical flux, and the variables at the cell interface for the local Riemann problem were reconstructed via the fourthorder monotone upstream-centered scheme for conservation laws(MUSCL). The time marching scheme based on the third-order TVD RungeKutta method was used to obtain numerical solutions. The model was validated through a series of numerical tests, in which wave breaking and a moving shoreline were treated. The good agreement between the computed results, documented analytical solutions, and experimental data demonstrates the correct discretization of the governing equations and high accuracy of the proposed scheme, and also conforms the advantages of the proposed shock-capturing scheme for the enhanced version of the Boussinesq model, including the convenience in the treatment of wave breaking and moving shorelines and without the need for a numerical filter.     

Modelling of 2-D extended Boussinesq equations using a hybrid numerical scheme

In this paper, a hybrid finite-difference and finite-volume numerical scheme is developed to solve the 2-D Boussinesq equations. The governing equations are the extended version of Madsen and Sorensen＇s formulations. The governing equations are firstly rearranged into a conservative form. The finite volume method with the HLLC Riemann solver is used to discretize the flux term while the remaining terms are discretized by using the finite difference method. The fourth order MUSCL-TVD scheme is employed to reconstruct the variables at the left and right states of the cell interface. The time marching is performed by using the explicit second-order MUSCL-Hancock scheme with the adaptive time step. The developed model is validated against various experimental measurements for wave propagation, breaking and runup on three dimensional bathymetries.     

Littoral drift by alongshore flow at Visakhapatnam – East Coast of India

The littoral drift in the surf zone of Visakhapatnam has been evaluated using simulated longshore current. In this study we examined littoral processes, driven by longshore currents using a set of numerical models (Mike-21 modeling system). Deepwater waves as they approach shallow water dissipate energy and the water from the broken waves flow parallel to the shoreline known as longshore current. In order to simulate the current from wave breaking, offshore wave data for the period 1995–2004, have been collected from British Meteorological Office (BMO), UK. Waves having an annual exceedance of 20% are allowed to propagate to nearshore using a nearshore spectral wind-wave model from predominant directions. The wave-induced radiation stress obtained from wave model then formed the basis for simulating the longshore current and associated sediment transport. The results of these simulations show the pattern of longshore flow and sedimentation. The net annual discharge at selected coastal stretches is estimated and presented. It has been inferred from the study that the sediment transport for the coast is of the order of 0.4–0.6 million m³/year.     

A robust WENO scheme for nonlinear waves in a moving reference frame

For robust nonlinear wave simulation in a moving reference frame, we recast the free surface problem in Hamilton-Jacobi form and propose a Weighted Essentially Non-Oscillatory(WENO) scheme to automatically handle the upwinding of the convective term. A new automatic procedure for deriving the linear WENO weights based on a Taylor series expansion is introduced. A simplified smoothness indicator is proposed and is shown to perform well. The scheme is combined with high-order explicit Runge-Kutta time integration and a dissipative Lax-Friedrichs-type flux to solve for nonlinear wave propagation in a moving frame of reference. The WENO scheme is robust and less dissipative than the equivalent order upwind-biased finite difference scheme for all ratios of frame of reference to wave propagation speed tested. This provides the basis for solving general nonlinear wave-structure interaction problems at forward speed.     

Modeling of random wave transformation with strong wave-induced coastal currents

The propagation and transformation of multi-directional and uni-directional random waves over a coast with complicated bathymetric and geometric features are studied experimentally and numerically. Laboratory investigation indicates that wave energy convergence and divergence cause strong coastal currents to develop and inversely modify the wave fields. A coastal spectral wave model, based on the wave action balance equation with diffraction effect （WABED）, is used to simulate the transformation of random waves over the complicated bathymetry. The diffraction effect in the wave model is derived from a parabolic approximation of wave theory, and the mean energy dissipation rate per unit horizontal area due to wave breaking is parameterized by the bore-based formulation with a breaker index of 0.73. The numerically simulated wave field without considering coastal currents is different from that of experiments, whereas model results considering currents clearly reproduce the intensification of wave height in front of concave shorelines.     

波流共同作用下细沙粉沙质海岸复合沿岸输沙率计算

应用能量原理建立波浪作用下沿岸输沙率公式时,通常采用波浪的“载沙量”与沿岸流的乘积推导而得.对于一般的沙质海岸,由于岸滩坡度较陡,波浪破碎带较窄,破波带内潮流流速与破波产生的沿岸流相比较小,常可忽略.而对于细沙粉沙质海岸,岸滩坡度相对较缓,风暴潮期间,近岸波浪较大,破波水深较深,破波带较宽,近岸潮流流速也较大.因此,细沙粉沙质海岸风暴潮期间波浪和潮流共同作用下的复合沿岸输沙率计算应当考虑波浪和潮流的共同作用.在以往波浪作用下沙质海岸沿岸输沙率研究的基础上,通过波浪潮流共同作用下近岸水流特性和沿岸输沙率特性港池试验研究,得出了波流共同作用下复合沿岸流计算公式,据此,将能量输沙原理导出的沿岸输沙率计算公式推广应用到波流共同作用下的复合沿岸输沙率计算,经与模型试验结果和现场实测资料对比,吻合良好.该公式可以有条件地推广应用到细沙粉沙质海岸波浪潮流共同作用下复合沿岸输沙率计算.     

A new three-dimensional finite-volume non-hydrostatic shock-capturing model for free surface flow

In this paper a new finite-volume non-hydrostatic and shock-capturing three-dimensional model for the simulation of wave-structure interaction and hydrodynamic phenomena(wave refraction, diffraction, shoaling and breaking) is proposed. The model is based on an integral formulation of the Navier-Stokes equations which are solved on a time dependent coordinate system: a coordinate transformation maps the varying coordinates in the physical domain to a uniform transformed space. The equations of motion are discretized by means of a finite-volume shock-capturing numerical procedure based on high order WENO reconstructions. The solution procedure for the equations of motion uses a third order accurate Runge-Kutta(SSPRK) fractional-step method and applies a pressure corrector formulation in order to obtain a divergence-free velocity field at each stage. The proposed model is validated against several benchmark test cases.     

TESTS AND APPLICATIONS OF A BOUSSINESQ MODEL WITH AMBIENT CURRENT

A new type Boussinesq model is proposed and applied for wave propagation in a wave flume of uniform depth and over a submerged bar with current present or absent, respectively. Firstly, for the propagation of monochromatic incident wave with current absent, the Boussinesq model is tested in its complete form, and in a form without the introduction of utility velocity variables. It is validated that the introduction of utility velocity variables can improve the characteristics of velocity field, dispersion and nonlinearity. Both versions of the Boussinesq models are of higher accuracy than the fully-nonlinear fourth-order model, which is one of the best forms among the existing traditional Boussinesq models that do not incorporate breaking mechanism in one dimension. Secondly, the Boussinesq model in its complete form is applied to simulating the propagation of bichromatic incident waves with current present or absent, respectively, and the modeled results are compared to the analytical ones or the experimental ones. The modeled results are reasonable in the case of inputting bichromatic incident waves with the strong opposing current present.     

NUMERICAL SIMULATION OF WAVE-INDUCED CURRENT WITH VERTICALLY VARIED RADIATION STRESS

This article analyzes the vertical structure of the onshore current including the wave-induced current by an equation developed for the radiation stress against water depth. A coupled model COHERENS-SED is adopted to calculate the wave, tidal current, wave-induced current and sediment simultaneously. By applying the new model to Yangpu Bay, its reliability is verified. Then an ideal coastal domain is defined to simulate the nearshore current and wave setup with normal incident waves. The numerical and experimental results for the vertical structure show two undertows, also a visible setup in the surf zone. It demonstrates the importance of the radiation stress in wave-induced currents and mean water levels (set-up/down).     

High effective WENO scheme for transonic inviscid flow computation on a helicopter rotor in hover

A high-order upwind scheme with high efficiency has been developed to compute the inviscid flow of a helicopter rotor in hover. For rotary-wing wake capturing, an improved fifth-order weighted essentially non-oscillatory (WENO) scheme is adopted to interpolate higher order left and right states across a cell interface with Roe Riemann solver updating inviscid flux. To improve the efficiency and convergence to steady state, three-level V-cycle multigrid relaxation scheme is used. The performance of the schemes is investigated in a transonic inviscid flow around hovering rotor. The results reveal that WENO has the great capabilities to capture shock with high resolution and has a lower numerical dissipation than MUSCL for capturing wake vorticity. Moreover, multigrid scheme can accelerate convergence to a great extent.

     

基于WENO格式的天然河道丁坝群二维水流数值模拟

本文应用高精度WENO(Weighted Essentially Non-oscillatory Schemes)格式结合有限体积法建立了河道丁坝群二维水流的数学模型。采用此模型对实际天然河道丁坝群水流水力特性进行了数值模拟,得到了流速场的分布,并与物理模型试验结果进行比较,表明这类格式精度高,稳定性能好,能够有效地计算复杂边界天然河道丁坝群二维水流水力特性问题。     

Numerical simulation of the internal wave propagation in continuously densitystratified ocean

A numerical model is proposed to simulate the internal wave propagation in a continuously density-stratified ocean, and in the model, the momentum equations are derived from the Euler equations on the basis of the Boussinesq approximation. The governing equations, including the continuity equation and the momentum equations, are discretized with the finite volume method. The advection terms are treated with the total variation diminishing （TVD） scheme, and the SIMPLE algorithm is employed to solve the discretized governing equations. After the modeling test, the suitable TVD scheme is selected. The SIMPLE algorithm is modified to simplify the calculation process, and it is easily made to adapt to the TVD scheme. The Sommerfeld＇s radiation condition combined with a sponge layer is adopted at the outflow boundary. In the water flume with a constant water depth, the numerical results are compared to the analytical solutions with a good agreement. The numerical simulations are carried out for a wave flume with a submerged dike, and the model results are analyzed in detail. The results show that the present numerical model can effectively simulate the propagation of the internal wave.     

NUMERICAL SIMULATION OF TWO-PHASE GRAVITY CURRENTS OVER A POROUS SUBSTRATE

1 .　INTRODUCTIONGravitycurrentsoccurinmanysituationsaris inginbothindustrialandnaturalsettings[1 2 ] .Commonlythecurrentisdrivenbycompositionalortemperaturedifference ,toleadtoahomoge nouscurrent ,orbysuspended particulatematter ,toleadtoaparticle drivencurrent.Combinationsbybothparticleandcompositionalortemperaturedifferencecanalsooccur[3] .Mostoftheresearchesareconcentratedonthesituationswherethecur rentsflowaboveanimpermeableboundary .How evertherearemanyimportantcaseswheregravitycurr…     

基于抛物型缓坡方程模拟近岸波流场

波浪向近岸传播的过程中由波浪破碎等效应所形成的近岸波流场是近岸缓坡区域重要的环境动力因素之一。本文基于近岸波浪传播的缓坡模型对近岸波浪场及近岸波浪斜向入射破碎后所产生的沿岸波流场进行了数值模拟。考虑到波浪向近岸传播中局部复杂区域波向不易确定，计算时直接从波浪辐射应力定义出发，采用抛物型缓坡方程所给出的辐射应力公式来计算波浪产生的辐射应力，在此基础上耦合近岸波流场数学模型对近岸波浪破碎形成的波流场进行了数值模拟研究，结果表明本文的数值模型是有效的。     

浅水问题动边界数值模拟

采用基于准确Riemann解的Godunov格式求解浅水流动方程，将仅适用于平底的干底Riemann解推广到处理非平底动边界问题．在计算干底溃坝波的基础上，将该方法应用到有大片滩地的钱塘江河口涌潮计算中，能较好地模拟钱塘江涌潮在滩地上的传播过程．     

基于三角形网格的浅水间断流动泥沙输移数值模拟

浅水间断流动条件下泥沙输移具有广阔的工程应用背景.采用基于准确Riemann解的Godunov格式求解法向数值通量,应用干底Riemann解计算动边界问题,建立了基于无结构三角形网格空间二阶精度的二维水流和泥沙输移有限体积法数值模型.模型在纯对流问题检验的基础上,模拟了孤立波在滩面上传播变形以及对圆柱周围的局部冲刷,复演了孤立波变形后流场和泥沙场突变的过程,并且圆柱周围局部冲刷坑计算结果与实验基本吻合.     

波流作用的近岸圆柱局部床面侵蚀

波浪流对近岸浅水带床面作用强烈,该区域结构物局部床面侵蚀显著,潜存致灾威胁。用三维数值方法研究了瞬态孤立波作用下非黏性沙海床上的近岸圆柱体局部冲刷规律,分析了波浪流冲刷的3类主要影响要素,讨论了近岸地形条件影响下的波流冲刷深度。研究认为,表征浅水波流特征和柱体尺度的无量纲数Urp与KC数存在非独立关系,二者均能分别反映波流冲刷的主要规律;表示泥沙运动的力学参数Shields数在波流动床条件下仍对柱体局部冲刷有贡献;近岸地形通过床面坡度对波破碎的增强及堤岸挡墙对波浪的反射,都会影响到局部冲刷。     

淤泥质海岸环抱式港池口门布置方案研究

以资料分析为基础,利用数学模型计算分析的手段,针对当地旋转流和黏性泥沙的运动特性,从水流、泥沙角度对连云港徐圩港区港池布置方案中的口门位置、口门宽度和布置形式进行了论证。分析认为,由于岸滩坡度较缓,大风天破波带影响范围较广,同时被波浪掀起的细颗粒泥沙可被潮流远距离输送,因此从减小泥沙回淤角度来看,港池应采用双环抱形式,而口门应布置在连云港理论基准面高程-5 m(破波区)以外,以此可以降低破波带内悬浮泥沙进入港池和外航道的可能性。同时分析论证认为,初期方案口门不宜过窄,以减小口门的水流强度;口门采用"八字"型布置,可以提高口门航道船舶航行和近口门泊位靠离泊的安全性。上述港池布置方案建议已被设计院接受并在实施方案中体现,可供类似港口布置方案借鉴参考。