A Wave Superposition-Finite Element Method for Calculating the Radiated Noise Generated by Volumetric Targets in Shallow Water

A combined method of wave superposition and finite element is proposed to solve the radiation noise of targets in shallow sea.Taking the sound propagation of spherical sound source in shallow sea as an example,the radiation sound field of the spherical sound source is equivalent to the linear superposition of the radiation sound field of several internal point sound sources,and then the radiated noise induced by spherical sound source can be predicted quickly.The accuracy and efficiency of the method are verified by comparing with the numerical results of finite element method,and the rapid prediction of underwater radiated noise of cylindrical shell is carried out based on the method.The results show that compared with the finite element method,the relative error of the calculation results under different simulation conditions does not exceed 0.1%,and the calculation time is about 1/10 of the finite element method,so this method can be used to solve the radiated noise of shallow underwater targets.

Entropy‑Conservative Discontinuous Galerkin Methods for the Shallow Water Equations with Uncertainty

In this paper,we develop an entropy-conservative discontinuous Galerkin(DG)method for the shallow water(SW)equation with random inputs.One of the most popular methods for uncertainty quantifcation is the generalized Polynomial Chaos(gPC)approach which we consider in the following manuscript.We apply the stochastic Galerkin(SG)method to the stochastic SW equations.Using the SG approach in the stochastic hyperbolic SW system yields a purely deterministic system that is not necessarily hyperbolic anymore.The lack of the hyperbolicity leads to ill-posedness and stability issues in numerical simulations.By transforming the system using Roe variables,the hyperbolicity can be ensured and an entropy-entropy fux pair is known from a recent investigation by Gerster and Herty(Commun.Comput.Phys.27(3):639–671,2020).We use this pair and determine a corresponding entropy fux potential.Then,we construct entropy conservative numerical twopoint fuxes for this augmented system.By applying these new numerical fuxes in a nodal DG spectral element method(DGSEM)with fux diferencing ansatz,we obtain a provable entropy conservative(dissipative)scheme.In numerical experiments,we validate our theoretical fndings.

A CFD Model to Evaluate Near-Surface Oil Spill from a Broken Loading Pipe in Shallow Coastal Waters

Oil spills continue to generate various issues and concerns regarding their effect and behavior in the marine environment,owing to the related potential for detrimental environmental,economic and social implications.It is essential to have a solid understanding of the ways in which oil interacts with the water and the coastal ecosystems that are located nearby.This study proposes a simplified model for predicting the plume-like transport behavior of heavy Bunker C fuel oil discharging downward from an acutely-angled broken pipeline located on the water surface.The results show that the spill overall profile is articulated in three major flow areas.The first,is the source field,i.e.,a region near the origin of the initial jet,followed by the intermediate or transport field,namely,the region where the jet oil flow transitions into an underwater oil plume flow and starts to move horizontally,and finally,the far-field,where the oil re-surface and spreads onto the shore at a significant distance from the spill site.The behavior of the oil in the intermediate field is investigated using a simplified injection-type oil spill model capable of mimicking the undersea trapping and lateral migration of an oil plume originating from a negatively buoyant jet spill.A rectangular domain with proper boundary conditions is used to implement the model.The Projection approach is used to discretize a modified version of the Navier-Stokes equations in two dimensions.A benchmark fluid flow issue is used to verify the model and the results indicate a reasonable relationship between specific gravity and depth as well as agreement with the aerial data and a vertical temperature profile plot.

A Numerical Study of Riemann Problem Solutions for the Homogeneous One-Dimensional Shallow Water Equations

The solution of the Riemann Problem (RP) for the one-dimensional (1D) non-linear Shallow Water Equations (SWEs) is known to produce four potential wave patterns for the scenario where the water depth is always positive. In this paper, we choose four test problems with exact solutions for the 1D SWEs. Each test problem is a RP with one of the four possible wave patterns as its solution. These problems are numerically solved using schemes from the family of Weighted Essentially Non-Oscillatory (WENO) methods. For comparison purposes, we also include results obtained from the Random Choice Method (RCM). This study has three main objectives. Firstly, we outline the procedures for the implementation of the methods employed in this paper. Secondly, we assess the performance of the schemes in conjunction with a second-order Total Variation Diminishing (TVD) flux on a variety of RPs for the 1D SWEs (for both short- and long-time simulations). Thirdly, we investigate if a single method yields optimal outcomes for all test problems. Optimal outcomes refer to numerical solutions devoid of spurious oscillations, exhibiting high resolution of discontinuities, and attaining high-order accuracy in the smooth parts of the solution.

A Well-Balanced Active Flux Method for the Shallow Water Equations with Wetting and Drying

Active Flux is a third order accurate numerical method which evolves cell averages and point values at cell interfaces independently.It naturally uses a continuous reconstruction,but is stable when applied to hyperbolic problems.In this work,the Active Flux method is extended for the first time to a nonlinear hyperbolic system of balance laws,namely,to the shallow water equations with bottom topography.We demonstrate how to achieve an Active Flux method that is well-balanced,positivity preserving,and allows for dry states in one spatial dimension.Because of the continuous reconstruction all these properties are achieved using new approaches.To maintain third order accuracy,we also propose a novel high-order approximate evolution operator for the update of the point values.A variety of test problems demonstrates the good performance of the method even in presence of shocks.

Shallow Water Effects on Surge Motion and Load of Soft Yoke Moored FPSO

Much attention should be paid to a large FPSO moored permanently in an oil field with water depth of only about 20 m, since shallow water effects on the hydrodynamics may bring about collision and damage. A 160kDWT FPSO with a permanent soft yoke mooring system is investigated with various shallow water depths and focuses are the low frequency surge motion and mooring load. Computation for the FPSO system is made based on linear 3-D potential fluid theory and time-domain numerical simulation method. Corresponding model test is carried out in the ocean engineering basin of Shanghai Jiao Tong University. It is shown that, in the surge natural period, low frequency surge motion and mooring force increase remarkably with the decrease of water depth. Especially, the smaller the ratio of water depth and draught is, the quicker the increase is. The shallow water effects should be taken into account carefully for determining the design load of a single point mooring system.

Wave Numerical Model for Shallow Water

The history of forecasting wind waves by wave energy conservation equation Is briefly described. Several currently used wave numerical models for shallow water based on different wave theories are discussed. Wave energy conservation models for the simulation of shallow water waves are introduced, with emphasis placed on the SWAN model, which takes use of the most advanced wave research achievements and has been applied to several theoretical and field conditions. The characteristics and applicability of the model, the finite difference numerical scheme of the action balance equation and its source terms computing methods are described in detail. The model has been verified with the propagation refraction numerical experiments for waves propagating in following and opposing currents; finally, the model is applied to the Haian Gulf area to simulate the wave height and wave period field there, and the results are compared with observed data.

Two-dimensional shallow water equations with porosity and their numerical scheme on unstructured grids

In this study, porosity was introduced into two-dimensional shallow water equations to reflect the effects of obstructions, leading to the modification of the expressions for the flux and source terms. An extra porosity source term appears in the momentum equation. The numerical model of the shallow water equations with porosity is presented with the finite volume method on unstructured grids and the modified Roe-type approximate Riemann solver. The source terms of the bed slope and porosity are both decomposed in the characteristic direction so that the numerical scheme can exactly satisfy the conservative property. The present model was tested with a dam break with discontinuous porosity and a flash flood in the Toce River Valley. The results show that the model can simulate the influence of obstructions, and the numerical scheme can maintain the flux balance at the interface with high efficiency and resolution.

Correction for Depth Biases to Shallow Water Multibeam Bathymetric Data

Vertical errors often present in multibeam swath bathymetric data. They are mainly sourced by sound refraction, internal wave disturbance, imperfect tide correction, transducer mounting, long period heave, static draft change, dynamic squat and dynamic motion residuals, etc. Although they can be partly removed or reduced by specific algorithms, the synthesized depth biases are unavoidable and sometimes have an important influence on high precise utilization of the final bathymetric data. In order to. confidently identify the decimeter-level changes in seabed morphology by MBES, we must remove or weaken depth biases and improve the precision of multibeam bathymetry further. The fixed-interval profiles that are perpendicular to the vessel track are generated to adjust depth biases between swaths. We present a kind of postprocessing method to minimize the depth biases by the histogram of cumulative depth biases. The datum line in each profile can be obtained by the maximum value of histogram. The corrections of depth biases can be calculated according to the datum line. And then the quality of final bathymetry can be improved by the corrections. The method is verified by a field test.

HYBRID FINITE ANALYTIC SOLUTIONS OF SHALLOW WATER CIRCULATION

The hybrid finite analytic(HFA) method is a kind of numerical scheme in rectangular element. In order to simulate the shallow circulation in irregular bathymetry by HFA scheme, the model in sigma coordinate system was obtained. The model has been tested against three cases: 1) Wind induced circulation; 2) Density driven circulation and 3) Seiche oscillation. The results obtained in the present study compare well with those obtained from the corresponding analytical solutions under idealized for the above three cases. The hybrid finite analytic method and the circulation model in sigma coordinate system can be used calculate the flow and water quality in estuaries and coastal waters.

Nonlinear Effect of Wave Propagation in Shallow Water

In this paper, a nonlinear model is presented to describe wave transformation in shallow water with the zero- vorticity equation of wave- number vector and energy conservation equation. The nonlinear effect due to an empirical dispersion relation (by Hedges) is compared with that of Dalrymple's dispersion relation. The model is tested against the laboratory measurements for the case of a submerged elliptical shoal on a slope beach, where both refraction and diffraction are significant. The computation results, compared with those obtained through linear dispersion relation, show that the nonlinear effect of wave transformation in shallow water is important. And the empirical dispersion relation is suitable for researching the nonlinearity of wave in shallow water.

Modified (2+1)-dimensional displacement shallow water wave system and its approximate similarity solutions

Recently, a new （2＋1）-dimensional shallow water wave system, the （2＋1）-dlmenslonal displacement shallow water wave system （2DDSWWS）, was constructed by applying the variational principle of the analytic mechanics in the Lagrange coordinates. The disadvantage is that fluid viscidity is not considered in the 2DDSWWS, which is the same as the famous Kadomtsev-Petviashvili equation and Korteweg-de Vries equation. Applying dimensional analysis, we modify the 2DDSWWS and add the term related to the fluid viscidity to the 2DDSWWS. The approximate similarity solutions of the modified 2DDSWWS （M2DDSWWS） is studied and four similarity solutions are obtained. For the perfect fluids, the coefficient of kinematic viscosity is zero, then the M2DDSWWS will degenerate to the 2DDSWWS.

Habitat suitability of Scapharca subcrenata (Lischke) inthe shallow water of the Xiaoheishan Island

The habitat suitability index(HSI) model was used to identify potential sites for sustainable restoration of ark shell, Scapharca subcrenata(Lischke), in the shallow water of Xiaoheishan Island, using a geographic information system framework. The seven input variables of the HSI model were sediment composition, water temperature, salinity, dissolved oxygen, water depth, p H, and ammonia. A non-linear suitability function for each variable factor was used to transform the value into a normalized quality index ranging from 0(nonsuitability) to 1(best suitability). In present study, the analysis of habitat suitability was conducted for four seasons respectively. The majority of the study area has a high HSI value(>0.6) year round, which implies a strong suitability for restoration, with the optimal habitat located on the eastern side of the island.Correspondence analysis indicated that water temperature was the main factor causing seasonal variation,while sediment composition and water depth were the two major reasons for the differences in sites. The results of this work could provide support for restoration decision making through identification of potential sites for sustainable establishment of S. subcrenata.

Wind-Driven Ocean Circulation in Shallow Water Lattice Boltzmann Model

A lattice Boltzmann (LB) model with overall second-order accuracy is applied to the 1.5-layer shallow water equation for a wind-driven double-gyre ocean circulation. By introducing the second-order integral approximation for the collision operator, the model becomes fully explicit. In this case, any iterative technique is not needed. The Coriolis force and other external forces are included in the model with second-order accuracy, which is consistent with the discretized accuracy of the LB equation. The numerical results show correct physics of the ocean circulation driven by the double-gyre wind stress with different Reynolds numbers and different spatial resolutions. An intrinsic low-frequency variability of the shallow water model is also found. The wind-driven ocean circulation exhibits subannual and interannual oscillations, which are comparable to those of models in which the conventional numerical methods are used.

A New Wetting and Drying Method for Moving Boundary in Shallow Water Flow Models

To deal with the moving boundary hydrodynamic problems of the tidal flats in shallow water flow models, a new wetting and drying （WD） method is proposed. In the new method, a ＂predicted water depth＂ is evaluated explicitly based on the simplified shallow water equations and used to determine the status （wet or dry） together with the direction of flow. Compared with previous WD method, besides the water elevation, more factors, such as the flow velocity and the surface shear stress, are taken into account in the new method to determine the moving boundary. In addition, a formula is deduced to determine the threshold, as critical water depth, which needs to be preset before simulations. The new WD method is tested with five cases including three 1D ones and two 2D ones. The results show that the new WD method can simulate the wetting and drying process, in beth typical and practical cases, with smooth manner and achieves effective estimation of the retention volume at shallow water body.

Simulation of Wetting and Drying Processes in A Depth Integrated Shallow Water Flow Model by Slot Method

A particular porosity method named ＂slot method＂ is implemented in a depth-integrated shallow water flow model （DIVAST） to simulate wetting and drying processes. Discussed is the relationship between the shape factors of the ＂slot＂ and the preset depth used in ＂wetting-drying＂ algorithm. Two typical tests are conducted to examine the performance of the method with the effect of the shape factors of the ＂slot＂ being checked in detail in the first test. Numerical results demonstrate that： 1 ） no additional effort to improve the finite difference scheme is needed to implement ＂slot method＂ in DIVAST, and 2） ＂slot method＂ will simulate wetting and diying processes correctly if the shape factors of the ＂slot＂ being selected properly.

An Explicit High Resolution Scheme for Nonlinear Shallow Water Equations

The present study develops a numerical model of the two-dimensional fully nonlinear shallow water equations （NSWE） for the wave run-up on a beach. The finite volume method （FVM） is used to solve the equations, and a second-order explicit scheme is developed to improve the computation efficiency. The numerical fluxes are obtained by the two dimensional Roe＇ s flux function to overcome the errors caused by the use of one dimensional fluxes in dimension splitting methods. The high-resolution Godunov-type TVD upwind scheme is employed and a second-order accuracy is achieved based on monotonic upstream schemes for conservation laws （MUSCL） variable extrapolation; a nonlinear limiter is applied to prevent unwanted spurious oscillation. A simple but efficient technique is adopted to deal with the moving shoreline boundary. The verification of the solution technique is carried out by comparing the model output with documented results and it shows that the solution technique is robust.

SELF-SIMILAR SOLUTIONS AND BLOW-UP PHENOMENA FOR A TWO-COMPONENT SHALLOW WATER SYSTEM

In this article, we consider a two-component nonlinear shallow water system, which includes the famous 2-component Camassa-Holm and Degasperis-Procesi equations as special cases. The local well-posedess for this equations is established. Some sufficient conditions for blow-up of the solutions in finite time are given. Moreover, by separation method, the self-similar solutions for the nonlinear shallow water equations are obtained, and which local or global behavior can be determined by the corresponding Emden equation.

Experimental Study of Wave Energy Spectrum in Shallow Water

Wave energy spectrum in shallow water can be studied in wind wave channel in combination with irregular wave- maker. Fetch length is successfully extended and by 'Relay' method the corresponding spectrum pattern and the wind velocity scale are obtained.

Moving-Water Equilibria Preserving HLL-Type Schemes for the Shallow Water Equations

We construct new HLL-type moving-water equilibria preserving upwind schemes for the one-dimensional Saint-Venant system of shallow water equations with nonflat bottom topography.The designed first-and secondorder schemes are tested on a number of numerical examples,in which we verify the well-balanced property as well as the ability of the proposed schemes to accurately capture small perturbations of moving-water steady states.