共查询到20条相似文献，搜索用时 362 毫秒
1.
A two-dimensional vertical (2DV) non-hydrostatic boundary fitted model based on a Godunov-type shock-capturing scheme is introduced and applied to the simulation of waves from deep water up to the swash zone. The effects of shoaling, breaking, surf zone dissipation and swash motions are considered. The application of a Godunov-type shock-capturing algorithm together with an implicit solver on a standard staggered grid is proposed as a new approach in the 2DV simulation of large gradient problems such as wave breaking and hydraulic jumps. The complete form of conservative Reynolds averaged Navier–Stokes (RANS) equations are solved using an implicit finite volume method with a pressure correction technique. The horizontal advection of the horizontal velocity is solved by an explicit predictor–corrector method. Fluxes are predicted by an exact Riemann solver and corrected by a downwind scheme. A simple total variation diminishing (TVD) method with a monotonic upstream-centered scheme for conservation laws (MUSCL) limiter function is employed to eliminate undesirable oscillations across discontinuities. Validation of the model is carried out by comparing the results of the simulations with several experimental test cases of wave breaking and run-up and the analytical solution to linear short waves in deep water. Promising performance of the model has been observed. 相似文献
2.
Efficient computation of surf zone waves using the nonlinear shallow water equations with non-hydrostatic pressure 总被引：2，自引：0，他引：2
A numerical method for non-hydrostatic, free-surface, irrotational flow governed by the nonlinear shallow water equations including the effects of vertical acceleration is presented at the aim of studying surf zone phenomena. A vertical boundary-fitted grid is used with the water depth divided into a number of layers. A compact finite difference scheme is employed for accurate computation of frequency dispersion requiring a limited vertical resolution and hence, capable of predicting the onset of wave breaking. A novel wet–dry algorithm is applied for a proper handling of moving shoreline. Mass and momentum are strictly conserved at discrete level while the method only dissipates energy in the case of wave breaking. The numerical results are verified with a number of tests and show that the proposed model using two layers without ad-hoc assumptions enables to resolve propagating nonlinear shoaling, breaking waves and wave run-up within the surf and swash zones in an efficient manner. 相似文献
3.
This paper presents CCHE2D-NHWAVE, a depth-integrated non-hydrostatic finite element model for simulating nearshore wave processes. The governing equations are a depth-integrated vertical momentum equation and the shallow water equations including extra non-hydrostatic pressure terms, which enable the model to simulate relatively short wave motions, where both frequency dispersion and nonlinear effects play important roles. A special type of finite element method, which was previously developed for a well-validated depth-integrated free surface flow model CCHE2D, is used to solve the governing equations on a partially staggered grid using a pressure projection method. To resolve discontinuous flows, involving breaking waves and hydraulic jumps, a momentum conservation advection scheme is developed based on the partially staggered grid. In addition, a simple and efficient wetting and drying algorithm is implemented to deal with the moving shoreline. The model is first verified by analytical solutions, and then validated by a series of laboratory experiments. The comparison shows that the developed wave model without the use of any empirical parameters is capable of accurately simulating a wide range of nearshore wave processes, including propagation, breaking, and run-up of nonlinear dispersive waves and transformation and inundation of tsunami waves. 相似文献
4.
A hybrid finite-volume and finite-difference method is proposed for numerically solving the two-dimensional (2D) extended Boussinesq equations. The governing equations are written in such a way that the convective flux is approximated using finite volume (FV) method while the remaining terms are discretized using finite difference (FD) method. Multi-stage (MUSTA) scheme, instead of commonly used HLL or Roe schemes, is adopted to evaluate the convective flux as it has the simplicity of centred scheme and accuracy of upwind scheme. The third order Runge–Kutta method is used for time marching. Wave breaking and wet–dry interface are also treated in the model. In addition to model validation, the emphasis is given to compare the merits and limitations of using MUSTA scheme and HLL scheme in the model. The analytical and experimental data available in the literature have been used for the assessment. Numerical tests demonstrate that the developed model has the advantages of stability preserving, shock-capturing and numerical efficiency when applied in the complex nearshore region. Compared with that using HLL scheme, the proposed model has comparable numerical accuracy, but requires slightly less computation time and is much simpler to code. 相似文献
5.
In this paper we propose an integral form of the fully non-linear Boussinesq equations in contravariant formulation, in which Christoffel symbols are avoided, in order to simulate wave transformation phenomena, wave breaking and nearshore currents in computational domains representing the complex morphology of real coastal regions. Following the approach proposed by Chen (2006), the motion equations retain the term related to the approximation to the second order of the vertical vorticity. A new Upwind Weighted Essentially Non-Oscillatory scheme for the solution of the fully non-linear Boussinesq equations on generalised curvilinear coordinate systems is proposed. The equations are rearranged in order to solve them by a high resolution hybrid finite volume–finite difference scheme. The conservative part of the above-mentioned equations, consisting of the convective terms and the terms related to the free surface elevation, is discretised by a high-order shock-capturing finite volume scheme in which an exact Riemann solver is involved; dispersive terms and the term related to the approximation to the second order of the vertical vorticity are discretised by a cell-centred finite difference scheme. The shock-capturing method makes it possible to intrinsically model the wave breaking, therefore no additional terms are needed to take into account the breaking related energy dissipation in the surf zone. The model is verified against several benchmark tests, and the results are compared with experimental, theoretical and alternative numerical solutions. 相似文献
6.
A higher-order non-hydrostatic model in a σ-coordinate system is developed. The model uses an implicit finite difference scheme on a staggered grid to simultaneously solve the unsteady Navier-Stokes equations (NSE) with the free-surface boundary conditions. An integral method is applied to resolve the top-layer non-hydrostatic pressure, allowing for accurately resolving free-surface wave propagation. In contrast to the previous work, a higher-order spatial discretization is utilized to approximate the large horizontal pressure gradient due to steep surface waves or rapidly varying topographies. An efficient direct solver is developed to solve the resulting block hepta-diagonal matrix system. Accuracy of the new model is validated by linear and nonlinear standing waves and progressive waves. The model is then used to examine freak (extreme) waves. Features of downshifting focusing location and wave asymmetry characteristics are predicted on the temporal and spatial domains of a freak wave. 相似文献
7.
In the present study,a semi-implicit finite difference model for non-bydrostatic,free-surface flows is analyzed and discussed.The governing equations are the three-dimensional free-surface Reynolds-averaged Navier-Stokes equations defined on a general,irregular domain of arbitrary scale.At outflow,a combination of a sponge layer technique and a radiation boundary condition is applied to minimize wave reflection.The equations are solved with the fractional step method where the hydrostatic pressure component is determined first,while the non-hydrostatic component of the pressure is computed from the pressure Poisson equation in which the coefficient matrix is positive definite and symmetric.The advectiou and horizontal viscosity terms are discretized by use of a semi-Lagrangian approach.The resulting model is computationally efficient and unrestricted to the CFL condition.The developed model is verified against analytical solutions and experimental data,with excellent agreement. 相似文献
8.
A higher-efficient three-dimensional numerical model for small amplitude free surface flows 总被引：1，自引：0，他引：1
A higher-efficient three-dimensional non-hydrostatic model is developed to simulate small amplitude free surface flows based on a staggered unstructured grid. In this model, a fractional step algorithm is adopted to solve the Navier-Stokes equations in two major steps. A top-layer pressure method is proposed to minimize the number of vertical layers and subsequently the computational cost. Three classical examples of small amplitude free surface flows are used to demonstrate the capability and efficiency of the model. The satisfactory results demonstrated the capability and efficiency of modelling a range of small amplitude free surface flows with only a small number of vertical layers. 相似文献
9.
A non-hydrostatic algorithm for the Regional Oceanic Modeling System (ROMS) is proposed. It is based on a decomposition technique for hydrostatic and non-hydrostatic pressure. The algorithm has a pressure-correction scheme with split-explicit time-stepping for baroclinic and barotropic vertical modes with a free surface. The algorithm implementation requires solving a Poisson equation for a non-hydrostatic pressure that has a non-symmetric matrix in discrete form. The efficiency of a different class of solvers and preconditioners were tested. The algorithm is successfully implemented with several examples where non-hydrostatic effects are important. These include standing external gravity waves; strongly nonlinear internal wave generation and transformation; stratified shear instability and its associated mixing; and nonlinear internal tidal generation over a ridge. The corresponding changes in the pre-processing and post-processing infrastructure in the existing hydrostatic ROMS code were performed to implement parallel elliptic solvers and a new set of dynamical equations. 相似文献
10.
Finite volume scheme for the solution of 2D extended Boussinesq equations in the surf zone 总被引：2，自引：0，他引：2
In this paper, a hybrid finite volume-finite difference scheme is applied to study surf zone dynamics. The numerical model solves the 2DH extended Boussinesq equations proposed by Madsen and Sørensen (1992) where nonlinear and dispersive effects are both relevant whereas it solves NSWE equations where nonlinearity prevails. The shock-capturing features of the finite volume method allow an intrinsic representation of wave breaking and runup; therefore no empirical (calibration) parameters are necessary. Comparison with laboratory measurements demonstrates that the proposed model can accurately predict wave height decay and mean water level setup, for both regular and solitary wave breaking on a sloping beach. The model is also applied to reproduce two-dimensional wave transformation and breaking over a submerged circular shoal, showing good agreement with experimental data. 相似文献
11.
为建立高效的Boussinesq类水波数值模型,提出了一种新型的、基于有限差分和有限体积方法的混合数值格式。针对守恒形式的一维控制方程,在等间距矩形控制体内对其进行积分并离散,采用有限体积方法计算界面数值通量,剩余源项采用有限差分方法计算。其中,采用MUSTA格式并结合高精度状态插值方法计算控制体界面数值通量。时间积分则采用具有TVD性质的三阶龙格-库塔多步积分法进行。除验证模型外,重点对MUSTA格式和广泛使用的HLL格式进行了比较。结果表明,MUSTA格式可用于Boussinesq类水波方程数值求解,综合考虑数值精度、计算效率、程序编制和实际应用这几个方面,其较HLL格式更具有优势。 相似文献
12.
In this paper, a hybrid scheme based on a set of 2DH extended Boussinesq equations for slowly varying bathymetries is introduced. The numerical code combines the finite volume technique, applied to solve the advective part of the equations, with the finite difference method, used to discretize dispersive and source terms. Time integration is performed using the fourth-order Adams–Bashforth–Moulton predictor–corrector method; the Riemann problem is solved employing an approximate HLL solver, a fourth-order MUSCL-TVD technique is applied. Five test cases, for non-breaking and breaking waves, are reproduced to verify the model comparing its results to laboratory data or analytical solutions. 相似文献
13.
In order to solve unsteady incompressible Navier–Stokes(N–S) equations, a new stabilized finite element method,called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split into diffusive and convective parts in each time step. The diffusive part is discretized by the backward difference method in time and discretized by the standard Galerkin method in space. The convective part is a first-order nonlinear equation.After the linearization of the nonlinear part by Newton's method, the convective part is also discretized by the backward difference method in time and discretized by least square scheme in space. C~0-type element can be used for interpolation of the velocity and pressure in the present model. Driven cavity flow and flow past a circular cylinder are conducted to validate the present model. Numerical results agree with previous numerical results, and the model has high accuracy and can be used to simulate problems with complex geometry. 相似文献
14.
Presented here is a compact explicit difference scheme of high accuracy for solving the extended Boussinesq equations.For time discretization,a three-stage explicit Runge-Kutta method with TVD property is used at predicting stage,a cubic spline function is adopted at correcting stage,which made the time discretization accuracy up to fourth order;For spatial discretization,a three-point explicit compact difference scheme with arbitrary order accuracy is employed.The extended Boussinesq equations derived by Beji and Nadaoka are solved by the proposed scheme.The numerical results agree well with the experimental data.At the same time,the comparisons of the two numerical results between the present scheme and low accuracy difference method are made,which further show the necessity of using high accuracy scheme to solve the extended Boussinesq equations.As a valid sample,the wave propagation on the rectangular step is formulated by the present scheme,the modelled results are in better agreement with the experimental data than those of Kittitanasuan. 相似文献
15.
A two dimensional implicit finite volume scheme for solving the shallow-water equations is developed. The effects of the Coriolis force, surface wind stress, and waves are included. A non-uniform rectilinear forward staggered grid is used with Cartesian coordinates. The time integration is performed using the Euler implicit technique. The convective flux is treated using the deferred correction method. The viscous terms are discretized using a second order central difference approximation. The SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm is used for coupling the velocity components and the water elevation gradient for the water level correction. The system of equations is solved sequentially using the Strongly Implicit Procedure (SIP). To simulate wave driven current, a phase averaged wave model is used first to simulate wave transformation and calculate radiation stresses. The performance of the developed model is validated for different sources of external forces and different combinations of boundary conditions. The validation cases include tidal circulation in a harbor and wave induced currents behind a breakwater parallel to the coastline. The model is finally applied to simulate the flow pattern in a closed artificial lagoon and along the coastline near Damietta Port located along the Northern coast of Egypt. Results of the developed model agree well with the published results for the considered cases. 相似文献
16.
Francis Auclair Claude Estournel Jochem W. Floor Marine Herrmann Cyril Nguyen Patrick Marsaleix 《Ocean Modelling》2011,36(1-2):49-70
An original implementation of a non-hydrostatic, free-surface algorithm based on a pressure correction method is proposed for ocean modelling. The free surface is implemented through an explicit scheme combined with a mode-spitting method but the depth-averaged velocity and the position of the free surface are updated at each non-hydrostatic iteration. The vertical momentum equation is also integrated up to the surface enabling a natural and accurate treatment of the surface layer. The consistent specification of the numerical schemes provides balanced transfers of potential and kinetic energy. This algorithm is well-suited for implementation as a non-hydrostatic kernel on originally hydrostatic free-surface ocean models such as Symphonie (http://poc.obs-mip.fr/pages/research_topics/modelling/symphonie/symphonie.htm) for which it has originally been developed.Energy balances associated with the propagation of short surface waves and solitary waves are presented for two dedicated well-documented configurations over closed domains. The buoyancy flux, the work rate of the pressure force together with the power of the advective terms are evaluated and discussed for the generation and the propagation of these two types of waves. The dissipation rate is in particular shown to be several orders of magnitude smaller than the work rates of the hydrostatic and non-hydrostatic pressure forces confirming the necessity for the exchanges of energy to be numerically balanced. The algorithm is subsequently applied to the complex generation of non-linear solitary internal waves by surface tides over Georges Bank, in the Gulf of Maine. The generation and the propagation of the observed non-linear and non-hydrostatic features in this region are correctly reproduced. 相似文献
17.
A staggered finite-volume technique for non-hydrostatic, small amplitude free surface flow governed by the incompressible Navier-Stokes equations is presented there is a proper balance between accuracy and computing time. The advection and horizontal diffusion terms in the momentum equation are discretized by an integral interpolation method on the orthogonal unstructured staggered mesh and, while it has the attractive property of being conservative. The pressure-correction algorithm is employed for the non-hydrostatic pressure in order to achieve second-order temporal accuracy. A conservative scalar transport algorithm is also applied to discretize k-ε equations in this model. The eddy viscosity is calculated from the k-ε turbulent model. The resulting model is mass and momentum conservative. The model is verified by two examples to simulate unsteady small amplitude free surface flows where non-hydrostatic pressures have a considerable effect on the velocity field,and then applied to simulate the tidal flow in the Bohai Sea. 相似文献
18.
A two-dimensional scour model based on coupled system of shallow water equations (SWEs) and sediment transport on unstructured mesh is developed. The coupled system of hydrodynamic and morphodynamic equations is solved by finite volume method using Godunov scheme. Roe's approximate Riemann solver is used to calculate the inviscid fluxes. The use of unstructured mesh makes the model applicable to complex domains. However, it is difficult to evaluate the eigenvalues and eigenvectors of the Jacobian matrix in the global coordinate. The method proposed herein to deal with this difficulty is to transform the system into the local coordinate with one of the axes in the same direction as the interface outward normal vector. In the local coordinate system, the Jacobian matrix is simplified and the eigenvalues are analyzed using asymptotic method. Regular expansion breaks down when the flow is near critical. Uniformity of the expansion is achieved by changing the scales. Rotational invariance theorem is used to relate the interfacial fluxes in the global and local coordinate systems. Special treatment of the source term on unstructured grid makes the scheme stable and physically balanced (both mass and momentum). The method proposed in this paper for the eigen-system is very efficient comparing to iterative numerical methods. Results from the test cases show good agreement with the experiments. 相似文献
19.
A numerical simulation algorithm based on the finite volume discretisation is presented for analyzing ship motions. The algorithm employs a fractional step method to deal with the coupling between the pressure and velocity fields. The free surface capturing is fulfilled by using a volume of fluid method in which the interface between the liquid (water) and gas (air) phases are computed by solving a scalar transport equation for the volume fraction of the liquid phase. The computed velocity field is employed to evaluate the acting forces and moments on the vessel. Using the strategy of boundary-fitted body-attached mesh and calculating all six degrees-of-freedom of motion in each time step, time history of ship motions including displacements, velocities and accelerations are evaluated.To verify the proposed algorithm, a series of verification tests are conducted. First, a two-dimensional asymmetrical wedge slamming is simulated as a simple type of a common case for high-speed vessels. Then, the steady-state forward motion of a high-speed planing catamaran is investigated. Results of both test cases show good agreement with experimental data. It is concluded that the proposed algorithm can be a promising strategy for both performance prediction and design of high-speed vessels. 相似文献
20.
In this paper, a numerical model is established for simulating the wave forces on a submarine pipeline. A set of two-dimensional Navier–Stokes equations is discretized numerically with a finite volume method in a moving mesh system. After each time step, the mesh is modified according to the changed wave surface boundary. The deffered correction second-order upwind scheme (SUDC) is adopted here to discretize the convective fluxes. The effects of the clearance between the pipeline and the seabed, water depth and wave height on wave forces are studied, respectively. The results by the numerical simulation agree well with the experimental data and theory value. 相似文献