共查询到19条相似文献，搜索用时 609 毫秒
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为了研究污染物对流扩散方程中不同时空格式的适用性,针对对流扩散方程的一维﹑二维和三维3种情况,分别建立了预报-校正的有限差分数值模型。在时间步进格式上分别采用了Crank-Nicolson格式或混合4阶Adams-Bashforth-Moulton格式,对对流项分别采用2阶精度或4阶精度,对扩散项采用了2阶精度。利用建立的数值模型求解了经典的污染物浓度场对流扩散,通过数值解与解析解的比较讨论了不同时空格式对数值模型计算结果的影响。结果表明:对空间一次导数采用4阶精度可以避免采用2阶精度带来的误差。采用混合4阶Adams-Bashforth-Moulton格式或Crank-Nicolson格式数值计算结果均与解析解吻合程度较好,但对于数组为[40,40,40]的三维对流扩散问题,前者比后者省时20.7%。 相似文献
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建立了求解一维全非线性Green-Naghdi水波方程的中心有限体积/有限差分混合数值格式。采用结构化网格对守恒形式的控制方程进行离散和积分,界面数值通量采用有限体积法计算,剩余项则采用中心有限差分格式求解。其中,采用中心迎风有限体积格式计算控制体界面数值通量,并结合界面变量的线性重构方法,使其在空间上具有四阶精度,通过引入静压重构技术和波浪破碎指标使模型具备处理海岸水-陆动边界及波浪破碎的能力。时间积分则采用具有总时间变差减小(Total Variation Diminishing,TVD)性质的三阶龙格-库塔法进行。应用该模型对孤立波在常水深和斜坡海岸上的传播过程及规则波跨越潜堤传播的实验进行了数值模型研究,数值计算同解析解及实验数据吻合良好。 相似文献
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用数值模式对河口海岸地区的物质输运进行计算时，平流项的数值格式必须要能对物质浓度锋面进行正确处理，以避免产生过多的数值耗散或频散。本文中设计了一种在网格内设置一些质点并对质点进行跟踪的格式计算平流项。结果表明，质点跟踪格式在一维情形下无频散和几乎没有耗散，在二维情形下无频散和在水深变化剧烈的地方基本避免了垂向数值耗散。与其他数值格式的耗散性和频散性相比，本文中设计的数值格式明显地提高了物质输运方程中平流项的计算精度，在河口海洋物质输运的计算中具有较大的应用价值。 相似文献
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此文应用Fourier方法和能量不等式研究了常系数和变系数的对流扩散方程在迎风差分格式的情形下数值解的稳定性,所得结果对实际计算有着重要的意义。 相似文献
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海洋流体动力学的一种交替方向隐式二维数值模式 总被引：5，自引：2，他引：5
本文提出一种计算浅海潮汐、风暴潮及其他长周期波动的二维数值模式.动力学方程用建立在交错网格上的二步差分子方程近似,两步均为隐格式,其中一步用于计算水位和x方向速度分量,另一步计算水位和y方向速度分量.两步交替进行以获得每一时间步长的值,该格式具有二阶精度.文章用Von Neumann方法证明了该计算格式的线性差分方程是无条件稳定的.为检验数值模式的可靠性,本文作了一系列数值实验.在有一开边界的长方形平底和斜底水域中以开边界处周期性振动和海面处定常风应力驱动下,数值模拟所得结果与解析解完全一致;在水深不连续,边界封闭的矩形水域中,水位对定常风响应的数值解也与Leendertse模式计算结果完全一致.模式还用于对南海风暴潮进行后报,良好地再现了风暴增水过程. 相似文献
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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
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为完全拟合河口近海复杂岸线和工程结构以及有效局部加密,设计并建立了一个无结构三角形网格二维河口海岸水动力数值模式。空间离散主要基于有限体积法以保证守恒性,时间积分采用预估修正法以提高精度。水位在三角形网格中心通过连续方程求解;水平x方向和y方向的流速U和V均在网格边中点上通过动量方程求解。流速平流项的求解中采用了TVD格式。TVD流速平流通量为一个一阶迎风格式通量和一个二阶格式通量的组合,一阶格式通量和二阶格式通量根据流速的局部分布情况得出配比,最终组合得到TVD通量。TVD格式具有低耗散和无频散的优点,提高了模式的稳定性。应用实测资料验证建立的模式,结果显示水位、流速和流向的计算值与实测值均符合良好。 相似文献
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基于一维阻尼潮波传播方程解析解,从求解数值格式及Heuristic稳定性分析方面,讨论了数值解的精度、计算耗时和摩阻系数选取等问题。研究结果表明:1)Courant数小于1时,潮波方程显格式解的精度略高于隐格式解,计算耗时少于隐格式解;2)为减少计算耗时,潮波方程的隐格式解允许较大的时间步长,但解的精度有所降低,须通过减小底床摩阻系数以保证计算精度;3)隐格式解摩阻系数的选取与Courant数有关,Courant数越大,摩阻系数的选取值比实际值越小,通过理论分析结合数值试验得到了相应的关系式。这些研究结论对实际海域的潮波传播的数值模拟具有重要的应用价值。 相似文献
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研究并行算法解决应用并行计算机完成规模尽可能大的偏微分方程的数值求解问题。利用Hopf-Cole变换,将一维非线性Burgers方程转化为线性扩散方程,基于第二类Saul’yev型非对称格式和Crank-Nicolson格式对扩散方程进行差分离散,建立解Burgers方程的交替分段并行差分格式,并讨论该方法的稳定性,给出了数值算例。此算法把剖分节点分成若干组,在每组上构造能够独立求解的差分方程,因此具有并行本性,适合在高性能多处理器的并行计算机上使用。数值试验的结果表明此方法是有效的,且有较高的精度。 相似文献
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A three-dimensional finite difference transport model appropriate for the coastal environment is developed for the solution of the three-dimensional convection-diffusion equation. A higher order upwind scheme is used for the convective terms of the convection-diffusion equation, to minimise the numerical diffusion. The validity of the numerical model is verified through five test problems, whose exact solutions are known. 相似文献
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David F. Paskausky 《Journal of Oceanography》1978,34(5):233-236
The diffusive temperature equation is solved analytically and numerically for a simple oceanic case. Errors introduced by various numerical schemes are determined by comparison with the analytical solution. Less error is introduced by the standard differencing scheme than by the DuFort-Frankel scheme. A variable grid scheme produces the least error and the greatest savings in computer core and time. Usefulness of various numerical schemes is situation dependent. Any numerical forecasting technique using initialization data and frequent data updating will need to be verified with adequate field data before it can be considered reliable and used to predict short term (1 to 7 days) events in the ocean. 相似文献
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Spurious diapycnal mixing in terrain-following coordinate models: The problem and a solution 总被引：5，自引：0，他引：5
In this paper, we identify a crucial numerical problem in sigma coordinate models, leading to unacceptable spurious diapycnal mixing. This error is a by-product of recent advances in numerical methods, namely the implementation of high-order diffusive advection schemes. In the case of ROMS, spurious mixing is produced by its third-order upwind advection scheme, but our analysis suggests that all diffusive advection schemes would behave similarly in all sigma models. We show that the common idea that spurious mixing decreases with resolution is generally false. In a coarse-resolution regime, spurious mixing increases as resolution is refined, and may reach its peak value when eddy-driven lateral mixing becomes explicitly resolved. At finer resolution, diffusivities are expected to decrease but with values that only become acceptable at resolutions finer than the kilometer. The solution to this problem requires a specifically designed advection scheme. We propose and validate the RSUP3 scheme, where diffusion is split from advection and is represented by a rotated biharmonic diffusion scheme with flow-dependent hyperdiffusivity satisfying the Peclet constraint. The rotated diffusion operator is designed for numerical stability, which includes improvements of linear stability limits and a clipping method adapted to the sigma-coordinate. Realistic model experiments in a southwest Pacific configuration show that RSUP3 is able to preserve low dispersion and diffusion capabilities of the original third-order upwind scheme, while preserving water mass characteristics. There are residual errors from the rotated diffusion operator, but they remain acceptable. The use of a constant diffusivity rather than the Peclet hyperdiffusivity tends to increase these residual errors which become unacceptable with Laplacian diffusion. Finally, we have left some options open concerning the use of time filters as an alternative to spatial diffusion. A temporal discretization approach to the present problem (including implicit discretization) will be reported in a following paper. 相似文献
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Chunyan Li Nan Walker Aixin Hou Ioannis Georgiou Harry Roberts Ed Laws J. Alex McCorquodale Eddie Weeks Xiaofeng Li Jessica Crochet 《Estuarine, Coastal and Shelf Science》2008
Circular shaped density plumes of low turbidity, low fecal indicator (Escherichia coli and enterococci) concentrations, and high salinity have been observed near the Industrial Canal in Lake Pontchartrain, north of the City of New Orleans. A conceptual model in polar coordinates and a numerical model are developed, together with data analysis, to illustrate the dense plume. It is demonstrated that the northward expansion of the plume occurs under northerly winds. The northward expansion of the plume occurs under northerly winds that drive downwind flow at the surface and upwind radial flow at the bottom. Northerly wind-induced straining, similar to tidal straining, promotes vertical stratification. As a result, the water becomes stratified near a thin bottom layer (<1 m), within which density currents are facilitated. The stability of the stratified plume suppresses wind-induced turbulent mixing inside the plume. The bottom water outside of the plume is more effectively stirred by the wind, the result being that the suspended sediment concentration outside of the plume area is much higher than inside. This contrast in mixing makes the plume visible from the surface by satellites even though the stratification is at the bottom. Laterally, wind stress produces a torque (vorticity) in areas of non-uniform depth such that upwind flow is developed in deep water and downwind flow in shallow water. The continuity requirement produces an upwind flow along the axis of the Industrial Canal (IC). The upwind flow is balanced by the downwind flow over the shallower peripheral areas along the coast. 相似文献
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《Coastal Engineering》2005,52(5):409-433
An implicit finite difference formulation of the nonlinear shallow water equations is developed to allow for the treatment of tidal bores and hydraulic jumps. Five different schemes are investigated involving upwind treatment of convective terms, central differences combined with dissipative interface, forward time-centering and various combinations of these techniques. The schemes are analyzed with respect to their effective amplification portraits, and they are tested on periodic bores, uniform bores and steady hydraulic jumps. In this connection the model results are verified against analytical solutions and a numerical solution obtained with a Godunov Riemann solver. Scheme 4, which combines forward time centering and dissipative interface, is found to be superior to the others and it is applicable for Courant numbers within the range 0.25 to 1.5. This scheme is applied to a case study of the tidal bore in Huangzhou Bay and Qiantang River. The model results are shown to be in very good agreement with field data. 相似文献
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A one-dimensional salt intrusion model is used to investigate the hydrography of the Ythan estuary, a small shallow macrotidal estuary in the north-east of Scotland. The model simulates the longitudinal distributions of water level, salinity and total oxidized nitrogen (TON) in the estuary. The model employs upstream differencing and the Smolarkiewicz anti-diffusion scheme to avoid the numerical difficulties typically encountered when modelling strong tidal flows using centred differences. The physical mechanisms driving the simulations are the tide at the entrance to the estuary and freshwater discharge at the head. The model was calibrated against measurements of water level made at three locations in the estuary, salinity observations made at a central platform and axial salinity distributions. At both spring and neap tides, the full range of salinity observed at the central platform was simulated. However, at the midway stage between springs and neaps, the simulated peak salinity was less than that observed. This was probably due to the sensitivity of the model to the digitisation of the estuarine bathymetry.The model successfully simulated salinity distributions for periods of high and low river flow, and was used to illustrate how TON concentrations fluctuated in response to variations in river flow. The potential implications of variations in the bathymetry of the estuary on salinity and nutrient distributions were predicted to be slight. However, the four fold increase in riverine TON concentrations that has occurred over the past 30 years was shown to increase TON distributions along the entire length of the estuary. The calculated estuary flushing time was strongly dependent on river flow and varied between 11–60 h. 相似文献
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A Vertical Two-Dimensional Model to Simulate Tidal Hydrodynamics in A Branched Estuary 总被引：1，自引：1，他引：1
A vertical (laterally averaged) two-dimensional hydrodynamic model is developed for tides, tidal current, and salinity in a branched estuarine system. The goveming equations are solved with the hydrostatic pressure distribution assumption and the Boussinesq approximation. An explicit scheme is employed to solve the continuity equations. The momentum and mass balance equations are solved implicitly in the Cartesian coordinate system. The tributaries are govemed by the same dynamic equations. A control volume at the junctions is designed to conserve mass and volume transport in the finite difference schemes, based on the physical principle of continuum medium of fluid. Predictions by the developed model are compared with the analytic solutions of steady wind-driven circulatory flow and tidal flow. The model results for the velocities and water surface elevations coincide with analytic results. The model is then applied to the Tanshui River estuarine system. Detailed model calibration and verification have been conducted with measured water surface elevations,tidal current, and salinity distributions. The overall performance of the model is in qualitative agreement with the available field data. The calibrated and verified numerical model has been used to quantify the tidal prism and flushing rate in the Tanshui River-Tahan Stream, Hsintien Stream, and Keelung River. 相似文献