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1.
A temporally second-order accurate Godunov-type scheme for solving the extended Boussinesq equations
A numerical scheme for solving the class of extended Boussinesq equations is presented. Unlike previous schemes, where the governing equations are integrated through time using a fourth-order method, a second-order Godunov-type scheme is used thus saving storage and computational resources. The spatial derivatives are discretised using a combination of finite-volume and finite-difference methods. A fourth-order MUSCL reconstruction technique is used to compute the values at the cell interfaces for use in the local Riemann problems, whilst the bed source and dispersion terms are discretised using centred finite-differences of up to fourth-order accuracy. Numerical results show that the class of extended Boussinesq equations can be accurately solved without the need for a fourth-order time discretisation, thus improving the computational speed of Boussinesq-type numerical models. The numerical scheme has been applied to model a number of standard test cases for the extended Boussinesq equations and comparisons made to physical wave flume experiments. 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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Ulf Gräwe 《Ocean Modelling》2011,36(1-2):80-89
Stochastic differential equations (SDEs) offer an attractively simple solution to complex transport-controlled problems, and have a wide range of physical, chemical, and biological applications, which are dominated by stochastic processes, such as diffusion. As for deterministic ordinary differential equations (ODEs), various numerical scheme exist for solving SDEs. In this paper various particle-tracking schemes are presented and tested for accuracy and efficiency (time vs. accuracy). To test the schemes, the particle tracking algorithms are implemented into a community wide used 1D water column model. Modelling individual particles allows a straightforward physical interpretation of the involved processes. Further, this approach is strictly mass conserving and does not suffer from the numerical diffusion that plagues grid-based methods. Moreover, the Lagrangian framework allows to assign properties to the individual particles, that can vary spatially and temporally. The movement of the particles is described by a stochastic differential equation, which is consistent with the advection–diffusion equation. Here, the concentration profile is represented by a set of independent moving particles, which are advected according to the velocity field, while the diffusive displacements of the particles are sampled from a random distribution, which is related to the eddy diffusivity field.The paper will show that especially the 2nd order schemes are accurate and highly efficient. At the same level of accuracy, the 2nd order scheme can be significantly faster than the 1st order counterpart. This gain in efficiency can be spent on a higher resolution for more accurate solutions at a lower cost. 相似文献
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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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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. 相似文献
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1 IntroductionThe shallow water equations (SWE) are frequent-ly used as a mathematical model for water flows incoastal areas, lakes, estuaries, etc. Thus, they are animportant tool to simulate a variety of problems relat-ed to coastal engineering, environment, ecology, etc.(Bermúdez et al., 1998). On the basis of solving theone-dimensional (1D) SWE, Hu et al. (2000) have de-veloped a model capable of simulating storm wavespropagating in the coastal surf zone and overtopping asea wall. Ano… 相似文献
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解四阶拟线性波动方程的一类二阶差分格式 总被引：2，自引：1，他引：2
建立了解一类四阶拟线性耗散、色散波动方程初边值问题的Crank-Nicolson差分方法，并结合外推的技巧，给出了1个线性化方法；证明了差分解的存在唯一性；用能量估计的方法证明了此格式的二阶收敛性和无条件稳定性；给出了一些数值结果。 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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A new adaptive Cartesian-grid for the CIP (constrained interpolation profile) method is proposed and applied to two-dimensional numerical simulations of violent free-surface flows. The CCUP (CIP combined and unified procedure) method is employed and combined with this adaptive Cartesian-grid for robust and efficient computation. This adaptive grid is capable of tracking regions where flows vary violently, and a much finer grid is then concentrated automatically on these regions to adapt to the violent changing of the flow. Unlike the abacus-like Soroban grid which is an adaptive meshless grid with complicated algorithms and inefficiency of evaluation of frequently computed spatial derivatives, the present approach not only simplifies computational algorithm but also enhances efficiency of frequently-computed spatial derivatives. It is also different from most of the remeshing schemes that no additional CPU-time for the value-mapping from the old grid to the new grid is taken in this adaptive grid system provided that the advection velocity is interpolated, since the value-mapping process is accomplished simultaneously within the advection process. To validate the accuracy and efficiency of this newly-proposed CFD model, several two-dimensional benchmark problems are performed, and the results are compared with experimental measurements and other published numerical results. Numerical simulations show that the proposed numerical model is robust, accurate, and efficient for strongly nonlinear free-surface flows. 相似文献
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The typical equation for bed level change in sediment transport in river, estuary and near shore systems is based on conservation of sediment mass. It is generally a nonlinear conservation equation for bed level. The physics here are similar to shallow water wave equations and gas dynamics equation which will develop shock waves in many circumstances. Many state-of-art morphological models use classical lower order Lax–Wendroff or modified Lax–Wendroff schemes for morphology which are not very stable for long time sediment transport processes simulation. Filtering or artificial diffusion are often added to achieve stability. In this paper, several shock capturing schemes are discussed for simulating bed level change with different accuracy and stability behaviors. The conclusion is in favor of a fifth order Euler-WENO scheme which is introduced to sediment transport simulations here over other schemes. The Euler-WENO scheme is shown to have significant advantages over schemes with artificial viscosity and filtering processes, hence is highly recommended especially for phase-resolving sediment transport models. 相似文献
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A. V. Glazunov 《Izvestiya Atmospheric and Oceanic Physics》2006,42(3):282-299
The neutrally stratified boundary layer over a smooth rough surface is consider. The turbulent flow is simulated using a finite-difference eddy-resolving model of the atmospheric boundary layer (ABL). The model includes different turbulence closure schemes and numerical approximations for advection components of the momentum balance equation. We investigate the quality of reproduction of spectral characteristics of the turbulent flow and the model’s capabilities to reproduce the observed profile of mean wind velocity near the rough surface. It is shown that the best result is obtained by coupling a numerical scheme of higher order of accuracy with a mixed closure scheme based on an adaptive estimation of the mixing length for subgrid-scale fluctuations. Here, we are able to reproduce the asymptotics of the fluctuation spectrum of the longitudinal component of wind velocity near the surface and within the boundary layer as well as the logarithmic profile of mean velocity near the surface. 相似文献
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W. E. Rogers J. M. Kaihatu H. A. H. Petit N. Booij L. H. Holthuijsen 《Ocean Engineering》2002,29(11):1357-1390
The numerical schemes for the geographic propagation of random, short-crested, wind-generated waves in third-generation wave models are either unconditionally stable or only conditionally stable. Having an unconditionally stable scheme gives greater freedom in choosing the time step (for given space steps). The third-generation wave model SWAN (“Simulated WAves Nearshore”, Booij et al., 1999) has been implemented with this type of scheme. This model uses a first order, upwind, implicit numerical scheme for geographic propagation. The scheme can be employed for both stationary (typically small scale) and nonstationary (i.e. time-stepping) computations. Though robust, this first order scheme is very diffusive. This degrades the accuracy of the model in a number of situations, including most model applications at larger scales. The authors reduce the diffusiveness of the model by replacing the existing numerical scheme with two alternative higher order schemes, a scheme that is intended for stationary, small-scale computations, and a scheme that is most appropriate for nonstationary computations. Examples representative of both large-scale and small-scale applications are presented. The alternative schemes are shown to be much less diffusive than the original scheme while retaining the implicit character of the particular SWAN set-up. The additional computational burden of the stationary alternative scheme is negligible, and the expense of the nonstationary alternative scheme is comparable to those used by other third generation wave models. To further accommodate large-scale applications of SWAN, the model is reformulated in terms of spherical coordinates rather than the original Cartesian coordinates. Thus the modified model can calculate wave energy propagation accurately and efficiently at any scale varying from laboratory dimensions (spatial scale O(10 m) with resolution O(0.1 m)), to near-shore coastal dimension (spatial scale O(10 km) with resolution O(100 m)) to oceanic dimensions (spatial scale O(10 000 km) with resolution O(100 km). 相似文献
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《Ocean Modelling》2002,4(3-4):249-267
During the course of developing new numerical algorithms for a terrain-following ocean modeling system (TOMS), different numerical aspects have been evaluated through a comparison between two widely used community ocean models, the Princeton ocean model (POM) and the regional ocean modeling system (ROMS). While both models aim at modeling coastal to basin-scale problems using similar grids, their numerical algorithms, code structure, and parameterization options are very different. Sensitivity studies with an idealized channel flow and a steep seamount configuration demonstrate how different algorithms in the two models may affect numerical errors, the stability of the code and the computational efficiency. For example, new pressure gradient schemes using polynomial fits and new time stepping algorithms may reduce numerical errors and allow using longer time steps than standard schemes do. However, the new schemes may require more careful choices of time steps and the use of higher order advection schemes to maintain numerical stability. 相似文献
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A variety of analytical models is used to investigate the effects on tidal propagation of a barrier reef system. These models specify reef geometry by two parameters. They can accommodate cases where water flows over reefs, as well as through inter-reef gaps, and also incorporate quadratic bottom friction. Although based on a one-dimensional approach, adaptations of a solution by Huthnance are used to account for the additional blockage effects associated with two-dimensional flow patterns near reef barriers. The present work adopts the philosophy that only a numerical approach can cope with the wide variations in reef geometry that are encountered in areas such as the Great Barrier Reef (GBR) region of Australia. Moreover, since typical model grids cannot resolve inter-reef gaps and other features with sufficient accuracy, a parameterised approach is needed to accommodate the conflicting demands of reef geometry and an economically feasible model resolution. The formulation of the analytical models is such that they can be applied immediately to standard numerical algorithms. Numerical experiments for flow in a channel, with a reef barrier across its centre, are used to test the parameterisation schemes. Comparison of the results for parameterised reefs with those obtained using extremely fine grids, shows convincing evidence of the success of the schemes. A separate method for automatically generating reef parameters has simplified the task of applying the methodology to real reefal systems. A tidal model of the Southern GBR, a region which exhibits unusual tidal behaviour, but which also has ample field data available for model testing, is used to demonstrate the accuracy that can be attained with the parameterised approach. Although tides are considered specifically in the present work, the formulation should be applicable with equal ease to the many other significant classes of low frequency motions in the GBR. 相似文献
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ZHENG Yonghong 《中国海洋工程》2001,(2):185-194
The original hyperbolic mild-slope equation can effectively take into account the combined effects of wave shoaling, refraction, diffraction and reflection, but does not consider the nonlinear effect of waves, and the existing numerical schemes for it show some deficiencies. Based on the original hyperbolic mild-slope equation, a nonlinear dispersion relation is introduced in present paper to effectively take the nonlinear effect of waves into account and a new numerical scheme is proposed. The weakly nonlinear dispersion relation and the improved numerical scheme are applied to the simulation of wave transformation over an elliptic shoal. Numerical tests show that the improvement of the numerical scheme makes efficient the solution to the hyperbolic mild-slope equation. A comparison of numerical results with experimental data indicates that the results obtained by use of the new scheme are satisfactory. 相似文献
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海冰热力模式的辐射参数化方案在渤海和波罗的海应用的比较 总被引：2，自引：0，他引：2
研究了海冰热力模式中的各种辐射参数化方案,对比了模式计算的太阳短波辐射、大气长波辐射以及海冰热力变化,并利用渤海和波罗的海观测资料进行比较和误差分析.冬季大部分时间太阳短波辐射对海冰热力过程的作用有限.简单计算方案一般满足海冰模式要求.误差主要受云和冰雪表面与大气之间的多重反射影响.长波辐射对表面热平衡和海冰质量变化起重要作用.长波辐射参数化方案的计算结果受环境因素影响.云量参数化有待进一步改进.海冰模式计算结果的精度与长波辐射计算精度有一致性. 相似文献
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The results of numerical experiments on computing the hydrophysical fields for the northern and tropical Atlantic Ocean carried out using two numerical models are analysed. A discrete analogue of the first model is developed using conservative schemes, and of the second using conservative-dissipation difference schemes. It is shown that the second model, having a spatial resolution, reconstructs the meridional heat transport and the vertical seawater motions better than the first one.Translated by Mikhail M. Trufanov. 相似文献