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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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In recent decades,a few Godunov-type,finite volume two-dimensional(2D)unstructured grid,coupled flow,and sediment models(GF2DUCM)have been developed for flows over erodible beds.These kinds of models are generally analyzed as a Vertex Model(VM)that define topography at the cell vertex,which can lead to the non-conservation of mass regarding flow,sediment,and bed evolution.Here,a full cellcantered variable storage method(Central Model or CM)is applied as the solution of the GF2DUCM.In this method,terrain elevation is defined at the cell centroids;this accurately describes the physical relations between the water depth and topography deformation.This approach can fully eliminate calculation errors in topography deformation at local cells caused by the interpolation of topography deformation at the cell vertex,and reduced uncertainty in the computation of the GF2DUCM.The model performance is systematically tested using a series of laboratory experiments,which demonstrate the mass conservation feature and high accuracy in reproducing hydrodynamic and morphological processes. 相似文献
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The multiscale finite-volume (MSFV) method has been developed to solve multiphase flow problems on large and highly heterogeneous
domains efficiently. It employs an auxiliary coarse grid, together with its dual, to define and solve a coarse-scale pressure
problem. A set of basis functions, which are local solutions on dual cells, is used to interpolate the coarse-grid pressure
and obtain an approximate fine-scale pressure distribution. However, if flow takes place in presence of gravity (or capillarity),
the basis functions are not good interpolators. To treat this case correctly, a correction function is added to the basis
function interpolated pressure. This function, which is similar to a supplementary basis function independent of the coarse-scale
pressure, allows for a very accurate fine-scale approximation. In the coarse-scale pressure equation, it appears as an additional
source term and can be regarded as a local correction to the coarse-scale operator: It modifies the fluxes across the coarse-cell
interfaces defined by the basis functions. Given the closure assumption that localizes the pressure problem in a dual cell,
the derivation of the local problem that defines the correction function is exact, and no additional hypothesis is needed.
Therefore, as in the original MSFV method, the only closure approximation is the localization assumption. The numerical experiments
performed for density-driven flow problems (counter-current flow and lock exchange) demonstrate excellent agreement between
the MSFV solutions and the corresponding fine-scale reference solutions. 相似文献
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This study presents a finite-volume explicit method to solve 2D two-layer shallow water equations. This numerical model is intended to describe two-layer shallow flows in which the superposed layers differ in velocity, density and rheology in a two-dimensional domain. The rheological behavior of mudflow or debris flow is called the Bingham fluid. Thus, the shear stress on rigid bed can be derived from the constitutive equation. The computational approach adopts the HLL scheme, a novel approach for the purpose of computing a Godunov flux and solving the Riemann problem approximately proposed by Harten, Lax and van Leer, as a basic building block, treats the bottom slope by lateralizing the momentum flux, and refines the scheme using the Strang splitting to manage the frictional source term. This study successfully performed 2D two-layer shallow water computations on a rigid bed. The proposed numerical model can describe the variety of depths and velocities of substances including water and mud, when the hyperconcentrated tributary flows into the main river. The analytical results in this study will be valuable for further advanced research and for designing or planning hydraulic engineering structures. 相似文献
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In the present work, the multiscale finite volume (MsFV) method is implemented on a new coarse grids arrangement. Like grids used in the MsFV methods, the new grid arrangement consists of both coarse and dual coarse grids but here each coarse block in the MsFV method is a dual coarse block and vice versa. Due to using the altered coarse grids, implementation, computational cost, and the reconstruction step differ from the original version of MsFV method. Two reconstruction procedures are proposed and their performances are compared with each other. For a wide range of 2-D and 3-D problem sizes and coarsening ratios, the computational costs of the MsFV methods are investigated. Furthermore, a matrix (operator) formulation is presented. Several 2-D test cases, including homogeneous and heterogeneous permeability fields extracted from different layers of the tenth SPE comparative study problem are solved. The results are compared with the fine-scale reference and basic MsFV solutions. 相似文献
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《国际泥沙研究》2020,35(4):386-394
Sediment transport simulations are important in practical engineering. In this study, a graphics processing unit (GPU)-based numerical model coupling hydrodynamical and morphological processes was developed to simulate water flow, sediment transport, and morphological changes. Aiming at accurately predicting the sediment transport and sediment scouring processes, the model resolved the realistic features of sediment transport and used a GPU-based parallel computing technique to the accelerate calculation. This model was created in the framework of a Godunov-type finite volume scheme to solve the shallow water equations (SWEs). The SWEs were discretized into algebraic equations by the finite volume method. The fluxes of mass and momentum were computed by the Harten, Lax, and van Leer Contact (HLLC) approximate Riemann solver, and the friction source terms were calculated by the proposed a splitting point-implicit method. These values were evaluated using a novel 2D edge-based MUSCL scheme. The code was programmed using C++ and CUDA, which could run on GPUs to substantially accelerate the computation. The aim of the work was to develop a GPU-based numerical model to simulate hydrodynamical and morphological processes. The novelty is the application of the GPU techniques in the numerical model, making it possible to simulate the sediment transport and bed evolution in a high-resolution but efficient manner. The model was applied to two cases to evaluate bed evolution and the effects of the morphological changes on the flood patterns with high resolution. This indicated that the GPU-based high-resolution hydro-geomorphological model was capable of reproducing morphological processes. The computational times for this test case on the GPU and CPU were 298.1 and 4531.2 s, respectively, indicating that the GPU could accelerate the computation 15.2 times. Compared with the traditional CPU high-grid resolution, the proposed GPU-based high-resolution numerical model improved the reconstruction speed more than 2.0–12.83 times for different grid resolutions while remaining computationally efficient. 相似文献
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为了克服空气层和地表耦合以及避免一次场计算,开发适合不同类型场源、不同应用范围的频率域三维正演模拟统一平台,本文从麦克斯韦基本方程出发,推导基于Lorenz规范条件的磁矢势和标势耦合方程;通过将不同类型场源分解成一系列短导线(电性)源组合,采用交错网格采样和有限体积技术对方程进行离散得到对称大型稀疏线性方程组,并采用Jacobi迭代预处理QMR(Quasi-Minimum-Residual,拟最小残差)算法进行求解,我们成功实现不同类型场源、不同应用范围的频率域电磁法三维正演模拟.通过层状模型下大地电磁法以及有限长接地导线和大回线磁性源激发下的电磁场响应模拟,并与一维解析解对比验证算法的有效性.进而,我们利用该算法平台的模拟结果对典型地电模型在不同场源激发下频率域电磁法响应特征进行对比分析.本文算法研究及实现为建立频率域电磁法三维正反演统一框架打下基础. 相似文献
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YU Bin Associate Professor Institute of Mountain Hazards Environment Chinese Academy of Science P. O. BOX . Chengdu. PR China. 《国际泥沙研究》1997,(3)
LINTRODUCTIONThedebrisflowisaverycomplexflow.Itdiffersfromwaterflowandsuspendedflowinmovingandstagnation.Thedebrisflowisgenerallydiscribedasthegravityflowofsoil.rock,waterandinitiatedbylandslide,usuallyduetohighrunoffflow.Theoccurrenceofdebrisflowisratherunpredictableandverydestwhve.Debrisflowcouldmovefasterthanthemorecommonlandslideandtendto~tareasatmuchgreaterdistancefromthesourceofhazard.Debrisflowdisastershavebeenrecognizedasacriticalproblemfacingtheworldtodayandincreasingattentionha… 相似文献
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蓬莱19-3 油田事故溢油数值模拟 总被引：2，自引：0，他引：2
利用FVCOM(Finite-volume coastal ocean numerical model)数值模型和MM5风场预报模式,在对渤海海域水动力场进行数值模拟的基础上,基于"油粒子"的欧拉-拉格朗日跟踪法和随机走动原理,并考虑风对溢油油膜漂移扩散的直接作用,建立了海洋溢油油膜漂移轨迹和扩散的数值预测模型。利用建立的模型对2011年6月蓬莱19-3油田事故溢油进行了数值模拟,模拟结果与RADARSAT卫星遥感监测数据相吻合。研究结果表明:在渤海中部地区夏季事故溢油模拟预测中,风漂移因子取0.024最为合理,模型可用于渤海蓬莱19-3油田附近事故溢油轨迹和扩散的快速预报,从而为该区域的溢油事故应急响应提供科学依据。 相似文献