共查询到20条相似文献，搜索用时 31 毫秒
1.
《Advances in water resources》1988,11(2):84-91
According to the theory of characteristics, the number of boundary conditions required for the adequate definition of a PDE problem is equal to the number of characteristic half planes entering the domain associated with the PDE problem.This theory was applied to the primitive form of the shallow water equations two decades ago to determine the number of initial and boundary conditions required by these equations. The results of this early study are remembered here. Subsequently, the same theory is applied to some wave formulations of the shallow water equations (the wave continuity and primitive momentum equation model, and the wave continuity and wave momentum equation model).Circumstances under which the number of boundary conditions required by the mathematical model can be reduced to the number of available boundary conditions are discussed for both the primitive and wave formulations of the shallow water equations. 相似文献
2.
《Advances in water resources》2005,28(4):345-358
Nearly all generalized wave continuity (GWC)-based models utilize the velocity-based, non-conservative form of the momentum equation to obtain the depth-averaged changes in velocity. It has been hypothesized that a flux-based, conservative form of the momentum equation may improve accuracy and stability. Herein, we study the impact of the choice of dependent variable and form of the momentum equation in a GWC-based finite element shallow water model. The impact of this change on mass balance, stability, and accuracy (spatial and temporal) is rigorously assessed, first for 1D barotropic flows and then for 2D barotropic flows in a variety of basins. Both 1D and 2D results indicate that the conservative form improves mass balance on both global and local scales, with the most significant gains found in local mass balance in areas with steep bathymetry gradients. This is also the region where the conservative form shows an increase in local spatial accuracy. Taylor series analysis and numerical simulations indicate a strong correlation between local spatial truncation errors and local mass balance errors. Stability, temporal accuracy and global spatial accuracy do not show statistically significant changes between the two algorithms in both 1D and 2D studies. 相似文献
3.
《Advances in water resources》2003,26(6):635-647
A kinetic flux vector splitting (KFVS) scheme for shallow water flows based on the collisionless Boltzmann equation is formulated and applied. The scheme is explicit and first order in space and time with stability governed by the Courant condition. The consistency of the KFVS scheme with the shallow water equations is proven using the equivalent differential equations approach. The accuracy and efficiency of the KFVS scheme in modeling complex flow features are compared to those of the Boltzmann Bhatnagar–Gross–Krook (BGK) scheme as well as a Riemann-based scheme. In particular, all schemes are applied to (i) strong shock waves, (ii) extreme expansion waves, (iii) a combination of strong shock waves and extreme expansion waves, and (iv) a one-dimensional dam break problem. Additionally, the KFVS, BGK and Riemann schemes are applied to a one-dimensional dam break problem for which laboratory data is available. These test cases reveal that all three schemes provide solutions of comparable accuracy, but the KFVS model is 1.5–2 times faster to execute than the BGK scheme and 2–3 times faster than the Riemann-based scheme. The absence of the collision term from the Boltzmann equation not only makes the mathematical formulation of KFVS easy but also helps elucidate this approach to the novice. The accuracy, efficiency, and simplicity of the KFVS scheme indicate its potential in modeling an array of water resources problems. Due to the scalar nature of the Boltzmann equation, the extension of the KFVS scheme to 2-D surface water flows is straightforward. 相似文献
4.
地震波场数值模拟在地球物理勘探和地震学中具有重要的支撑作用.本文将组合型紧致差分格式用于声波和弹性波方程的数值模拟中.根据泰勒级数展开和声波方程,建立了位移场时间四阶离散格式,并将组合型紧致差分格式用于位移场空间导数的求取,然后对该差分格式进行了精度分析、误差分析、频散分析和稳定性分析.理论研究结果表明：①该差分格式为时间四阶、空间六阶精度,与常规七点六阶中心差分和五点六阶紧致差分相比,具有更小的截断误差和更高的模拟精度;②每个波长仅需要5.6个采样点,且满足稳定性条件的库郎数为0.792,可以使用粗网格和较大时间步长进行计算.所以该方法具有占用内存少、计算效率高和低数值频散等优势.最后,本文进行了二维各向同性完全弹性介质的声波和弹性波方程的数值模拟,实验结果表明本文提出的方法具有更高的计算精度,能够大幅度的节约计算量和内存需求,对于三维大尺度模型问题具有更好的适应性. 相似文献
5.
Wilhelm BECHTELER Davood FARSHI Institute of Hydroscience Federal Armed Forces University Munich Neubiberg Germany 《国际泥沙研究》2001,16(2)
1 INTRODUCTIONFor many hydraulic engineering problems, the analysis of flow and bed level variations in openchannels is a fundamental prerequisite. forcal methOds fOr alluvial rivers are well develoPednowadays as far as onediInensional descriPtions are concemed. A cOmPrhensive analysis of Ihe wellknown models is Presented by Habersack(l998). HOwever, for a number of Problems such as channelwidening, flow pattem close to sPuds and etc. a more deailed knowledge of the bed level behavio… 相似文献
6.
Dam-break flows usually propagate along rivers and floodplains, where the processes of fluid flow, sediment transport and bed evolution are closely linked. However, the majority of existing two-dimensional (2D) models used to simulate dam-break flows are only applicable to fixed beds. Details are given in this paper of the development of a 2D morphodynamic model for predicting dam-break flows over mobile beds. In this model, the common 2D shallow water equations are modified, so that the effects of sediment concentrations and bed evolution on the flood wave propagation can be considered. These equations are used together with the non-equilibrium transport equations for graded sediments and the equation of bed evolution. The governing equations are solved using a matrix method, thus the hydrodynamic, sediment transport and morphological processes can be jointly solved. The model employs an unstructured finite volume algorithm, with an approximate Riemann solver, based on the Roe-MUSCL scheme. A predictor–corrector scheme is used in time stepping, leading to a second-order accurate solution in both time and space. In addition, the model considers the adjustment process of bed material composition during the morphological evolution process. The model was first verified against results from existing numerical models and laboratory experiments. It was then used to simulate dam-break flows over a fixed bed and a mobile bed to examine the differences in the predicted flood wave speed and depth. The effects of bed material size distributions on the flood flow and bed evolution were also investigated. The results indicate that there is a great difference between the dam-break flow predictions made over a fixed bed and a mobile bed. At the initial stage of a dam-break flow, the rate of bed evolution could be comparable to that of water depth change. Therefore, it is often necessary to employ the turbid water governing equations using a coupled approach for simulating dam-break flows. 相似文献
7.
Alberto Canestrelli Michael Dumbser Annunziato Siviglia Eleuterio F. Toro 《Advances in water resources》2010
In this paper, we study the numerical approximation of the two-dimensional morphodynamic model governed by the shallow water equations and bed-load transport following a coupled solution strategy. The resulting system of governing equations contains non-conservative products and it is solved simultaneously within each time step. The numerical solution is obtained using a new high-order accurate centered scheme of the finite volume type on unstructured meshes, which is an extension of the one-dimensional PRICE-C scheme recently proposed in Canestrelli et al. (2009) [5]. The resulting first-order accurate centered method is then extended to high order of accuracy in space via a high order WENO reconstruction technique and in time via a local continuous space–time Galerkin predictor method. The scheme is applied to the shallow water equations and the well-balanced properties of the method are investigated. Finally, we apply the new scheme to different test cases with both fixed and movable bed. An attractive future of the proposed method is that it is particularly suitable for engineering applications since it allows practitioners to adopt the most suitable sediment transport formula which better fits the field data. 相似文献
8.
In order to simulate the dynamics of fine sediments in short tidal basins, like the Wadden Sea basins, a 1D cross-sectional averaged model is constructed to simulate tidal flow, depth-limited waves, and fine sediment transport. The key for this 1D model lies in the definition of the geometry (width and depth as function of the streamwise coordinate). The geometry is computed by implementing the water level and flow data, from a 2D flow simulation, and the hypsometric curve in the continuity equation. By means of a finite volume method, the shallow-water equations and sediment transport equations are solved. The bed shear stress consists of the sum of shear stresses by waves and flow, in which the waves are computed with a depth-limited growth equation for wave height and wave frequency. A new formulation for erosion of fines from a sandy bed is proposed in the transport equation for fine sediment. It is shown by comparison with 2D simulations and field measurements that a 1D schematization gives a proper representation of the dynamics in short tidal basins. 相似文献
9.
J. J. Westerink 《Advances in water resources》1987,10(4)
A finite element method formulation for solving the harmonic shallow water equations in their primitive or unmodified form is developed and analysed. The scheme, referred to as the Primitive Pseudo Wave Equation Formulation (PPWE), involves developing a weak weighted residual form of the continuity equation and furthermore forming a pseudo wave equation by substituting the discretized form of the momentum equation into the discretized form of the continuity equation. The final set of equations to be solved, the pseudo wave equation and the primitive momentum equations, deceptively resemble the discretized equations of the wave equation formulation of Lynch and Gray. Despite this resemblance, Fourier analysis indicates that the PPWE scheme is still fundamentally primitive.However, application of the PPWE scheme to a set of stringent test problems results in very good solutions with well controlled nodal oscillations. It is shown that this low degree of spurious oscillations is due to the treatment of the boundary conditions such that elevation is taken as an essential condition and normal flux is taken as a natural condition. This particular boundary condition treatment is suggested by the formation of the pseudo wave equation. Furthermore, even though the equation re-arrangement does not in itself effect the solutions, it does make the scheme much more efficient. 相似文献
10.
A modified nearly analytic discrete method and wavefield simulations in transversely isotropic media
LU Ming & YANG Dinghui Department of Mathematical Sciences Tsinghua University Beijing China 《中国科学D辑(英文版)》2005,48(8):1321-1328
Under the general case, rocks under the ground can be approximately considered as an elastic medium. Elastic wave equation is a partial differential equation, which describes the elastic wave propagation in elastic media. Simple elastic wave equation can be solved analytically, however most wave equations are very complex, which can only be solved by using numerical methods. Numerical simulations of seismic wave fields have become an important method for studying seismic wave propagation in co… 相似文献
11.
In order to simulate the dynamics of fine sediments in short tidal basins, like the Wadden Sea basins, a 1D cross-sectional averaged model is constructed to simulate tidal flow, depth-limited waves, and fine sediment transport. The key for this 1D model lies in the definition of the geometry (width and depth as function of the streamwise coordinate). The geometry is computed by implementing the water level and flow data, from a 2D flow simulation, and the hypsometric curve in the continuity equation. By means of a finite volume method, the shallow-water equations and sediment transport equations are solved. The bed shear stress consists of the sum of shear stresses by waves and flow, in which the waves are computed with a depth-limited growth equation for wave height and wave frequency. A new formulation for erosion of fines from a sandy bed is proposed in the transport equation for fine sediment. It is shown by comparison with 2D simulations and field measurements that a 1D schematization gives a proper representation of the dynamics in short tidal basins.
相似文献12.
Alberto Canestrelli Annunziato Siviglia Michael Dumbser Eleuterio F. Toro 《Advances in water resources》2009
This paper concerns the development of high-order accurate centred schemes for the numerical solution of one-dimensional hyperbolic systems containing non-conservative products and source terms. Combining the PRICE-T method developed in [Toro E, Siviglia A. PRICE: primitive centred schemes for hyperbolic system of equations. Int J Numer Methods Fluids 2003;42:1263–91] with the theoretical insights gained by the recently developed path-conservative schemes [Castro M, Gallardo J, Parés C. High-order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products applications to shallow-water systems. Math Comput 2006;75:1103–34; Parés C. Numerical methods for nonconservative hyperbolic systems: a theoretical framework. SIAM J Numer Anal 2006;44:300–21], we propose the new PRICE-C scheme that automatically reduces to a modified conservative FORCE scheme if the underlying PDE system is a conservation law. The resulting first-order accurate centred method is then extended to high order of accuracy in space and time via the ADER approach together with a WENO reconstruction technique. The well-balanced properties of the PRICE-C method are investigated for the shallow water equations. Finally, we apply the new scheme to the shallow water equations with fix bottom topography and with variable bottom solving an additional sediment transport equation. 相似文献
13.
An efficient method for simulating 2-D river flow is developed in which horizontal turbulent shears are omitted from the 2-D depth-averaged momentum equations. It is shown that a pseudo-viscosity can be reproduced to take into account the lost shear action, by incorporating the vertically integrated continuity equation to the momentum equations and transforming the latter into a discrete integral form. To simulate river flows with wet and dry areas, negative water depths are allowed when solving the continuity equation. The concept of negative water depth enables us to track flow boundaries with about the same accuracy but much less effort as compared with traditional numerical methods. An optimal threshold value defining dry areas is first obtained by one-dimensional theoretical analysis and then sought by trial-and-error for two-dimensional flow simulation with tolerable node-to-node spurious oscillations, while mass is best conserved. Numerical solutions using the new procedure are compared with the one-dimensional benchmark solution of the Saint Venant equations and the experimental data from a two-stage channel. Robustness of the present approach is also tested through the study of water flow in a natural river and a hypothetical channel with several bumps. 相似文献
14.
Shaohua Marko HSU Associate Professor Dr. Department of Hydraulic Engineering Feng Chia University Taichung Taiwan China Wei-Sheng YU Environment Section Agricultural Engineering Research Center Chungli Taiwan China Tzu-Ming LIU Graduate stu 《国际泥沙研究》1997,(3)
1.IN~DUCTIONTurbiditycurrentisoneclassofflowsnameddensitycurrentorgravitycurrent(therHunterRouse(Yih(1980)),whichdePictstheintmsionofheaVyfluidintoalighterone.Usually,thedensitydifferencebetWeentWonuidisrelativelysmallandmixingacrosstheimerfaceoccurs.ThedrivingforceofdensitycurrentsisnotdensitydifferenceitselfbutthedifferenceinspeCmcweights.Turbiditycurrentisnamedwhenthedensitydifferenceisespeciallycausedbysuspendedfinesedimentparticles.Sincesediment-ladenflowcaninteraCtwiththelowerbou… 相似文献
15.
Romain Teyssier 《地球物理与天体物理流体动力学》2013,107(3-4):199-225
We propose to extend the well-known MUSCL-Hancock scheme for Euler equations to the induction equation modeling the magnetic field evolution in kinematic dynamo problems. The scheme is based on an integral form of the underlying conservation law which, in our formulation, results in a “finite-surface” scheme for the induction equation. This naturally leads to the well-known “constrained transport” method, with additional continuity requirement on the magnetic field representation. The second ingredient in the MUSCL scheme is the predictor step that ensures second order accuracy both in space and time. We explore specific constraints that the mathematical properties of the induction equations place on this predictor step, showing that three possible variants can be considered. We show that the most aggressive formulations reach the same level of accuracy than the other ones, at a lower computational cost. More interestingly, these schemes are compatible with the Adaptive Mesh Refinement (AMR) framework. It has been implemented in the AMR code RAMSES. It offers a novel and efficient implementation of a second order scheme for the induction equation. The scheme is then adaptated to solve for the full MHD equations using the same methodology. Through a series of test problems, we illustrate the performances of this new code using two different MHD Riemann solvers (Lax–Friedrich and Roe) and the need of the Adaptive Mesh Refinement capabilities in some cases. Finally, we show its versatility by applying it to the ABC dynamo problem and to the collapse of a magnetized cloud core. 相似文献
16.
Seokkoo KangAnne Lightbody Craig HillFotis Sotiropoulos 《Advances in water resources》2011,34(1):98-113
We develop an efficient and versatile numerical model for carrying out high-resolution simulations of turbulent flows in natural meandering streams with arbitrarily complex bathymetry. The numerical model solves the 3D, unsteady, incompressible Navier-Stokes and continuity equations in generalized curvilinear coordinates. The method can handle the arbitrary geometrical complexity of natural streams using the sharp-interface curvilinear immersed boundary (CURVIB) method of Ge and Sotiropoulos (2007) [1]. The governing equations are discretized with three-point, central, second-order accurate finite-difference formulas and integrated in time using an efficient, second-order accurate fractional step method. To enable efficient simulations on grids with tens of millions of grid nodes in long and shallow domains typical of natural streams, the algebraic multigrid (AMG) method is used to solve the Poisson equation for the pressure coupled with a matrix-free Krylov solver for the momentum equations. Depending on the desired level of resolution and available computational resources, the numerical model can either simulate, via direct numerical simulation (DNS), large-eddy simulation (LES), or unsteady Reynolds-averaged Navier-Stokes (URANS) modeling. The potential of the model as a powerful tool for simulating energetic coherent structures in turbulent flows in natural river reaches is demonstrated by applying it to carry out LES and URANS in a 50-m long natural meandering stream at resolution sufficiently fine to capture vortex shedding from centimeter-scale roughness elements on the bed. The accuracy of the simulations is demonstrated by comparisons with experimental data and the relative performance of the LES and URANS models is also discussed. 相似文献
17.
A. C. LIAKOPOULOS Dr. Eng. 《水文科学杂志》2013,58(1):69-110
ABSTRACT The one-dimensional transient downward entry of water in unsaturated soils is investigated theoretically. The mathematical equation describing the infiltration process is derived by combining Darcy's dynamic equation of motion with the continuity and thermodynamic state equations adjusted for the unsaturated flow conditions. The resulting equation together with the corresponding initial and boundary conditions constitues a mathematical initial boundary value problem requiring the solution of a nonlinear partial differential equation of the parabolic type. The volumetric water content is taken as the dependent variable and the time and the position along the vertical direction are taken as the independent variables. The governing equation is of such nature that a solution exists for t > 0 and is uniquely determined if two relationships are defined, together with the specified state of the system, at the initial time t = 0 and at the two boundaries. The two required relations are those of pressure versus permeability and pressure versus volumetric water content. Since the partial differential equation has strong non-linear terms, a discrete solution is obtained by approximating the derivatives with finite-differences at discrete mesh points in the solution domain and integrated for the corresponding initial and boundary conditions. The use of an implicit difference scheme is employed in order to generate a system of simultaneous non-linear equations that has to be solved for each time increment. For n mesh points the two boundary conditions provide two equations and the repetition of the recurrence formula provides n—2 equations, the total being n equations for each time increment. The solution of the system is obtained by matrix inversion and particularly with a back-substitution technique. The FORTRAN statements used for obtaining the solution with an electronic digital computer (IBM 704) are presented together with the input data. Analysis of the errors involved in the numerical solution is made and the stability and convergence of the solution of the approximate difference equation to that of the differential equation is investigated. The method applied is that of making a Fourier series expansion of a whole line of errors and then following the progress of the general term of the series expansion and also the behavior of each constituent harmonic. The errors (forming a continuous function of points in an abstract Banach space) are represented by vectors with the Fourier coefficients constituting a second Banach space. The amplification factor of the difference equation is shown to be always less than unity which guarantees the stability of the employed implicit recurrence scheme. Experiments conducted on a vertical column packed uniformly with very fine sand, show a satisfactory agreement between the theoretically and experimentally obtained values. Many experimental results are shown in an attempt to explain the infiltration phenomenon with emphasis on the shape and movement of the wet front, and the effects of the degree of compaction, initial water content and deaired water on the infiltration rate. 相似文献
18.
We report a two-dimensional multi-block lattice Boltzmann model for solute transport in shallow water flows, which is developed based on the advection–diffusion equation for mass transport and the shallow water equations for the flows. A weighting factor is included in the centered scheme for improved accuracy. The model is firstly verified by simulating three benchmark tests: wind-driven circulation in a dish-shaped lake, jet-forced flow in a circular basin, and flow formed by two parallel streams containing different uniform concentrations at the same constant velocity; and then it is applied to a practical wind-induced flow, Baiyangdian Lake, which is characterized by irregular geometries and complex bathymetries. The numerical results have shown that the model is able to produce accurate and detailed results for both water flows and solute transport, which is attractive, especially for flows in narrow zones of practical terrains and certain areas with largely varying pollutant concentrations. 相似文献
19.
The artificial replenishment of sediment is used as a method to re-establish sediment continuity downstream of a dam. However, the impact of this technique on the hydraulics conditions, and resulting bed morphology, is yet to be understood. Several numerical tools have been developed during last years for modeling sediment transport and morphology evolution which can be used for this application. These models range from 1D to 3D approaches: the first being over simplistic for the simulation of such a complex geometry; the latter requires often a prohibitive computational effort. However, 2D models are computationally efficient and in these cases may already provide sufficiently accurate predictions of the morphology evolution caused by the sediment replenishment in a river. Here, the 2D shallow water equations in combination with the Exner equation are solved by means of a weak-coupled strategy. The classical friction approach considered for reproducing the bed channel roughness has been modified to take into account the morphological effect of replenishment which provokes a channel bed fining. Computational outcomes are compared with four sets of experimental data obtained from several replenishment configurations studied in the laboratory. The experiments differ in terms of placement volume and configuration. A set of analysis parameters is proposed for the experimental-numerical comparison, with particular attention to the spreading, covered surface and travel distance of placed replenishment grains. The numerical tool is reliable in reproducing the overall tendency shown by the experimental data. The effect of fining roughness is better reproduced with the approach herein proposed. However, it is also highlighted that the sediment clusters found in the experiment are not well numerically reproduced in the regions of the channel with a limited number of sediment grains. 相似文献
20.
Planetary equatorial waves are studied with the shallow water equations in the presence of a mean zonal thermocline gradient. The interactions between this gradient and waves are represented by three non-linear terms in the equations: one in the wind-forcing formulation in the x-momentum equation, and two for the advection of mass and divergence of the velocity field in the continuity equation. When the mean gradient is imposed but small, these three (linearized) terms will perturb the behavior of the equatorial waves. This paper gives a simple analytic treatment of this problem.The equatorial Kelvin mode is first solved with all three contributions, using a Wentzel-Kramers-Brillouin method. The Kelvin mode shows a spatial or/and temporal growth when the thermocline gradient is negative which is the usual situation in the equatorial Pacific ocean (deep thermocline in the west and shallow in the east). The more robust and efficient contribution comes from the advection term.The single effect of the advection of the mean zonal thermocline gradient is then studied for the Kelvin and planetary Rossby modes. The Kelvin mode remains unstable (damped), while the Rossby modes appear damped (unstable) for a negative (positive) thermocline gradient. 相似文献