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1.
This is the first paper in a two-part series on the implementation of Godunov-type schemes on unstructured grids for atmospheric flow simulations. Construction of a high-resolution flow solver for the scalar transport equation is described in detail. Higher-order accuracy in space is achieved via a MUSCL-type gradient reconstruction after van Leer and the monotonicity of solution is enforced by slope limiters. Accuracy in time is maintained by implementing a multi-stage explicit Runge-Kutta time-marching algorithm. The scheme is conservative and exhibits minimal numerical dispersion and diffusion. Five different benchmark test cases are simulated for the validation of the numerical scheme.  相似文献   

2.
This short note reports the extension of the f-waves approximate Riemann solver (Ahmad and Lindeman, 2007; LeVeque, 2002; Bale et al., 2002) for three-dimensional meso- and micro-scale atmospheric flows. The Riemann solver employs flux-based wave decomposition for the calculation of Godunov fluxes and does not require the explicit definition of the Roe matrix to enforce conservation. The other important feature of the Riemann solver is its ability to incorporate source term due to gravity without introducing discretization errors. The resulting finite volume scheme is second-order accurate in space and time. The finite-difference schemes currently used in atmospheric flow models are neither conservative nor able to resolve regions of sharp gradients. The finite volume scheme described in this paper is fully conservative and has the ability to resolve regions of sharp gradients without introducing spurious oscillations in the solution. The scheme shows promise in accurately resolving flows on the meso- and micro-scales and should be considered for implementation in the dynamical cores of next generation meso- and micro-scale atmospheric flow models.  相似文献   

3.
This paper presents a well-balanced numerical scheme for simulating frictional shallow flows over complex domains involving wetting and drying. The proposed scheme solves, in a finite volume Godunov-type framework, a set of pre-balanced shallow water equations derived by considering pressure balancing. Non-negative reconstruction of Riemann states and compatible discretization of slope source term produce stable and well-balanced solutions to shallow flow hydrodynamics over complex topography. The friction source term is discretized using a splitting implicit scheme. Limiting value of the friction force is derived to ensure stability. This new numerical scheme is validated against four theoretical benchmark tests and then applied to reproduce a laboratory dam break over a domain with irregular bed profile.  相似文献   

4.
A total variation diminishing (TVD) modification of the MacCormack scheme is developed for simulating shallow water dynamics on a uniform Cartesian grid. Results obtained using conventional and deviatoric forms of the conservative non-linear shallow water equations (SWEs) are compared for cases where the bed has a varying topography. The comparisons demonstrate that the deviatoric form of the SWEs gives more accurate results than the conventional form, in the absence of numerical balancing of the flux-gradient and source terms. A further comparison is undertaken between the TVD-MacCormack model and an alternating direction implicit (ADI) model for cases involving steep-fronted shallow flows. It is demonstrated that the ADI model is unable to predict trans-critical flows correctly, and artificial viscosity has to be introduced to remove spurious oscillations. The TVD-MacCormack model reproduces all flow regimes accurately. Finally, the TVD-MacCormack model is used to predict a laboratory-scale dyke break undertaken at Delft University of Technology. The predictions agree closely with the experimental data, and are in excellent agreement with results from an alternative Godunov-type model.  相似文献   

5.
The unsteady free surface flow caused by sudden collapse of a dam produces discontinuities in the flow variables. As the flow surges downstream, it forms a moving bore front with steep gradients of water height and velocity. In the numerical simulation of this flow, proper grid distribution can play a crucial part in the prediction and resolution of the solutions. The use of presently available numerical schemes to solve this problem on a uniform course grid system fails to resolve the characteristic flow features and hence do a poor job in simulating this flow. In this paper, an adaptive grid which adjusts itself as the solution evolves is used for a better resolution of the flow properties. Rai and Anderson's12 method is used to determine the grid speed; however, a different partial differential equation based on the conservative principle of grid arc lengths for clustering grids in one-dimensional flow is used along with the St. Venant equations to numerically simulate the flow. Both the subcritical and the supercritical flows under extreme boundary conditions are solved using this technique. With a specified number of grid points, this provides better quality solutions as compared to those obtained with uniformly distributed grids.  相似文献   

6.
Most available numerical methods face problems, in the presence of variable topographies, due to the imbalance between the source and flux terms. Treatments for this problem generally work well for structured grids, but most of them are not directly applicable for unstructured grids. On the other hand, despite of their good performance for discontinuous flows, most available numerical schemes (such as HLL flux and ENO schemes) induce a high level of numerical diffusion in simulating recirculating flows. A numerical method for simulating shallow recirculating flows over a variable topography on unstructured grids is presented. This mass conservative approach can simulate different flow conditions including recirculating, transcritical and discontinuous flows over variable topographies without upwinding of source terms and with a low level of numerical diffusion. Different numerical tests cases are presented to show the performance of the scheme for some challenging problems.  相似文献   

7.
A two-dimensional (2D) numerical model has been developed to solve shallow water equations for simulation of dam-break flows. The spatial derivatives are discretized using a well-balanced explicit central upwind conservative scheme. The scheme is Riemann solver free and guarantees the positivity of the flow depth over complex topography if the Courant number is kept less than 0.25. The time integration is performed by Euler’s scheme. The model is verified against analytical results for water surface elevation and discharge for three benchmark test cases. A good agreement between analytical solutions and computed results is observed. The property of well-balancing in still water over an uneven bottom is also confirmed. The model is then validated by simulating a laboratory experiment in which a dam break flow propagates over a triangular obstacle. The model performance was found to be satisfactory. A dam break laboratory experimental test case on a frictionless horizontal bottom is also simulated for 2D validation of the model, and good agreement between simulation and the experimental data is observed. The suitability of the proposed model for real life applications is demonstrated by simulating the Malpasset dam-break event, which occurred in 1959 in France. The computed arrival time of the flood wave front and the maximum flow depths at various observation points matched well with the measurements on a 1/400 scale physical model. The overall performance indicates that this model can be applied for simulation of dam-break waves in real life cases.  相似文献   

8.
Abstract

An investigation is made of steady thermal convection of a Boussinesq fluid confined in a vertically-mounted rotating cylinder. The top and bottom endwall disks are thermal conductors at temperatures Tt and Tb with δT = Tt ? Tb >0. The vertical sidewall has a finite thermal conductance. A Newtonian heat flux condition is adopted at the sidewall. The Rayleigh number of the fluid system is large to render a boundary layer-type flow. Finite-difference numerical solutions to the full Navier-Stokes equations are obtained. The vertical motions within the buoyancy layer along the sidewall induce weak meridional flows in the interior. Because of the Coriolis acceleration, the meridional flows give rise to azimuthal flows relative to the rotating container. Strong vertical gradients of azimuthal flows exist in the regions near the endwalls. As the stratification effect increases, concentration of flow gradients in thin endwall boundary layers becomes more pronounced. The azimuthal flow field exhibits considerable horizontal gradients. The temperature field develops horizontal variations superposed on the dominant vertical distribution. As either the sidewall thermal conductance or the stratification effect decreases, the temperature distribution tends to the profile varying linearly with height. Comparisons of the sizes of the dynamic effects demonstrate that, in the bulk of flow field, the vertical shear of azimuthal velocity is supported by the horizontal temperature gradient, resulting in a thermal-wind relation.  相似文献   

9.
1 INTRODUCTION In recent years, due to the increase in population and industrial developments, mankind has faced manyproblems associated with rivers, coastal waters and reservoirs. Some of these problems are flood control,water supply, power generation, and irrigation. In addition, making new hydraulic structures changesnatural conditions. Prediction of these changes is necessary for designing such constructions. For solutionof these problems usually an assessment of flow pattern, sedim…  相似文献   

10.
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   

11.
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12.
A numerical experiment is carried out to investigate the suitability of a Boussinesq-type momentum model for simulating transcritical flows at short length transitions in open channel flow measuring structures. Two one-dimensional Boussinesq-type equation models, which incorporate different degrees of dynamic pressure corrections, are considered for this purpose. A finite difference method is employed to discretise and solve the equations. The models are then applied to simulate different test cases for flows in such channels with predominant non-hydrostatic pressure distribution effects. A comparison of the computed results with the corresponding experimental data is presented. Results of this study reveal that the proposed model, which includes a higher-order correction for the effect of the centrifugal pressure, describes well even relatively abrupt changes from sub- to super-critical flow state.  相似文献   

13.
An unstructured Godunov-type finite volume model is developed for the numerical simulation of geometrically challenging two-dimensional shallow water flows with wetting and drying over convoluted topography. In the framework of sloping bottom model, a modified formulation of shallow water equations is used to preserve mass conservation during flooding and recession. The key ingredient of the model is the use of this combination of the sloping bottom model and the modified shallow water equations to provide a robust technique for wet/dry fronts tracking and, together with centered discretization of the bed slope source term, to exactly preserve the static flow on irregular topographies. The variable reconstruction technique ensures nonnegative reconstructed water depth and reasonable reconstructed velocity, and the friction terms are solved by semi-implicit scheme that does not invert the direction of velocity components. The robustness and accuracy of the proposed model are assessed by comparing numerical and reference results of extensive test cases. Moreover, the results of a dam-break flooding over real topography are presented to show the capability of the model on field-scale application.  相似文献   

14.
A shallow flow generally features complex hydrodynamics induced by complicated domain topography and geometry. A numerical scheme with well-balanced flux and source term gradients is therefore essential before a shallow flow model can be applied to simulate real-world problems. The issue of source term balancing has been exhaustively investigated in grid-based numerical approaches, e.g. discontinuous Galerkin finite element methods and finite volume Godunov-type methods. In recent years, a relatively new computational method, smooth particle hydrodynamics (SPH), has started to gain popularity in solving the shallow water equations (SWEs). However, the well-balanced problem has not been fully investigated and resolved in the context of SPH. This work aims to discuss the well-balanced problem caused by a standard SPH discretization to the SWEs with slope source terms and derive a corrected SPH algorithm that is able to preserve the solution of lake at rest. In order to enhance the shock capturing capability of the resulting SPH model, the Monotone Upwind-centered Scheme for Conservation Laws (MUSCL) is also explored and applied to enable Riemann solver based artificial viscosity. The new SPH model is validated against several idealized benchmark tests and a real-world dam-break case and promising results are obtained.  相似文献   

15.
The effect of cloud feedback on the response of a radiative-convective model to a change in cloud model parameters, atmospheric CO2 concentration, and solar constant has been studied using two different parameterization schemes. The method for simulating the vertical distribution of both cloud cover and cloud optical thickness, which depends on the relative humidity and on the saturation mixing ratio of water vapor, respectively, is the same in both approaches, but the schemes differ with respect to modeling the water vapor profile. In scheme I atmospheric water vapor is coupled to surface parameters, while in scheme II an explicit balance equation for water vapor in the individual atmospheric layers is used. For both models the combined effect of feedbacks due to variations in lapse rate, cloud cover, and cloud optical thickness results in different relationships between changes in surface temperature, planetary temperature, and cloud cover. Specifically, for a CO2 doubling and a 2% increase in solar constant, in both models the surface warming is reduced by cloud feedback, in contrast to no feedback, with the greater reduction in scheme I as compared to that of scheme II.  相似文献   

16.
The fluid-structure interaction curvilinear immersed boundary (FSI-CURVIB) numerical method of Borazjani et al. [3] is extended to simulate coupled flow and sediment transport phenomena in turbulent open-channel flows. The mobile channel bed is discretized with an unstructured triangular mesh and is treated as a sharp-interface immersed boundary embedded in a background curvilinear mesh used to discretize the general channel outline. The unsteady Reynolds-averaged Navier-Stokes (URANS) equations closed with the k − ω turbulence model are solved numerically on a hybrid staggered/non-staggered grid using a second-order accurate fractional step method. The bed deformation is calculated by solving the sediment continuity equation in the bed-load layer using an unstructured, finite-volume formulation that is consistent with the CURVIB framework. Both the first-order upwind and the higher-order hybrid GAMMA schemes [12] are implemented to discretize the bed-load flux gradients and their relative accuracy is evaluated through a systematic grid refinement study. The GAMMA scheme is employed in conjunction with a sand-slide algorithm for limiting the bed slope at locations where the material angle of repose condition is violated. The flow and bed deformation equations are coupled using the partitioned loose-coupling FSI-CURVIB approach [3]. The hydrodynamic module of the method is validated by applying it to simulate the flow in an 180° open-channel bend with fixed bed. To demonstrate the ability of the model to simulate bed morphodynamics and evaluate its accuracy, we apply it to calculate turbulent flow through two mobile-bed open channels, with 90° and 135° bends, respectively, for which experimental measurements are available.  相似文献   

17.
The shallow water equations are used to model flows in rivers and coastal areas, and have wide applications in ocean, hydraulic engineering, and atmospheric modeling. These equations have still water steady state solutions in which the flux gradients are balanced by the source term. It is desirable to develop numerical methods which preserve exactly these steady state solutions. Another main difficulty usually arising from the simulation of dam breaks and flood waves flows is the appearance of dry areas where no water is present. If no special attention is paid, standard numerical methods may fail near dry/wet front and produce non-physical negative water height. A high-order accurate finite volume weighted essentially non-oscillatory (WENO) scheme is proposed in this paper to address these difficulties and to provide an efficient and robust method for solving the shallow water equations. A simple, easy-to-implement positivity-preserving limiter is introduced. One- and two-dimensional numerical examples are provided to verify the positivity-preserving property, well-balanced property, high-order accuracy, and good resolution for smooth and discontinuous solutions.  相似文献   

18.
Analytical Solution for Testing Debris Avalanche Numerical Models   总被引：4，自引：0，他引：4  
—We present here the analytical solution of a one-dimensional dam-break problem over inclined planes. This solution is used to test a numerical model developed for debris avalanches. We consider a dam with infinite length in one direction where material is released from rest at the initial instant. We solve analytically and numerically the depth-averaged long-wave equations derived in a topography-linked coordinate system. The numerical and analytical solutions provide for a Coulomb-type friction law at the base of the flow. The analytical solution is obtained by using the method of characteristics and describes the flow over a constant slope, provided that the angle is higher than the friction angle. The numerical model utilizes a finite-difference method based on a Godunov-type scheme. Comparison between analytical and numerical results illustrates the remarkable stability and precision of the numerical method as well as its ability to deal with strong discontinuities.  相似文献   

19.
Existing numerical investigations of dam-break flows rarely consider the effects of vegetation.This paper presents a depth-averaged two-dimensional model for dam-break flows over mobile and vegetated beds.In the model,both the consequences of reducing space for storing mass and momentum by the existence of vegetation and dragging the flow are considered:the former is considered by introducing a factor (1-c) to the flow depth,where c is the vegetation density;the later is considered by including an additional sink term in the momentum equations.The new governing equations are discretized by the finite volume method;and an existing second-order central-upwind scheme embedded with the hydrostatic reconstruction method for water depth,is used to estimate the fluxes;the source terms are estimated by either explicit or semi-explicit methods fulfilling the stability requirement.Laboratory experiments of dam-break flows or quasi-steady flows with/without vegetation effects/sediment transport are simulated.The good agreements between the measurements and the numerical simulations demonstrate a satisfactory performance of the model in reproducing the flow depth,velocity and bed deformation depth.Numerical case studies of six scenarios of dam-break flows over a mobile and vegetated bed are conducted.It is shown that when the area of the vegetation zone,the vegetation density,and the pattern of the vegetation distribution are varied,the resulted bed morphological change differs greatly,suggesting a great influence of vegetation on the dam-break flow evolution.Specifically,the vegetation may divert the direction of the main flow,hindering the flow and thus result in increased deposition upstream of the vegetation.  相似文献   

20.
Summary In numerical weather forecasting process, with primitive equations, the wind and pressure fields mutually adjust to each other until some form of balance is achieved. The type of balance so achieved by the mass and wind fields during the numerical integration of the primitive equations governing atmospheric motions is not knowna priori. This is particularly so in the case of tropical regions where the pressure wind adjustment laws prevailing in a tropical atmosphere are not well understood.In this study we perform a systematic investigation of the pressure wind adjustment relations during a numerical integration of the primitive equations governing atmospheric motions in a tropical atmosphere. Therefore, a two-day prediction experiment is carried out using the Florida State University Tropical Prediction (FSU) Model (Krishnamurti, 1969;Krishnamurti,et al. 1973;Kanamitsu, 1975). The 200 mb predicted motion (u, v) and height (z) fields are then extracted at 0, 12, 24, 36 and 48 hours of forecast time. Using these motion (u, v) fields three other 200 mb height (z) fields were computed from the inverse nonlinear, linear and quasigeostrophic balance equations. Each of these three diagnostic heights for the 200 mb pressure surface were compared with the respective 200 mb heights obtained from the Florida State University Tropical Preciction Model. The comparison is done by computing the root-mean-square differences between the predicted 200 mb height fields and each of the three 200 mb heights obtained from the inverse non-linear, linear and quasigeostrophic balance equations. The results show that the root-meansquare differences between thez fields from the FSU model and those obtained from the non-linear and linear balance equations lie within the ranges 23 to 44 and 25 to 50 metres respectively. The root-mean-square differences between the predicted heights and the heights computed from the quasigeostrophic balance equation lie in the range 54 to 62 metres. These root-mean-square differences are of significant magnitude since large-scale disturbances in the tropical atmosphere are associated with rather small pressure changes.The variations of these root-mean-square differences as one moves from one forecast time to another exhibit no clear increasing or decreasing trend. In fact the variations appear somewhat random. This rather unsystematic time variation of the root-mean-square differences is a manifestation of the constant changes of the physics in the model as different weather systems evolve in the course of the forecasting process. It seems therefore that the pressure-wind adjustments that take place during a numerical integration of the model equations are of complex nature and cannot simply be approximated by simple diagnostic relations like the ones used in this study.Most of this work was done while the author was at the Florida State University, tallahassee, USA.  相似文献   

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