共查询到20条相似文献，搜索用时 359 毫秒
1.
A Godunov-Type Scheme for Atmospheric Flows on Unstructured Grids: Euler and Navier-Stokes Equations
Nash'at Ahmad Zafer Boybeyi Rainald Löhner Ananthakrishna Sarma 《Pure and Applied Geophysics》2007,164(1):217-244
In recent years there has been a growing interest in using Godunov-type methods for atmospheric flow problems. Godunov's unique
approach to numerical modeling of fluid flow is characterized by introducing physical reasoning in the development of the
numerical scheme (van Leer, 1999). The construction of the scheme itself is based upon the physical phenomenon described by the equation sets. These
finite volume discretizations are conservative and have the ability to resolve regions of steep gradients accurately, thus
avoiding dispersion errors in the solution. Positivity of scalars (an important factor when considering the transport of microphysical
quantities) is also guaranteed by applying the total variation diminishing condition appropriately. This paper describes the implementation of a Godunov-type finite volume scheme based on unstructured
adaptive grids for simulating flows on the meso-, micro- and urban-scales. The Harten-Lax-van Leer-Contact (HLLC) approximate
Riemann solver used to calculate the Godunov fluxes is described in detail. The higher-order spatial accuracy is achieved
via gradient reconstruction techniques after van Leer and the total variation diminishing condition is enforced with the aid of slope-limiters. A multi-stage explicit Runge-Kutta time marching scheme is used for
maintaining higher-order accuracy in time. The scheme is conservative and exhibits minimal numerical dispersion and diffusion.
The subgrid scale diffusion in the model is parameterized via the Smagorinsky-Lilly turbulence closure. The scheme uses a non-staggered mesh arrangement of variables (all quantities are
cell-centered) and requires no explicit filtering for stability. A comparison with exact solutions shows that the scheme can
resolve the different types of wave structures admitted by the atmospheric flow equation set. A qualitative evaluation for
an idealized test case of convection in a neutral atmosphere is also presented. The scheme was able to simulate the onset
of Kelvin-Helmholtz type instability and shows promise in simulating atmospheric flows characterized by sharp gradients without
using explicit filtering for numerical stability. 相似文献
2.
A two‐dimensional (2D) finite‐difference shallow water model based on a second‐order hybrid type of total variation diminishing (TVD) approximate solver with a MUSCL limiter function was developed to model flooding and inundation problems where the evolution of the drying and wetting interface is numerically challenging. Both a minimum positive depth (MPD) scheme and a non‐MPD scheme were employed to handle the advancement of drying and wetting fronts. We used several model problems to verify the model, including a dam break in a slope channel, a dam break flooding over a triangular obstacle, an idealized circular dam‐break, and a tide flow over a mound. Computed results agreed well with the experiment data and other numerical results available. The model was then applied to simulate the dam breaking and flooding of Hsindien Creek, Taiwan, with the detailed river basin topography. Computed flooding scenarios show reasonable flow characteristics. Though the average speed of flooding is 6–7 m s?1, which corresponds to the subcritical flow condition (Fr < 1), the local maximum speed of flooding is 14·12 m s?1, which corresponds to the supercritical flow condition (Fr ≈ 1·31). It is necessary to conduct some kind of comparison of the numerical results with measurements/experiments in further studies. Nevertheless, the model exhibits its capability to capture the essential features of dam‐break flows with drying and wetting fronts. It also exhibits the potential to provide the basis for computationally efficient flood routing and warning information. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
3.
１ＩＮＴＲＯＤＵＣＴＩＯＮＲｉｖｅｒｓｉｎＴａｉｗａｎａｒｅｒｅｌａｔｉｖｅｌｙｓｔｅｅｐｅｒｃｏｍｐａｒｅｄｔｏｔｈｏｓｅｉｎｏｔｈｅｒｃｏｎｔｉｎｅｎｔ．Ｌｏｃａｌｙｏｃｕｒｅｄｓｕｐｅｒｃｒｉｔｉｃａｌｆｌｏｗａｒｅｆａｉｒｌｙｃｏｍｍｏｎｉｎ... 相似文献
4.
Grid refinement is introduced in a numerical groundwater model to increase the accuracy of the solution over local areas without compromising the run time of the model. Numerical methods developed for grid refinement suffered certain drawbacks, for example, deficiencies in the implemented interpolation technique; the non‐reciprocity in head calculations or flow calculations; lack of accuracy resulting from high truncation errors, and numerical problems resulting from the construction of elongated meshes. A refinement scheme based on the divergence theorem and Taylor's expansions is presented in this article. This scheme is based on the work of De Marsily (1986) but includes more terms of the Taylor's series to improve the numerical solution. In this scheme, flow reciprocity is maintained and high order of refinement was achievable. The new numerical method is applied to simulate groundwater flows in homogeneous and heterogeneous confined aquifers. It produced results with acceptable degrees of accuracy. This method shows the potential for its application to solving groundwater heads over nested meshes with irregular shapes. 相似文献
5.
In this paper a fuzzy dynamic wave routing model (FDWRM) for unsteady flow simulation in open channels is presented. The continuity equation of the dynamic wave routing model is preserved in its original form while the momentum equation is replaced by a fuzzy rule based model which is developed on the principle that during unsteady flow the disturbances in the form of discontinuities in the gradient of the physical parameters will propagate along the characteristics with a velocity equal to that of velocity of the shallow water wave. The model gets rid off the assumptions associated with the momentum equation by replacing it with the fuzzy rule based model. It overcomes the necessity of calculating friction slope (Sf) in flow routing and hence the associated uncertainties are eliminated. The robustness of the fuzzy rule based model enables the FDWRM to march the solution even in regions where the aforementioned assumptions are violated. Also the model can be used for flow routing in curved channels. When the model is applied to hypothetical flood routing problems in a river it is observed that the results are comparable to those of an implicit numerical model (INM) which solves the dynamic wave equations using an implicit numerical scheme. The model is also applied to a real case of flow routing in a field canal. The results match well with the measured data and the model performs better than the INM. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
6.
《Advances in water resources》1998,21(7):567-579
In this paper, details of a conjunctive surface-subsurface numerical model for the simulation of overland flow are presented. In this model, the complete one-dimensional Saint-Venant equations for the surface flow are solved by a simple, explicit, essentially non-oscillating (ENO) scheme. The two-dimensional Richards equation in the mixed form for the subsurface flow is solved using an efficient strongly implicit finite-difference scheme. The explicit scheme for the surface flow component results in a simple method for connecting the surface and subsurface components. The model is verified using the experimental data and previous numerical results available in the literature. The proposed model is used to study the two-dimensionality effects due to non-homogeneous subsurface characteristics. Applicability of the model to handle complex subsurface conditions is demonstrated. 相似文献
7.
《Advances in water resources》2005,28(7):661-670
Use of characteristics method integrated with cubic-spline interpolation technique (CSMOC scheme) for computation of one-dimensional and two-dimensional kinematic overland flow has been examined in this study. The characteristic trajectory is allowed to fall on space line and time line for interpolating the corresponding values at the foot of trajectory in terms of neighboring grid points. The effects of different endpoint constraints on use of cubic-spline interpolation are investigated. As far as accuracy and simplicity are concerned, the not-a-knot constraint could be a better choice. Three hypothetical examples are used to examine the capabilities of CSMOC scheme through the comparison with the analytical solution and the well-known Preissmann scheme. Some degrees of numerical diffusion and numerical oscillation, attenuating and overestimating the peak discharge, are induced by the Preissmann scheme. In contrast, the CSMOC scheme gives convincing results for the kinematic overland flow computations. 相似文献
8.
ABSTRACT Supercritical flow with sediment transport is a common phenomenon in steep rivers. This kind of flow presents features not present in rivers flowing in subcritical conditions. The development of a mathematical model to simulate supercritical flow with sediment transport in sandy rivers is described. The model is based on a numerical scheme for the integral version of the full governing equations and takes into account bottom configurations. 相似文献
9.
10.
The ground water flow model MODFLOW inherently implements a nongeneralized integrated finite-difference (IFD) numerical scheme. The IFD numerical scheme allows for construction of finite-difference model grids with curvilinear (piecewise linear) rows. The resulting grid comprises model cells in the shape of trapezoids and is distorted in comparison to a traditional MODFLOW finite-difference grid. A version of MODFLOW-88 (herein referred to as MODFLOW IFD) with the code adapted to make the one-dimensional DELR and DELC arrays two dimensional, so that equivalent conductance between distorted grid cells can be calculated, is described. MODFLOW IFD is used to inspect the sensitivity of the numerical head and velocity solutions to the level of distortion in trapezoidal grid cells within a converging radial flow domain. A test problem designed for the analysis implements a grid oriented such that flow is parallel to columns with converging widths. The sensitivity analysis demonstrates MODFLOW IFD's capacity to numerically derive a head solution and resulting intercell volumetric flow when the internal calculation of equivalent conductance accounts for the distortion of the grid cells. The sensitivity of the velocity solution to grid cell distortion indicates criteria for distorted grid design. In the radial flow test problem described, the numerical head solution is not sensitive to grid cell distortion. The accuracy of the velocity solution is sensitive to cell distortion with error <1% if the angle between the nonparallel sides of trapezoidal cells is <12.5 degrees. The error of the velocity solution is related to the degree to which the spatial discretization of a curve is approximated with piecewise linear segments. Curvilinear finite-difference grid construction adds versatility to spatial discretization of the flow domain. MODFLOW-88's inherent IFD numerical scheme and the test problem results imply that more recent versions of MODFLOW 2000, with minor modifications, have the potential to make use of a curvilinear grid. 相似文献
11.
《Advances in water resources》2003,26(11):1189-1198
A two-dimensional finite element based overland flow model was developed and used to study the accuracy and stability of three numerical schemes and watershed parameter aggregation error. The conventional consistent finite element scheme results in oscillations for certain time step ranges. The lumped and the upwind finite element schemes are tested as alternatives to the consistent scheme. The upwind scheme did not improve on the stability or the accuracy of the solution, while the lumped scheme provided stable and accurate solutions for time steps twice the size of time steps needed for the consistent scheme. A new accuracy based dynamic time step estimate for the two-dimensional overland flow kinematic wave solution is developed for the lumped scheme. The newly developed dynamic time step estimates are functions of the mesh size, and time of concentration of the watershed hydrograph. Due to lack of analytical solutions, the time step was developed by comparing numerical solutions of various levels of discretization to a reference solution using a very fine mesh and a very small time step. The time step criteria were tested on a different set of problems and proved to be adequate for accurate and stable solutions. A sensitivity analysis for the watershed slope, Manning’s roughness coefficient and excess rainfall rate was conducted in order to test the effect of parameter aggregation on the stability and accuracy of the solution. The results of this analysis show that aggregation of the slope data resulted in the highest error. The roughness coefficient had a smaller effect on the solution while the rainfall intensity did not show any significant effect on the flow rate solution for the range of rainfall intensity used. This work pioneers the challenge of providing guidelines for accurate and stable numerical solutions of the two-dimensional kinematic wave equations for overland flow. 相似文献
12.
Olu Agunloye 《Pure and Applied Geophysics》1981,119(5):1003-1023
A simple numerical inversion scheme for estimatingn-layer model parameters from observed geoelectrical resistivity data can be used in either the space or wavenumber domain. The technique utilizes Madden's Transmission Line Analogy to compute the resistivity transforms and linear filter theory to accomplish the excursions between the space and wavenumber domains. The inversion is effected by an iterative refinement scheme employing the stochastic inverse which is approximate to the generalized inverse. No singular decomposition analysis is required and the scheme is stable under ill conditions. The inversion scheme not only gives the desired estimates; it exposes redundant parameters and irrelevant data and is easily programmed on a desk-top mini computer. Examples of inverse modeling with hypothetical and field data are discussed. 相似文献
13.
We present a new streamline-based numerical method for simulating reactive solute transport in porous media. The key innovation of the method is that both longitudinal and transverse dispersion are incorporated accurately without numerical dispersion. Dispersion is approximated in a flow-oriented grid using a combination of a one-dimensional finite difference scheme and a meshless approximation. In contrast to previous hybrid alternatives to incorporate dispersion in streamline-based simulations, the proposed scheme does not require a grid and, hence, it does not introduce numerical dispersion. In addition, the proposed scheme eliminates numerical oscillations and negative concentration values even when the dispersion tensor includes the off-diagonal coefficients and the flow field is non-uniform. We demonstrate that for a set of two- and three-dimensional benchmark problems, the new proposed streamline-based formulation compares favorably to two state of the art finite volume and hybrid Eulerian–Lagrangian solvers. 相似文献
14.
Wang Jia Fujisaki‑Manome Ayumi Kessler James Cannon David Chu Philip 《Ocean Dynamics》2023,73(7):407-429
This study investigates the inertial stability properties and phase error of numerical time integration schemes in several widely-used ocean and atmospheric models. These schemes include the most widely used centered differencing (i.e., leapfrog scheme or the 3-time step scheme at n-1, n, n+1) and 2-time step (n, n+1) 1st-order Euler forward schemes, as well as 2nd-stage and 3rd- and 4th-stage Euler predictor-corrector (PC) schemes. Previous work has proved that the leapfrog scheme is neutrally stable with respect to the Coriolis force, with perfect inertial motion preservation, an amplification factor (AF) equal to unity, and a minor overestimation of the phase speed. The 1st-order Euler forward scheme, on the other hand, is known to be unconditionally inertially unstable since its AF is always greater than unity. In this study, it is shown that 3rd- and 4th-order predictor-corrector schemes 1) are inertially stable with weak damping if the Coriolis terms are equally split to n+1 (new value) and n (old value); and 2) introduce an artificial computational mode. The inevitable phase error associated with the Coriolis parameter is analyzed in depth for all numerical schemes. Some schemes (leapfrog and 2nd-stage PC schemes) overestimate the phase speed, while the others (1st-order Euler forward, 3rd- and 4th-stage PC schemes) underestimate it. To preserve phase speed as best as possible in a numerical model, alternating a scheme that overestimates the phase speed with a scheme that underestimates the phase speed is recommended. Considering all properties investigated, the leapfrog scheme is still highly recommended for a time integration scheme. As an example, a comparison between a leapfrog scheme and a 1st-order Euler forward scheme is presented to show that the leapfrog scheme reproduces much better vertical thermal stratification and circulation in the weakly-stratified Great Lakes.
相似文献15.
《Advances in water resources》2004,27(9):875-887
A physically based numerical approach is presented for modeling fracture–matrix interaction, which is a key issue for fractured reservoir simulation. Commonly used mathematical models for dealing with such interactions employ a dual- or multiple-continuum concept, in which fractures and matrix are represented as overlapping, different, but interconnected continua, described by parallel sets of conservation equations. The conventional single-point upstream weighting scheme, in which the fracture relative permeability is used to represent the counterpart at the fracture–matrix interface, is the most common scheme by which to estimate flow mobility for fracture–matrix flow terms. However, such a scheme has a serious flaw, which may lead to unphysical solutions or significant numerical errors. To overcome the limitation of the conventional upstream weighting scheme, this paper presents a physically based modeling approach for estimating physically correct relative permeability in calculating multiphase flow between fractures and the matrix, using continuity of capillary pressure at the fracture–matrix interface. The proposed approach has been implemented into two multiphase reservoir simulators and verified using analytical solutions and laboratory experimental data. The new method is demonstrated to be accurate, numerically efficient, and easy to implement in dual- or multiple-continuum models. 相似文献
16.
《Advances in water resources》1998,21(5):351-362
Flow and displacement of non-Newtonian fluids in porous media occurs in many subsurface systems, related to underground natural resource recovery and storage projects, as well as environmental remediation schemes. A thorough understanding of non-Newtonian fluid flow through porous media is of fundamental importance in these engineering applications. Considerable progress has been made in our understanding of single-phase porous flow behavior of non-Newtonian fluids through many quantitative and experimental studies over the past few decades. However, very little research can be found in the literature regarding multi-phase non-Newtonian fluid flow or numerical modeling approaches for such analyses.For non-Newtonian fluid flow through porous media, the governing equations become nonlinear, even under single-phase flow conditions, because effective viscosity for the non-Newtonian fluid is a highly nonlinear function of the shear rate, or the pore velocity. The solution for such problems can in general only be obtained by numerical methods.We have developed a three-dimensional, fully implicit, integral finite difference simulator for single- and multi-phase flow of non-Newtonian fluids in porous/fractured media. The methodology, architecture and numerical scheme of the model are based on a general multi-phase, multi-component fluid and heat flow simulator — TOUGH2. Several rheological models for power-law and Bingham non-Newtonian fluids have been incorporated into the model. In addition, the model predictions on single- and multi-phase flow of the power-law and Bingham fluids have been verified against the analytical solutions available for these problems, and in all the cases the numerical simulations are in good agreement with the analytical solutions. In this presentation, we will discuss the numerical scheme used in the treatment of non-Newtonian properties, and several benchmark problems for model verification.In an effort to demonstrate the three-dimensional modeling capability of the model, a three-dimensional, two-phase flow example is also presented to examine the model results using laboratory and simulation results existing for the three-dimensional problem with Newtonian fluid flow. 相似文献
17.
《水文科学杂志》2013,58(4):868-882
Abstract Non-Darcian flow in a finite fractured confined aquifer is studied. A stream bounds the aquifer at one side and an impervious stratum at the other. The aquifer consists of fractures capable of transmitting water rapidly, and porous blocks which mainly store water. Unsteady flow in the aquifer due to a sudden rise in the stream level is analysed by the double-porosity conceptual model. Governing equations for the flow in fractures and blocks are developed using the continuity equation. The fluid velocity in fractures is often too high for the linear Darcian flow so that the governing equation for fracture flow is modified by Forcheimer's equation, which incorporates a nonlinear term. Governing equations are coupled by an interaction term that controls the quasi-steady-state fracture—block interflow. Governing equations are solved numerically by the Crank-Nicolson implicit scheme. The numerical results are compared to the analytical results for the same problem which assumes Darcian flow in both fractures and blocks. Numerical and analytical solutions give the same results when the Reynolds number is less than 0.1. The effect of nonlinearity on the flow appears when the Reynolds number is greater than 0.1. The higher the rate of flow from the stream to the aquifer, the higher the degree of nonlinearity. The effect of aquifer parameters on the flow is also investigated. The proposed model and its numerical solution provide a useful application of nonlinear flow models to fractured aquifers. It is possible to extend the model to different types of aquifer, as well as boundary conditions at the stream side. Time-dependent flow rates in the analysis of recession hydrographs could also be evaluated by this model. 相似文献
18.
Abstract Thermal convection in a vertically-mounted, rotating annulus of a particular design proposed by Davies and Walin (1977) is investigated. The annulus used in the present study differs from the conventional type in some important aspects: the sidewalls are finitely conducting, and the thermal conductance of the sidewalls is height-dependent. The theoretical model due to Davies and Walin is briefly recounted. The present study aims to verify the theoretical model; we have acquired numerical solutions to the governing Navier-Stokes equations. The numerical results are supportive of the theoretical contentions. The near-linear dependence of the isothermal slope on the parameter D, which is a function of Ω and ΔT, is corroborated within reasonable limits. New data on the vertical and radial structures of the meridional and azimuthal flows are presented. The numerical results also confirm that the shape of the sidewall thickness has a substantial influence on the meridional flow patterns. In the bulk of the interior flow field, the dominant azimuthal flow field and the temperature field are linked by the thermal wind relation. 相似文献
19.
By implementing the moisture-based form of Richards’ equation into the geochemical modelling framework PHREEQC, a generic tool for the simulation of one-dimensional flow and solute transport in the vadose zone undergoing complex geochemical reactions was developed. A second-order, cell-centred, explicit finite difference scheme was employed for the numerical solution of the partial differential equations of flow and transport. In this scheme, the charge-balanced soil solution is treated as an assembly of elements, where changes in water and solute contents result from fluxes of elements across cell boundaries. Therefore, water flow is considered in terms of oxygen and hydrogen transport. 相似文献
20.
Numerical resolution of well-balanced shallow water equations with complex source terms 总被引：3，自引：0，他引：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