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1.
Comparison of finite difference and finite element solutions to the variably saturated flow equation
《Journal of Hydrology》2003,270(1-2):49-64
Numerical solutions to the equation governing variably saturated flow are usually obtained using either the finite difference (FD) method or the finite element (FE) method. A detailed comparison of these methods shows that the main difference between them is in how the numerical schemes spatially average the variation of material properties. Further differences are also observed in the way that flux boundaries are represented in FE and FD methods. A modified finite element (MFE) algorithm is used to explore the significance of these differences. The MFE algorithm enables a direct comparison with a typical FD solution scheme, and explicitly demonstrates the differences between FE and FD methods. The MFE algorithm provides an improved approximation to the partial differential equation over the usual FD approach while being computationally simpler to implement than the standard FE solution. One of the main limitations of the MFE algorithm is that the algorithm was developed by imposing several restrictions upon the more general FE solution; however, the MFE is shown to be preferable over the usual FE and FD solutions for some of the test problems considered in this study. The comparison results show that the FE (or MFE) solution can avoid the erroneous results encountered in the FD solution for coarsely discretized problems. The improvement in the FE solution is attributed to the broader hydraulic conductivity averaging and differences in the representation of flux type boundaries. 相似文献
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Abstract The singular differential equations for finite temperature relativistic magnetohydrodynamic (MHD) winds integrate to two algebraic equations when the source magnetic field is a monopole. This simplification enables an extensive characterization of the asymptotic wind solutions in terms of source parameters. We will consider only the critical solutions-those that pass smoothly through both an intermediate (Alfvenic) and a fast MHD critical point and expand to zero pressure at infinite radial distance from the source. Because the constants of motion must be specified to extremely high accuracy, the critical solutions cannot be found analytically. Synopsis of many numerical solutions reveals a uniform parametric characterization of the asymptotic wind in terms of one combination of source parameters, Z, the mean source particle energy divided by mc2[sgrave]½, where [sgrave] is a generalization of Michel's (1969) cold relativistic wind strength parameter. Cool winds, with Z<1, behave asymptotically much as Michel's cold wind minimum torque solution; Z1 hot winds have quite different, but simply characterized, asymptotic solutions. Thus, the strength of magnetized relativistic outflows can depend critically upon the temperature of the source. 相似文献
4.
The mechanisms of finite brittle strain 总被引：1，自引：0，他引：1
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A finite element model which solves the vertically integrated momentum and continuity equations is described. Linear triangular elements are used to describe the geometry and parameter variations. The Galerkin method of weighted residuals is employed to cast the equations in a form amenable to numerical solution. The model is based on a fully implicit formulation using finite differences for the temporal derivatives.Means of evaluating the non-linear terms of the governing equations are described, and model results are presented for a frictionless tidal channel. The example is chosen such that the non-linearities have a large influence on the solution, and as a result the linearization scheme significantly affects the model's behaviour.Suppression of the non-linear instabilities generated by the convective terms in the momentum equations is examined for the case of flow around a 180° bend. Both the imposition of artificially high roughness coefficients and the use of an effective eddy viscosity are examined in terms of their ability to damp the oscillations which arise for this example.Finally, model results are presented for a case study involving determination of remedial measures to improve flow conditions at a river outfall in Southern Ontario. 相似文献
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Summary The anomalies in relativistic theory resulting from the infinities present in Riemannian geometry as used by Einstein are discussed and a better solution proposed by introducing a discrete and indivisible time unit. In considering the approach of non-simultaneity, as recently published in this Journal (Thyssen-Bornemisza andGrayson [11]), all infinities are assumed eliminated in our universe. To fully develop the geodesic of a four-dimensional universe the perspective of discreteness seems a basic requirement.Professor Emeritus, 15 Central Park West, New York (Leaders in American Science, 8th Edition, page 611). 相似文献
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Water jet flow has many usages in the field of management and water resource operation that can be applied in mixing, dilution and aerification. The current study has calculated the flow velocity, length and height of jet penetration area (jet and main flow are of opposite directions) by the use of methods of finite element (FEM) and finite volume (FVM) and k–ε model. In order to evaluate and verify this turbulent model, the results of the numerical model have been compared with the experimental results. This model has been studied for consideration of various jet flow velocities and thicknesses. The conclusions have indicated that the length and the height of the penetration area have linear relationship with jet flow velocity; therefore, as the jet flow velocity increases, the length of jet penetration increases as well. The comparison of the results of numerical method with the experimental data have demonstrated that the FVM holds less convergence time and better results compared with FEM. 相似文献
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The finite strip method is used to study the dynamic response of surface strip foundations. This method is simple to use and versatile. The two-dimensional problem is effectively reduced to an equivalent one-dimensional problem. The choice of trigonometric series for the displacement functions results in the uncoupling of the terms of the series and a significant reduction in the semi-bandwidth of the complex set of equations, making the method well suited to small computers. Non-homogeneous soil profiles are treated as a matter of course. The finite strip solutions are shown to be in general agreement with other theoretical methods of analysis. 相似文献
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Summary The problem of the propagation of finite Love Waves in a heterogeneous elastic half space lying over a homogeneous elastic half space, using the quasilinear stress-strain relation due toS. Ferhst [4] is considered in detail. The variations of the parameter in the layer assumed to be of the form 1= 0e
z, 0e
z where is a constant andz is distance measured from the surface into the layer. 相似文献
10.
S. S. De 《Pure and Applied Geophysics》1968,69(1):46-59
Summary The displacements and shearing stresses in an infinite medium are obtained for a finite line source, taken as the limit of a prolate ellipsoid with the shearing stresses prescribed on its surface. The results have been extended to the case of a semi-infinite medium by the method of images. 相似文献
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The nonlinear equilibration of finite amplitude baroclinic waves in Phillips two-layer model is investigated at finite supercriticality. The aims are to quantify the robustness and relevance of the nonlinear theory of Warn, Gauthier and Pedlosky (WGP) for the evolution of the developing baroclinic wave, and to assess the tightness of pseudomomentum and improved pseudoenergy bounds for disturbance amplitude and energy. A high-resolution numerical model is used to perform a parameter sweep in (β,?W)-space, where β is the inverse criticality of the initial flow, and W is the ratio of the channel width to the (internal) Rossby radius. At low supercriticalities, the main predictions of WGP are found to be accurate at short times, but at long times the fully nonlinear results are found to diverge from WGP's solution. The mechanism for equilibration involves the elimination of the lower layer potential vorticity (PV) gradient, but as the supercriticality increases this is achieved by the roll-up of a train of opposite-signed vortices, rather than by coarse-grain PV homogenization as in WGP. Peak wave amplitudes are typically ≈90% of the maximum attainable under the pseudomomentum bound. New formulae are given for the pseudoenergy bound on disturbance energy which, unlike the WGP solution and the pseudomomentum bound, have non-trivial dependence on W. A detailed assessment is made of the extent to which these bounds are attained. 相似文献
12.
The problem of harbour resonance is discussed, and the probabilistic analysis of a harbour's response is carried out using a finite element technique. The results presented in this paper show the importance of considering two types of damping (radiation and friction) in the study of harbour resonance phenomena. The radiation, or energy transfer between the harbour and the open sea, is introduced using an expression similar to Sommerfeld's radiation condition, and appears as a boundary only damping term.The three analyses with or without damping and with or without radiation are compared, and it is shown that it is important to include both effects to avoid distortion of the response spectrum. The probability of exceedance for elevations is calculated for the Duncan Basin, and a way of calculating the horizontal displacements is indicated. 相似文献
13.
P. Wilh Werner 《Pure and Applied Geophysics》1952,22(3-4):166-170
Summary The study deals with expansion waves in fluids, with particular reference to hydrodynamic earthquake effects. The current assumption of steady harmonic motion is compared with the assumption that the motion is discontinuous in the sense that it starts from the initial condition of rest. A numerical example shows that the impulsive start may have a considerable influence on the dynamic water pressure. 相似文献
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A finite element model (namely TELEMAC) with a range of mesh refinements and assumptions of coastal water depths is used to
determine an optimal mesh for computing the M
2 tide in a region of significant geographical extent. The region adopted is the west coast of Britain covering the Irish and
Celtic Seas. The nature of the spatially varying topography and tidal distribution, together with a comprehensive set of measurements
and existing accurate finite difference model makes it ideal for such a study. Calculations show that a water-depth dependent
criterion for determining element size gives an optimal distribution over the majority of the region. However, local refinements
in narrow channels such as the North Channel and Bristol Channel are required. Although the specification of a zero coastal
water depth, leads to a fine near coastal grid, this does not yield the most accurate solution. In addition the computational
cost is high. In practice in a large area model the use of a non-zero coastal water depth yields optimum accuracy at minimal
computational cost. However, calculations show that accuracy is critically dependent upon nearshore water depths. Comparison
with the finite difference model shows that the bias in elevation amplitude in the finite difference solution is removed in
the finite element calculation. 相似文献
16.
J. F. Andrier 《Pure and Applied Geophysics》1991,136(2-3):281-296
It is a common feature to observe on deep reflection profiles, short (less than the Fresnel area diameter) and strongly discontinuous lower crustal reflections. Such wave patterns can be attributed to variations in the crustal properties on the scale of a few wavelengths. In order to explain these characteristics, we have computed finite-difference synthetic seismograms for various types of deep heterogeneities. Focusing, defocusing and interference effects were especially studied. The results can only be interpreted in a qualitative manner because our models exhibit departures from the real cases (lower frequency content, and only two-dimensional structures). It is found that simple undulations of the deep interfaces can hardly produce the discontinuous pattern observed, but high velocity intrusions generate complex interferences matching the reflection character of real data. Furthermore, the reflection patterns strongly depend both on length and shape of the inclusions. 相似文献
17.
The subject of this paper is the finite element analysis of axisymmetric solids subjected to axisymmetric static and dynamic loading, and taking into account material as well as geometric non-linearities. A general Lagrangian formulation forms the basis for the incremental equations of motion which are solved using direct integration methods. Solution accuracy is improved by applying equilibrium correction loads at each step. Finite element discretization is achieved through the use of quadrilateral plane stress and axisymmetric elements with incompatible modes added for improvement of the element flexural characteristics. Several numerical examples are presented to demonstrate the effectiveness of the developed computer program. 相似文献
18.
Luděk Klimeš 《Pure and Applied Geophysics》1996,148(1-2):39-76
The accuracy of finite-difference schemes of the 2nd and 4th order in 2-D and 3-D regular rectangular grids is studied. The method of designing the schemes and estimating their accuracy is proposed. The paper is devoted to the point schemes, expressed in terms of the discretized (point) values of the wave field and material parameters. Only the common schemes applicable in smooth parts of seismic models, outside structural interfaces, are taken into account. Finite differences at structural interfaces are studied elsewhere.The inaccuracy of finite-difference schemes is governed, above all, by the error in the phase velocity, caused by discretization. This error is estimated for several finite-difference schemes. It is explicitly dependent on the direction of propagation and on wave polarization. The maximum phase-velocity error over all directions of propagation enables the accuracy of the individual schemes to be appreciated in order to select the best one. The proposed approach is general and applicable to other finite-difference schemes, for example, of the 6th and higher orders. 相似文献
19.
《Advances in water resources》2001,24(8):843-862
We present a numerical scheme for the computation of conservative fluid velocity, pressure and temperature fields in a porous medium. For the velocity and pressure we use the primal–dual mixed finite element method of Trujillo and Thomas while for the temperature we use a cell-centered finite volume method. The motivation for this choice of discretization is to compute accurate conservative quantities. Since the variant of the mixed finite element method we use is not commonly used, the numerical schemes are presented in detail. We sketch the computational details and present numerical experiments that justify the accuracy predicted by the theory. 相似文献
20.
Sedimentary basin formation with finite extension rates 总被引：4，自引：0，他引：4
Thinning of continental crust by rapid stretching of the lithosphere produces an initial subsidence and thermal anomaly. When stretching ceases, slow decay of the thermal anomaly produces subsidence (due to thermal contraction) on a time scale of approximately 60 Ma. The dependence of the heat flow and subsidence histories on the rate of extension is determined here using a time-dependent analytical model. Results are compared with the predictions of a simpler instantaneous stretching model and constraints on the use of the latter are provided in terms of the duration and amount of stretching. For most basins the simple model gives reasonably accurate results provided the duration of stretching is less than 20 Ma. 相似文献