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1.
异重流的形成是影响活性污泥系统二沉池水力学性能的主要因素,形成异重流的主要原因包括沉淀池内不均匀的污泥分布和温度分布。采用多相流欧拉模型、标准k-ε湍流模型和Boussinesq假设研究了二沉池中活性污泥和表面散热引起的异重流。表面散热的计算采用经验方程,数值计算结果同实验结果作了比较,结果表明模型能较好地预测辐流式二沉池的流场、温度场和污泥分布。研究还表明,Frp2Gr/Re2表示了不均匀温度分布引起的浮升力与不均匀污泥分布引起的作用力的比值,用它可以判断两种作用力在异重流的形成当中的相对大小。 相似文献
2.
The construction of regions of stability in a linear approximation for the triangular libration points in the planar, elliptical, restricted three-body problem is considered, together with the main scenarios for bifurcation when the parameters of the system pass through a boundary of such a region. A new scheme for constructing the boundaries of regions of stability is proposed, which leads to approximate formulas describing these boundaries. The resonance properties of the boundary points (from the point of view of the theory of local bifurcations) are studied. It is shown that one of the main scenarios for bifurcation is the appearance of non-stationary, 4π-periodic solutions close to a triangular libration point. 相似文献
3.
In this paper, a large‐scale diffuse interface model is used to describe the evolution of a gypsum cavity formation induced by dissolution. The method is based upon the assumption of a pseudo‐component dissolving with a thermodynamic equilibrium boundary condition. A methodology is proposed based on numerical computations with fixed boundaries in order to choose suitable parameters for the diffuse interface model, and hence predict the correct dissolution fluxes and surface recession velocity. Additional simulations were performed to check which type of momentum balance equation should be used. The numerical results did not show a strong impact of this choice for the typical initial boundary value problems under consideration. Calculations with a variable density and Boussinesq approximation were also performed to evaluate the potential for natural convection. The results showed that the impact of density driven flows was negligible in the cases under investigation. The potential of the methodology is illustrated on two large‐scale configurations: one corresponding to a gypsum lens located strictly within a porous rock formation and the other to an isolated pillar in a flooded gypsum room and pillar quarry. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
4.
The multiscale finite-volume (MSFV) method has been developed to solve multiphase flow problems on large and highly heterogeneous
domains efficiently. It employs an auxiliary coarse grid, together with its dual, to define and solve a coarse-scale pressure
problem. A set of basis functions, which are local solutions on dual cells, is used to interpolate the coarse-grid pressure
and obtain an approximate fine-scale pressure distribution. However, if flow takes place in presence of gravity (or capillarity),
the basis functions are not good interpolators. To treat this case correctly, a correction function is added to the basis
function interpolated pressure. This function, which is similar to a supplementary basis function independent of the coarse-scale
pressure, allows for a very accurate fine-scale approximation. In the coarse-scale pressure equation, it appears as an additional
source term and can be regarded as a local correction to the coarse-scale operator: It modifies the fluxes across the coarse-cell
interfaces defined by the basis functions. Given the closure assumption that localizes the pressure problem in a dual cell,
the derivation of the local problem that defines the correction function is exact, and no additional hypothesis is needed.
Therefore, as in the original MSFV method, the only closure approximation is the localization assumption. The numerical experiments
performed for density-driven flow problems (counter-current flow and lock exchange) demonstrate excellent agreement between
the MSFV solutions and the corresponding fine-scale reference solutions. 相似文献
5.
Transient bifurcation condition of partially saturated porous media at finite strain 总被引：1，自引：0，他引：1 
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下载免费PDF全文 Xiaoyu Song 《国际地质力学数值与分析法杂志》2017,41(1):135-156
Bifurcation of unsaturated soils into a localized shear band is a ubiquitous failure mode of partially saturated soils. The density and degree of saturation have major impacts on the inception of localized deformations in unsaturated soils. Unsaturated fluid flow may dramatically change the density and degree of fluid saturation of unsaturated soils. Therefore, the unsaturated fluid flow is a potential trigger for shear banding in such materials. In this paper, we derive a simplified bifurcation condition of localized deformation in unsaturated soils under the local transient condition at finite strain. This transient bifurcation condition is implemented into a nonlinear finite element code to study the inception of localized deformation in unsaturated soil specimens. Numerical simulations are conducted to study the impact of soil fabrics of density, a ‘bonding’ variable, and intrinsic permeability on the inception of localized failures via the transient bifurcation criterion. Mesh sensitivity analysis is performed to demonstrate the viscosity effect of unsaturated fluid flow on the localized deformation. Numerical simulations demonstrate that the transient bifurcation condition can detect the localized deformation triggered by the internal unsaturated fluid flow process in unsaturated soils. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
6.
Discontinuous Galerkin numerical simulations of single phase flow problem are described in this paper. The simulations show the advantages of using discontinuous approximation spaces. hp convergence results are obtained for smooth solutions. Unstructured meshes and unsmooth solutions are also considered. 相似文献
7.
This paper presents the practical closed‐form solutions for elastic settlement under the linear full‐contact pressures on rectangular areas resting upon an elastic mass. The linear pressure distribution is mostly assumed in practice for the rectangular footing having biaxial bending. The equations presented here are determined by evaluating the integration of Steinbrenner's strain approximation based on the stress solutions from the Boussinesq equations. The presented formulae are validated to be used for the elastic settlement under any point of linear full‐contact loading, triangular and embankment types of pressure cases. In this respect, it represents a significant step forward in the understanding of elastic settlement and rotation under the practical loading cases. The presented solutions are concise and easy to use. The numerical examples are demonstrated and the resulting influence factors in graphical forms are presented for their practical use especially in the elastic settlement calculations of rectangular footing subjected to the biaxial bending. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
8.
9.
Modelling shear band is an important problem in analysing failure of earth structures in soil mechanics. Shear banding is the result of localization of deformation in soil masses. Most finite element schemes are unable to model discrete shear band formation and propagation due to the difficulties in modelling strain and displacement discontinuities. In this paper, a framework to generate shear band elements automatically and continuously is developed. The propagating shear band is modelled using discrete shear band elements by splitting the original finite element mesh. The location or orientation of the shear band is not predetermined in the original finite element mesh. Based on the elasto‐perfect plasticity with an associated flow rule, empirical bifurcation and location criteria are proposed which make band propagation as realistic as possible. Using the Mohr–Coulomb material model, various results from numerical simulations of biaxial tests and passive earth pressure problems have shown that the proposed framework is able to display actual patterns of shear banding in geomaterials. In the numerical examples, the occurrence of multiple shear bands in biaxial test and in the passive earth pressure problem is confirmed by field and laboratory observations. The effects of mesh density and mesh alignment on the shear band patterns and limit loads are also investigated. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
10.
The Henry saltwater intrusion problem provides a semi-analytical solution that is largely used for benchmarking density-dependent groundwater flow models. The major drawback of this problem arises from the high dispersion value used by Henry (represented by the dimensionless parameter b?=?0.1). Finding a stable semi-analytical solution for small values of b is challenging due to the low convergence of the corresponding nonlinear system. In this work, an accurate semi-analytical solution is developed in the case of a very narrow transition zone corresponding to b?=?0.005. About 6,330 terms are used in the Fourier series to accurately represent the solution. The resolution of the corresponding highly nonlinear system is made possible by the modified Powell hybrid algorithm due to the analytical evaluation of the Jacobian, which drastically reduces the computational time. The new test problem is also investigated numerically using different numerical methods and different mesh sizes to show its high worthiness, compared to the standard Henry problem, for benchmarking density driven flow codes. 相似文献
11.
Solution for a plane strain rough‐walled hydraulic fracture driven by turbulent fluid through impermeable rock 下载免费PDF全文
下载免费PDF全文 The impact of turbulent flow on plane strain fluid‐driven crack propagation is an important but still poorly understood consideration in hydraulic fracture modeling. The changes that hydraulic fracturing has experienced over the past decade, especially in the area of fracturing fluids, have played a major role in the transition of the typical fluid regime from laminar to turbulent flow. Motivated by the increasing preponderance of high‐rate, water‐driven hydraulic fractures with high Reynolds number, we present a semianalytical solution for the propagation of a plane strain hydraulic fracture driven by a turbulent fluid in an impermeable formation. The formulation uses a power law relationship between the Darcy‐Weisbach friction factor and the scale of the fracture roughness, where one specific manifestation of this generalized friction factor is the classical Gauckler‐Manning‐Strickler approximation for turbulent flow in a rough‐walled channel. Conservation of mass, elasticity, and crack propagation are also solved simultaneously. We obtain a semianalytical solution using an orthogonal polynomial series. An approximate closed‐form solution is enabled by a choice of orthogonal polynomials embedding the near‐tip asymptotic behavior and thus giving very rapid convergence; a precise solution is obtained with 2 terms of the series. By comparison with numerical simulations, we show that the transition region between the laminar and turbulent regimes can be relatively small so that full solutions can often be well approximated by either a fully laminar or fully turbulent solution. 相似文献
12.
This paper is dedicated to numerical simulations of spiral–vortical structures in rotating gaseous disks using a simple model based on two-dimensional, non-stationary, barotropic Euler equations with a body force. The results suggest the possibility of a purely hydrodynamical basis for the formation and evolution of such structures. New, axially symmetric, stationary solutions of these equations are derived that modify known approximate solutions. These solutions with added small perturbations are used as initial data in the non-stationary problem, whose solution demonstrates the formation of density arms with bifurcation. The associated redistribution of angular momentum is analyzed. The correctness of laboratory experiments using shallow water to describe the formation of large-scale vortical structures in thin gaseous disks is confirmed. The computations are based on a special quasi-gas-dynamical regularization of the Euler equations in polar coordinates. 相似文献
13.
Egor V. Dontsov 《国际地质力学数值与分析法杂志》2019,43(2):519-529
This study investigates parametric space of solutions for a planar hydraulic fracture propagating in a homogeneous anisotropic rock. It is assumed that the fracture has an elliptical shape and is driven by a power-law fluid. The purpose of this study is to investigate the influence of anisotropy and power-law fluid rheology on the parametric space of solutions. Rock anisotropy is represented by having two values of fracture toughness, one in the vertical direction and another one in the horizontal direction. Similarly, the effect of elastic anisotropy is approximated by using two different effective elastic moduli in the vertical and horizontal directions. In contrast to the isotropic case, for which there are four limiting solutions, the problem for anisotropic rocks features six different limiting cases. These cases represent competition between toughness and viscosity in the vertical and horizontal directions and competition between fluid storage inside the fracture and fluid leak-off into formation. Approximate expressions for the limiting solutions are obtained using global volume balance and tip asymptotic solutions. Despite the developed solutions rely on a series of approximations, they precisely capture all the scaling laws associated with the problem. Zones of applicability of these limiting solutions are calculated, and their dependence on the problem parameters is investigated. 相似文献
14.
In this paper the second order characteristic (discontinuous bifurcation) condition is derived for the granular flow (fully plastic) equations. This second order bifurcation equation is shown to be formally identical to the first order localization requirement during steady elastoplastic deformation provided the elastic compliance tensor is substituted for the product of the plastic multiplier with the flow Hessian. For isotropic yield and flow functions the invariant form of the characteristic condition is given in detail, as well as an alternative expression in adapted co‐ordinates. The characteristic condition can be regarded as defining a hardening function which is maximized to identify the critical angles. When the method is applied to 3D Coulomb flow, Mohr's 3D fracture plane conditions are obtained uniquely. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
15.
从水头?诱导电位耦合驱动的角度,探讨分析黏土?水溶液体系的流体动力学性状。为此,借助动电输运原理,耦合Poisson-Boltzmann、Nernst-Planck、Navier-Stokes方程,建立了“广义力”驱动“广义流”的耦合关系。模型从黏土代表性单元体入手,计算确定各项耦合系数,用以定量考察离子迁移、流体运动的耦合性状。计算表明：采用Debye-Huckel近似计算黏土双电层电位将引起显著的误差;诱导电位产生的原因在于维持体系的电中性,其梯度大小正比于正负离子间因水头迁移性的差异而产生的潜在分离程度;诱导电位作用于离子迁移的方式在于阻滞正离子迁移,助推负离子迁移,而作用于流体运动的方式在于引起反向电渗,进而削弱水头驱动下的正向渗流;高表面带电密度的黏土矿物（如蒙脱土）处于低孔隙率的状态时,诱导电位对于渗流的削弱程度有可能异常显著。因此,建议相应的水头渗透系数的测定需要充分考虑诱导电位的影响,否则将导致较为显著的误差。 相似文献
16.
M. Schneider B. Flemisch R. Helmig K. Terekhov H. Tchelepi 《Computational Geosciences》2018,22(2):565-586
This article presents a new positivity-preserving finite-volume scheme with a nonlinear two-point flux approximation, which uses optimization techniques for the face stencil calculation. The gradient is reconstructed using harmonic averaging points with the constraint that the sum of the coefficients included in the face stencils must be positive. We compare the proposed scheme to a nonlinear two-point scheme available in literature and a few linear schemes. Using two test cases, taken from the FVCA6 benchmarks, the accuracy of the scheme is investigated. Furthermore, it is shown that the scheme is linearity-preserving on highly complex corner-point grids. Moreover, a two-phase flow problem on the Norne formation, a geological formation in the Norwegian Sea, is simulated. It is demonstrated that the proposed scheme is consistent in contrast to the linear Two-Point Flux Approximation scheme, which is industry standard for simulating subsurface flow on corner-point grids. 相似文献
17.
This work deals with sequential implicit schemes for incompressible and immiscible two-phase Darcy flows which are commonly used and well understood in the case of spatially homogeneous capillary pressure functions. To our knowledge, the stability of this type of splitting schemes solving sequentially a pressure equation followed by the saturation equation has not been investigated so far in the case of discontinuous capillary pressure curves at different rock type interfaces. It will be shown here to raise severe stability issues for which stabilization strategies are investigated in this work. To fix ideas, the spatial discretization is based on the Vertex Approximate Gradient (VAG) scheme accounting for unstructured polyhedral meshes combined with an Hybrid Upwinding (HU) of the transport term and an upwind positive approximation of the capillary and gravity fluxes. The sequential implicit schemes are built from the total velocity formulation of the two-phase flow model and only differ in the way the conservative VAG total velocity fluxes are approximated. The stability, accuracy and computational cost of the sequential implicit schemes studied in this work are tested on oil migration test cases in 1D, 2D and 3D basins with a large range of capillary pressure parameters for the drain and barrier rock types. It will be shown that usual splitting strategies fail to capture the right solutions for highly contrasted rock types and that it can be fixed by maintaining locally the pressure saturation coupling at different rock type interfaces in the definition of the conservative total velocity fluxes. The numerical investigation of the sequential schemes is also extended to the widely used finite volume Two-Point Flux Approximation spatial discretization.
相似文献18.
This study concerns the identification of parameters of soil constitutive models from geotechnical measurements by inverse analysis. To deal with the non‐uniqueness of the solution, the inverse analysis is based on a genetic algorithm (GA) optimization process. For a given uncertainty on the measurements, the GA identifies a set of solutions. A statistical method based on a principal component analysis (PCA) is, then, proposed to evaluate the representativeness of this set. It is shown that this representativeness is controlled by the GA population size for which an optimal value can be defined. The PCA also gives a first‐order approximation of the solution set of the inverse problem as an ellipsoid. These developments are first made on a synthetic excavation problem and on a pressuremeter test. Some experimental applications are, then, studied in a companion paper, to show the reliability of the method. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
19.
探索了利用数学软件Mathematica对经典课题Mindlin解进行二次积分的方法,并以矩形均布荷载为例,分析讨论了Boussinesq解和Mindlin解在地基土体中引起的应力场分布的差异,从而为工程分析采用比较合理的方法打下了基础。 相似文献
20.
Comparing the Gradual Deformation with the Probability Perturbation Method for Solving Inverse Problems 总被引：1，自引：0，他引：1
Jef Caers 《Mathematical Geology》2007,39(1):27-52
Inverse problems are ubiquitous in the Earth Sciences. Many such problems are ill-posed in the sense that multiple solutions
can be found that match the data to be inverted. To impose restrictions on these solutions, a prior distribution of the model
parameters is required. In a spatial context this prior model can be as simple as a Multi-Gaussian law with prior covariance
matrix, or could come in the form of a complex training image describing the prior statistics of the model parameters. In
this paper, two methods for generating inverse solutions constrained to such prior model are compared. The gradual deformation
method treats the problem of finding inverse solution as an optimization problem. Using a perturbation mechanism, the gradual
deformation method searches (optimizes) in the prior model space for those solutions that match the data to be inverted. The
perturbation mechanism guarantees that the prior model statistics are honored. However, it is shown with a simple example
that this perturbation method does not necessarily draw accurately samples from a given posterior distribution when the inverse
problem is framed within a Bayesian context. On the other hand, the probability perturbation method approaches the inverse
problem as a data integration problem. This method explicitly deals with the problem of combining prior probabilities with
pre-posterior probabilities derived from the data. It is shown that the sampling properties of the probability perturbation
method approach the accuracy of well-known Markov chain Monte Carlo samplers such as the rejection sampler. The paper uses
simple examples to illustrate the clear differences between these two methods 相似文献