Model for large strain consolidation with compressible pore fluid

A numerical model, called CCPF1 (C onsolidation with C ompressible P ore F luid 1 ), is presented for one‐dimensional large strain consolidation of a saturated porous medium with compressible pore fluid. The algorithm includes all the capabilities of a previous large strain consolidation code, CS2, written for incompressible pore fluid. In addition, fluid density and fluid viscosity are functions of fluid pressure in CCPF1. Generalization of the numerical approach to accommodate these functions requires several modifications to the CS2 method, including phase relationships, intrinsic permeability, pore pressure, fluid potential, and mass flux. Inertial forces are neglected and isothermal conditions are assumed. The development of CCPF1 is first presented, followed by an example that illustrates the effects of pore fluid compressibility on the mechanics of consolidation of saturated porous media. Copyright © 2004 John Wiley & Sons, Ltd.     

Perturbations of the Kepler Problem in Global Coordinates: A Program

The present paper is a brief report of how, along the lines of a previous paper, the implementation of the program KEPLER¹, for the numerical integration of the perturbations of the Kepler problem, has been carried out.     

Tidal disruption model for the interacting pair of galaxies VV 117 (NGC 2444/45)

A series of N-body simulations have been performed to interpret the interacting pair of galaxies VV 117 (NGC 2444/45). The galaxies have been modelled assuming a mass ratio two. The simulations use various values for the distance of closest approach and the eccentricity of the relative orbit of the pair. A plausible scenario for the tidal disruption of the less massive galaxy is proposed. NGC2444, having double the mass of NGC 2445, has undergone penetrating collision with the latter in a hyperbolic or a parabolic orbit. After the first collision, the orbit has become bound. Our results show that VV 117 has either just emerged from the first collision or are on the verge of a second collision. NGC 2445suffers considerable disruption and mass loss. NGC 2444 is not affected much. The second collision is expected to culminate in the merger of the two galaxies. This revised version was published online in July 2006 with corrections to the Cover Date.     

MULTI-DIMENSIONAL NUMERICAL STUDIES OF CONVECTION-RELATED STELLAR PROBLEMS

1　IntroductionManybottlenecksinthetheoreticalstudyofstellarevolutionarisefromthelackofunder standingofsomehighlycomplicatedprocessesthatcannotbetreatedwithanalyticaltech niques .Alargeportionoftheseprocessesisrelatedtohydrodynamics,particularlyconvec tion .Theapplicationofmultidimensionalnumericalcomputationstotheinvestigationofthesedifficultproblemshasmadegreatprogressinrecentyears .Here ,weprovideasurveyoftherecentnumericalstudiesofconvectionrelatedproblems.Theobjectiveistoassistthosewhoar…     

Modelling the outcomes of high-velocity impacts between small solar system bodies

We present a self-consistent numerical algorithm aimed at predicting the outcomes of high-velocity impacts between asteroids (or other small bodies of the solar system), based on a set of model input parameters which can be estimated from the available experimental evidence, and including the possible gravitational reaccumulation of ejected fragments whose velocity is less than a suitably defined escape velocity. All the fragment mass distributions are modelled by truncated power laws, and a possible correlation between fragment ejection velocity and mass is taken into account in different ways, including a probabilistic one. We analyze in particular the effectiveness of the gravitational reaccumulation process in terms of different choices of the collisional parameters and the assumed relationship between fragment speed and mass. Both the transition size beyond which solid targets are likely to reaccumulate a large fraction of the fragment mass and the collision energy needed to disperse most of the fragments are sensitive functions of the assumed fragment velocity versus mass relationship. We also give some examples of how our algorithm can be applied to study the origin and collisional history of small solar system bodies, including the asteroid 951 Gaspra (recently imaged by the Galileo probe) and the asteroid families.     

Kepler Equation solver

Kepler's Equation is solved over the entire range of elliptic motion by a fifth-order refinement of the solution of a cubic equation. This method is not iterative, and requires only four transcendental function evaluations: a square root, a cube root, and two trigonometric functions. The maximum relative error of the algorithm is less than one part in 10¹⁸, exceeding the capability of double-precision computer arithmetic. Roundoff errors in double-precision implementation of the algorithm are addressed, and procedures to avoid them are developed.     

Evaluation of superficial settlements in low overburden tunnel TBM excavation: Numerical approaches

In this paper the problem of the superficial settlements related to tunnel mechanised excavation is analysed considering a low overburden application example. The excavation of tunnels in urban areas has actually important diffusion. This kind of work always implies to guarantee the safety and the stability of the existing superficial structures. The use of a tunnel boring machine (TBM) represents a good method in these conditions and the estimation of the induced settlement represents a difficult engineering problem. The study shows the differences between three different numerical approaches; the results, function of the same loss of volume, evidence from a quantitative point of view, the ground settlement.     

极不充分采动条件下地表下沉规律及计算方法研究

随着煤矿开采的不断加深,地表呆动程度(开采宽度D与开采深度H之比DIH)不断降低,并逐渐趋向于极不充分采动,同样长度的工作面对地表的影响程度极不同于浅部开采。因此,需要重新认识深部开采时的地表下沉规律。极不充分采动条件下地表下沉规律具有特殊性。经过对国内外大量观测资料的综合分析,发现当开采宽度小于地表下沉起动距时(极不充分采动),地表的下沉或地表下沉率(q′／q)为零。当开采宽度达到地表移动起动距时,地表下沉缓慢增长;达到临界采动距时,地表下沉急剧增大。地表下沉率(q′／q)与开采宽、深比D／H之间为负指数函数关系。在极不充分采动条件下进行地表下沉预计时必须对概率积分法的下沉系数进行修正。算例证明了本文给出计算方法的可行性。但这种修正方法如何与概率积分法相统一仍需进一步研究。     

The general solution of the HENON–HEILES problem

The general solution of the Henon–Heiles system is approximated inside a domain of the (x, C) of initial conditions (C is the energy constant). The method applied is that described by Poincaré as ‘the only “crack” permitting penetration into the non-integrable problems’ and involves calculation of a dense set of families of periodic solutions that covers the solution space of the problem. In the case of the Henon–Heiles potential we calculated the families of periodic solutions that re-enter after 1–108 oscillations. The density of the set of such families is defined by a pre-assigned parameter ε (Poincaré parameter), which ascertains that at least one periodic solution is computed and available within a distance ε from any point of the domain (x, C) for which the approximate general solution computed. The approximate general solution presented here corresponds to ε = 0.07. The same solution is further improved by “zooming” into four square sub-domain of (x, C), i.e. by computing sufficient number of families that reduce the density parameter to ε = 0.003. Further zooming to reduce the density parameter, say to ε = 10⁻⁶, or even smaller, although easily performable in both areas occupied by stable as well as unstable solutions, was found unnecessary. The stability of all members of each and all families computed was calculated and presented in this paper for both the large solution domain and for the sub-domains. The correspondence between areas of the approximate general solution occupied by stable periodic solutions and Poincaré sections with well-aligned section points and also correspondence between areas occupied by unstable solutions and Poincaré sections with randomly scattered section points is shown by calculating such sections. All calculations were performed using the Runge-Kutta (R-K) 8th order direct integration method and the large output received, consisting of many thousands of families is saved as “Atlas of the General Solution of the Henon–Heiles Problem,” including their stability and is available at request. It is concluded that approximation of the general solution of this system is straightforward and that the chaotic character of its Poincaré sections imposes no limitations or difficulties.