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1.
We investigate static spherically symmetric perfect fluid models in Newtonian gravity for barotropic equations of state that are asymptotically polytropic at low and high pressures. This is done by casting the equations into a three-dimensional regular dynamical system with bounded dependent variables. The low and high central pressure limits correspond to two two-dimensional boundary subsets, described by homology invariant equations for exact polytropes. Thus the formulation naturally places work about polytropes in a more general context. The introduced framework yields a visual aid for obtaining qualitative information about the solution space and is also suitable for numerical investigations. Moreover, it makes a host of mathematical tools from dynamical systems theory available, which allows us to prove several theorems about the relationship between the equation of state and properties concerning total masses and radii. 相似文献
2.
K.-M. Shyue 《Journal of computational physics》2010,229(23):8780-8801
We describe a simple mapped-grid approach for the efficient numerical simulation of compressible multiphase flow in general multi-dimensional geometries. The algorithm uses a curvilinear coordinate formulation of the equations that is derived for the Euler equations with the stiffened gas equation of state to ensure the correct fluid mixing when approximating the equations numerically with material interfaces. A γ-based and a α-based model have been described that is an easy extension of the Cartesian coordinates counterpart devised previously by the author [30]. A standard high-resolution mapped grid method in wave-propagation form is employed to solve the proposed multiphase models, giving the natural generalization of the previous one from single-phase to multiphase flow problems. We validate our algorithm by performing numerical tests in two and three dimensions that show second order accurate results for smooth flow problems and also free of spurious oscillations in the pressure for problems with interfaces. This includes also some tests where our quadrilateral-grid results in two dimensions are in direct comparisons with those obtained using a wave-propagation based Cartesian grid embedded boundary method. 相似文献
3.
Two-dimensional thermoelasticity analysis of functionally graded thick beams is presented using the state space method coupled
with the technique of differential quadrature. Material properties vary continuously and smoothly through the beam thickness,
leading to variable coefficients in the state equation derived from the elasticity equations. Approximate laminate model is
employed to translate the state equation into the one with constant coefficients in each layer. To avoid numerical instability,
joint coupling matrices are introduced according to the continuity conditions at interfaces in the approximate model. The
differential quadrature procedure is applied to discretizing the beam in the axial direction to make easy the treatment of
arbitrary end conditions. A simply-supported beam with exponentially varying material properties is considered to validate
the present method. Numerical examples are performed to investigate the influences of relative parameters. 相似文献
4.
John D. Ramshaw 《Journal of statistical physics》1989,56(1-2):149-158
Phase space density representations of inviscid fluid dynamics were recently discussed by Abarbanel and Rouhi. Here it is shown that such representations may be simply derived and interpreted by means of the Liouville equation corresponding to the dynamical system of ordinary differential equations that describes fluid particle trajectories. The Hamiltonian and Poisson bracket for the phase space density then emerge as immediate consequences of the corresponding structure of the dynamics. For barotropic fluids, this approach leads by direct construction to the formulation presented by Abarbanel and Rouhi. Extensions of this formulation to inhomogeneous incompressible fluids and to fluids in which the state equation involves an additional transported scalar variable are constructed by augmenting the single-particle dynamics and phase space to include the relevant additional variable. 相似文献
5.
本文研究二维多相反应流的数值模拟方法.对于非完全流体,考虑两种状态方程:刚性气体状态方程和JWL(Jones-Wilkins-Lee)型的状态方程.针对这些非完全流体,研究一种混合单元物理量重构法,它由单元内的已知物理量出发,应用单元内不同相的物理量之间的关系:混合密度与各自密度之间的关系、及混合内能与各物质内能之间的关系,再由温度与压强平衡条件,建立关于单变量的非线性方程,对所得方程通过"移动跟踪法"求解,得到单元内的压力、温度及声速等.再利用HLLC解法器,求解各个单元边界数值通量,从而构造一种高效的数值方法.数值结果表明:该算法能清晰地捕捉爆轰波的结构特征,胞格排列有序,三波点的特征明显. 相似文献
6.
本文利用数值模拟方法对多孔铝在热击波作用下的力学效应进行了分析和研究。文中对用于描述多孔材料本构关系的p-a方程进行了改进,使其具有更为广泛的适用性和合理性,尤其是在描述多孔材料发生熔化出现零压时,具有突出的优越性。在处理压强p和多孔材料的多空度a的关系时,我们采用了M. M. Carroll的空心球壳模型,并考虑到热辐射引起的能量沉积作用,对其进行了修正,使其能恰当地反映出在热辐射条件下所遵循的规律。描述材料状态变化的是GRAY的金属三相物态方程。由上所述建立起来的这套方程及其对多孔材料中热击波的处理结果都具有一定的价值。 相似文献
7.
Numerical method of the Riemann problem for two-dimensional multi-fluid flows with general equation of state
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Based on the classical Roe method, we develop an interface capture method
according to the general
equation of state, and extend the single-fluid Roe method to the
two-dimensional (2D) multi-fluid flows, as
well as construct the continuous Roe matrix for the whole flow field. The
interface capture equations and
fluid dynamic conservative equations are coupled together and solved by
using any high-resolution
schemes that usually suit for the single-fluid flows. Some numerical
examples are given to illustrate the
solution of 1D and 2D multi-fluid Riemann problems. 相似文献
8.
H. L. Frisch 《Journal of statistical physics》1977,17(2):89-94
The pairwise additive potential energy and molecular distribution functions are obtained for a one-dimensional fluid satisfying a version of the Kirkwood-modified Tait equation of state.This work was supported by the National Science Foundation Grant CHE 7404171A02. 相似文献
9.
We propose a new model and a solution method for two-phase compressible flows. The model involves six equations obtained from conservation principles applied to each phase, completed by a seventh equation for the evolution of the volume fraction. This equation is necessary to close the overall system. The model is valid for fluid mixtures, as well as for pure fluids. The system of partial differential equations is hyperbolic. Hyperbolicity is obtained because each phase is considered to be compressible. Two difficulties arise for the solution: one of the equations is written in non-conservative form; non-conservative terms exist in the momentum and energy equations. We propose robust and accurate discretisation of these terms. The method solves the same system at each mesh point with the same algorithm. It allows the simulation of interface problems between pure fluids as well as multiphase mixtures. Several test cases where fluids have compressible behavior are shown as well as some other test problems where one of the phases is incompressible. The method provides reliable results, is able to compute strong shock waves, and deals with complex equations of state. 相似文献
10.
多介质流体动力学过程的数值模拟往往涉及混合物状态方程的计算. 做图法和Newton 法是混合物状态方程计算常采用的方法, 前者虽直观精度却差, 后者计算效率高却只具有局部收敛性, 当解与其初始猜测值相差较远时Newton法不一定能够获得收敛解. 为此, 本文给出一种具有大范围收敛性的嵌入算法(imbedding method)求解混合物状态方程, 其基本思想是通过引入嵌入参数, 将待解的混合物状态方程和易解的混合物状态方程线性组合, 构成嵌入方程组, 当嵌入参数从0连续地变化到1 时, 嵌入方程组的解由易解的混合物状态方程的解连续地变化为待解的混合物状态方程的解. 嵌入方程组可由Newton法迭代求解, 也可转化为以嵌入参数为自变量的常微分方程组, 从而易于由成熟的计算方法如梯形法等进行求解. 进一步利用热力学基本关系, Maxwell形式的微分方程描述了压力和温度随嵌入参数的演化速率与应变速率和组分质量分数演化速率的关系. 对铅锡混合物热力学量的计算表明了本文算法的有效性. 相似文献
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使用Weierstrass和Chebyshev定理, 并参考标度粒子理论和Percus-Yevick积分方程理论的状态方程,证明硬球流体存在一个多项式序列,致使其状态方程由该序列的极限给出. 获得了从三阶到八阶的最佳多项式,这样Carnahan-Starling方程可以逐级改进. 得到的状态方程和在稳定和亚稳定流体分支上的模拟结果符合得很好. 相似文献
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Some points about the search for analytical expressions for the equation of state of the hard-disc fluid are discussed in the light of the most recent advances in the field. New and accurate equations of state for this fluid are proposed. 相似文献
16.
Spectrum of Binding System for Heavy Quark (Q) with an Anti-sbottom (b) or for a Sbottom and Anti-sbottom Pair 总被引:1,自引:0,他引:1
Since long-lived light bottom squark (sbottom) and its anti-particle with a mass close to the bottomquark have not been excluded by experiments so far, so we would like to consider such a sbottom to combine with itsanti-particle to form a color singlet meson-like bound state or to combine with a common anti-quark to form a fermion-like one, or accordingly their anti-particles to form an anti-particle bound system. Namely we calculate the low-lyingspectrum of the systems specifically based on QCD inspired potential model. To be relativistic as much as possible, westart with the framework of Bethe-Salpeter (BS) equation even for non-relativistic binding systems. Finally, we obtainthe requested spectrum by constructing general forms of the BS wave functions and solving the BS equations underinstantaneous approximation. 相似文献
17.
A state space model(SSM) is derived for quantum-dot semiconductor optical amplifiers(QD-SOAs).Rate equations of QD-SOA are formulated in the form of state update equations,where average occupation probabilities along QD-SOA cavity are considered as state variables of the system.Simulations show that SSM calculates QD-SOA's static and dynamic characteristics with high accuracy. 相似文献
18.
A universal cubic equation of state (UC EOS) is proposed based on a modification of the virial Percus-Yevick (PY) integral equation EOS for hard-sphere fluid. The UC EOS is extended to multi-component hard-sphere mixtures based on a modification of Lebowitz solution of PY equation for hard-sphere mixtures. And expressions of the radial distribution functions at contact (RDFC) are improved with the form as simple as the original one. The numerical results for the compressibility factor and RDFC are in good agreement with the simulation results. The average errors of the compressibility factor relative to MC data are 3.40%, 1.84% and 0.92% for CP3P, BMCSL equations and UC EOS, respectively. The UC EOS is a unique cubic one with satisfactory precision among many EOSs in the literature both for pure and mixture fluids of hard spheres. 相似文献
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Ghost Fluid方法与双介质可压缩流动计算 总被引:1,自引:1,他引:0
应用带有Isobaric修正的GhostFluid方法配合LevelSet方法计算可压缩双介质无粘流动.该方法可以消除计算流体界面时所产生的数值跳动和耗散,且编程上比界面跟踪法简单.应用WENO格式数值求解欧拉方程和LevelSet方程,对由刚性气体状态方程所支配的一二维双介质流动进行数值计算,得到了分辨率较高的计算结果. 相似文献