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1.
The level lines of the Gaussian free field are known to be related to SLE4. It is shown how this relation allows to define chordal SLE4 processes on doubly connected domains, describing traces that are anchored on one of the two boundary components. The precise
nature of the processes depends on the conformally invariant boundary conditions imposed on the second boundary component.
Extensions of Schramm’s formula to doubly connected domains are given for the standard Dirichlet and Neumann conditions and
a relation to first-exit problems for Brownian bridges is established. For the free field compactified at the self-dual radius,
the extended symmetry leads to a class of conformally invariant boundary conditions parametrised by elements of SU(2). It
is shown how to extend SLE4 to this setting. This allows for a derivation of new passage probabilities à la Schramm that interpolate continuously from
Dirichlet to Neumann conditions. 相似文献
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3.
离子推力器推力密度分布对航天器轨道维持和修正具有重要影响.采用粒子模拟-蒙特卡罗碰撞方法模拟束流等离子体输运过程,分析束流多组分粒子喷出数量和速度等微观参数,并计算得到单孔束流推力,结合放电室出口等离子体密度分布,进一步对推力密度分布特性分析,最后开展实验验证.研究结果显示:束流中单价离子、双荷离子以及交换电荷离子的推力贡献比分别为84.63%,15.35%和1.82%,可见推力主要来源于束流中的单价离子和双荷离子,交换电荷离子对推力贡献很小;推力密度分布具有较好的中心轴对称性,从推力器中心沿着径向先快速下降后趋于缓慢;与实验结果对比,经验模型相对误差约为4.1%,数值模型相对误差约为2.8%,相比经验模型,数值模型具有更好的准确性.研究结果可为离子推力器推力密度分布均匀性等优化提供参考. 相似文献
4.
Jeffrey W. Banks William D. Henshaw Donald W. Schwendeman 《Journal of computational physics》2012,231(9):3518-3547
We describe a mixed Eulerian–Lagrangian approach for solving fluid–structure interaction (FSI) problems. The technique, which uses deforming composite grids (DCG), is applied to FSI problems that couple high speed compressible flow with elastic solids. The fluid and solid domains are discretized with composite overlapping grids. Curvilinear grids are aligned with each interface and these grids deform as the interface evolves. The majority of grid points in the fluid domain generally belong to background Cartesian grids which do not move during a simulation. The FSI-DCG approach allows large displacements of the interfaces while retaining high quality grids. Efficiency is obtained through the use of structured grids and Cartesian grids. The governing equations in the fluid and solid domains are evolved in a partitioned approach. We solve the compressible Euler equations in the fluid domains using a high-order Godunov finite-volume scheme. We solve the linear elastodynamic equations in the solid domains using a second-order upwind scheme. We develop interface approximations based on the solution of a fluid–solid Riemann problem that results in a stable scheme even for the difficult case of light solids coupled to heavy fluids. The FSI-DCG approach is verified for three problems with known solutions, an elastic-piston problem, the superseismic shock problem and a deforming diffuser. In addition, a self convergence study is performed for an elastic shock hitting a fluid filled cavity. The overall FSI-DCG scheme is shown to be second-order accurate in the max-norm for smooth solutions, and robust and stable for problems with discontinuous solutions for a wide range of constitutive parameters. 相似文献
5.
提出一种并行求解不规则区域上的Poisson方程方法,将不规则区域转化为带约束的三维结构网格表示,在该区域采用红黑排序并行求解Poisson方程.数值实验表明,方法可较好地解决不规则区域上的Poisson并行求解问题.同时评估了不规则区域对并行性能带来的影响. 相似文献
6.
In this paper, a multigrid method based on the high order compact (HOC) difference scheme on nonuniform grids, which has been proposed by Kalita et al. [J.C. Kalita, A.K. Dass, D.C. Dalal, A transformation-free HOC scheme for steady convection–diffusion on non-uniform grids, Int. J. Numer. Methods Fluids 44 (2004) 33–53], is proposed to solve the two-dimensional (2D) convection diffusion equation. The HOC scheme is not involved in any grid transformation to map the nonuniform grids to uniform grids, consequently, the multigrid method is brand-new for solving the discrete system arising from the difference equation on nonuniform grids. The corresponding multigrid projection and interpolation operators are constructed by the area ratio. Some boundary layer and local singularity problems are used to demonstrate the superiority of the present method. Numerical results show that the multigrid method with the HOC scheme on nonuniform grids almost gets as equally efficient convergence rate as on uniform grids and the computed solution on nonuniform grids retains fourth order accuracy while on uniform grids just gets very poor solution for very steep boundary layer or high local singularity problems. The present method is also applied to solve the 2D incompressible Navier–Stokes equations using the stream function–vorticity formulation and the numerical solutions of the lid-driven cavity flow problem are obtained and compared with solutions available in the literature. 相似文献
7.
We describe a numerical method for modeling temperature-dependent fluid flow coupled to heat transfer in solids. This approach to conjugate heat transfer can be used to compute transient and steady state solutions to a wide range of fluid–solid systems in complex two- and three-dimensional geometry. Fluids are modeled with the temperature-dependent incompressible Navier–Stokes equations using the Boussinesq approximation. Solids with heat transfer are modeled with the heat equation. Appropriate interface equations are applied to couple the solutions across different domains. The computational region is divided into a number of sub-domains corresponding to fluid domains and solid domains. There may be multiple fluid domains and multiple solid domains. Each fluid or solid sub-domain is discretized with an overlapping grid. The entire region is associated with a composite grid which is the union of the overlapping grids for the sub-domains. A different physics solver (fluid solver or solid solver) is associated with each sub-domain. A higher-level multi-domain solver manages the entire solution process. 相似文献
8.
LIU Chun-Ping 《理论物理通讯》2005,43(1):13-16
By using the general solutions of a new coupled Riccati equations, a direct algebraic method is described to construct doubly periodic solutions (Jacobi elliptic function solution) for the coupled nonlinear Klein-Gordon equations.It is shown that more doubly periodic solutions and the corresponding solitary wave solutions and trigonometric function solutions can be obtained in a unified way by this method. 相似文献
9.
Mohammad Mirzadeh Maxime Theillard Frédéric Gibou 《Journal of computational physics》2011,230(5):2125-2140
In this paper we present a finite difference scheme for the discretization of the nonlinear Poisson–Boltzmann (PB) equation over irregular domains that is second-order accurate. The interface is represented by a zero level set of a signed distance function using Octree data structure, allowing a natural and systematic approach to generate non-graded adaptive grids. Such a method guaranties computational efficiency by ensuring that the finest level of grid is located near the interface. The nonlinear PB equation is discretized using finite difference method and several numerical experiments are carried which indicate the second-order accuracy of method. Finally the method is used to study the supercapacitor behaviour of porous electrodes. 相似文献
10.
用非结构网格与欧拉方程计算复杂区域的二维流动 总被引:5,自引:1,他引:4
提出用Delaunay三角化方法生成非结构网格的一种过程。所生成的网格可用于复杂多连通域内的可压流计算。采用Euler方程和格心有限体积法,研制出程序,给出了算例。 相似文献
11.
The sinh-Gordon equation expansion method is further extended by generalizing the sinh-Gordon equation and constructing new ansatz solution of the considered equation. As its application, the (2+1)-dimensional Konopelchenko-Dubrovsky equation is investigated and abundant exact travelling wave solutions are explicitly obtained including
solitary wave solutions, trigonometric function solutions and Jacobi
elliptic doubly periodic function solutions, some of which are new exact
solutions that we have never seen before within our knowledge. The method can be applied to other nonlinear evolution equations in mathematical physics. 相似文献
12.
《Journal of computational physics》2003,184(1):215-243
Second-order accurate elliptic solvers using Cartesian grids are presented for three-dimensional interface problems in which the coefficients, the source term, the solution and its normal flux may be discontinuous across an interface. One of our methods is designed for general interface problems with variable but discontinuous coefficient. The scheme preserves the discrete maximum principle using constrained optimization techniques. An algebraic multigrid solver is applied to solve the discrete system. The second method is designed for interface problems with piecewise constant coefficient. The method is based on the fast immersed interface method and a fast 3D Poisson solver. The second method has been modified to solve Helmholtz/Poisson equations on irregular domains. An application of our method to an inverse interface problem of shape identification is also presented. In this application, the level set method is applied to find the unknown surface iteratively. 相似文献
13.
ZHAO Hu RAO Ze-Lang CHEN Jin HUANG Fu YANG Shi-Jie 《理论物理通讯》2007,47(4):728-732
We have theoretically studied the nucleation of superconductivity in doubly connected superconductors in the form of long superconducting cylinders. The giant vortex states are investigated with the nonlinear Ginzburg-Landau theory. The solutions of Ginzburg-Landau equations are solved numerically with relaxation method. The quantum size effect is clearly shown through the calculation of free energy. 相似文献
14.
《Journal of Electrostatics》2014,72(5):372-380
Impulse coefficient is calculated, for the first time, by considering the response of the current injection electrode connected to ground grids for lightning subsequent return strokes. It is observed that the impulse coefficient can be substantially amplified specially for low resistivity soils (e.g. forest grounds) and the enlargement is a function of the length of the injection electrode. Several rigorous finite-difference time-domain (FDTD)-based simulations have been performed and a new semi-empirical formula for impulse coefficient, which takes into account the injection electrode's length, is provided. The proposed expression is verified experimentally. 相似文献
15.
使用混合网格计算非达西渗流 总被引:1,自引:0,他引:1
针对垂直裂缝井的特殊流动模式,从非达西定律出发,建立二维平面的非达西渗流方程.通过建立一组无量纲量,最终得到无量纲的渗流方程及其定解条件.假定外边界为圆形,用PEBI网格及混合网格对求解区域进行网格划分,用有限差分法对无量纲的方程进行离散,最终得到垂直裂缝井的井底压力数值解.根据此数值解并考虑井筒存储和表皮因子的影响,得到真实垂直裂缝井的井底压力.对计算结果的分析表明,使用混合网格求解非达西渗流井底压力相当准确,该方法也适用于水平井等更复杂井型及复杂边界的问题求解. 相似文献
16.
Kyohei Shibano Reo Kontani Hiroshi Hirai Mikio Hasegawa Kazuyuki Aihara Hisao Taoka David McQuilkin Rikiya Abe 《The European physical journal. Special topics》2014,223(12):2611-2620
In recent years, practical research related to distributed power generation and networked distribution grids has been increasing. This research uses a relatively abstract model for the cost reduction in the Digital Grid Power Network. In the Digital Grid, the traditional wide-area synchronous grid is divided into smaller segmented grids which are connected asynchronously. In this paper, we demonstrate how to formulate the minimized cost of power generation by using linear programming methods, while considering the cost of electric transmission and distribution and using asynchronous power interchange among separate grids. 相似文献
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18.
In the present paper, the mathematical expectation and variance of the number of queries in an infinite linear queue are calculated for the Poisson synchronous doubly stochastic stream of incoming queries with two intensity states. 相似文献
19.
Paul C. Fife Hansjrg Kielhfer Stanislaus Maier-Paape Thomas Wanner 《Physica D: Nonlinear Phenomena》1997,100(3-4):257-278
In this paper we prove the existence of doubly periodic solutions of certain nonlinear elliptic problems on
2 and study the geometry of their nodal domains. In particular, we will show that if we perturb a nonlinear elliptic equation exhibiting a small amplitude doubly periodic solution whose nodal domains form a checkerboard pattern, then the perturbed equation will have a unique nearby solution which is still doubly periodic, but for which the nodal line structure breaks up. Moreover, we indicate what can happen if we start with a large amplitude doubly periodic solution whose nodal domains form a checkerboard pattern, and we relate these solutions to the Cahn-Hilliard equation and spinodal decomposition. 相似文献
20.
YANZhen-Ya 《理论物理通讯》2004,42(5):645-648
A Weierstrass elliptic function expansion method and its algorithm are developed in this paper. The method changes the problem solving nonlinear evolution equations into another one solving the corresponding system of nonlinear algebraic equations. With the aid of symbolic computation (e.g. Maple), the method is applied to the combined KdV-mKdV equation and (2 1)-dimensional coupled Davey-Stewartson equation. As a consequence, many new types of doubly periodic solutions are obtained in terms of the Weierstrass elliptic function. Jacobi elliptic function solutions and solitary wave solutions are also given as simple limits of doubly periodic solutions. 相似文献