共查询到20条相似文献,搜索用时 31 毫秒
1.
A residual-based (RB) scheme relies on the vanishing of residual at the steady-state to design a transient first-order dissipation, which becomes high-order at steady-state. Initially designed within a finite-difference framework for computations of compressible flows on structured grids, the RB schemes displayed good convergence, accuracy and shock-capturing properties which motivated their extension to unstructured grids using a finite volume (FV) method. A second-order formulation of the FV–RB scheme for compressible flows on general unstructured grids was presented in a previous paper. The present paper describes the derivation of a third-order FV–RB scheme and its application to hyperbolic model problems as well as subsonic, transonic and supersonic internal and external inviscid flows. 相似文献
2.
Floraine Cordier Pierre Degond Anela Kumbaro 《Journal of computational physics》2012,231(17):5685-5704
We present an Asymptotic-Preserving ‘all-speed’ scheme for the simulation of compressible flows valid at all Mach-numbers ranging from very small to order unity. The scheme is based on a semi-implicit discretization which treats the acoustic part implicitly and the convective and diffusive parts explicitly. This discretization, which is the key to the Asymptotic-Preserving property, provides a consistent approximation of both the hyperbolic compressible regime and the elliptic incompressible regime. The divergence-free condition on the velocity in the incompressible regime is respected, and an the pressure is computed via an elliptic equation resulting from a suitable combination of the momentum and energy equations. The implicit treatment of the acoustic part allows the time-step to be independent of the Mach number. The scheme is conservative and applies to steady or unsteady flows and to general equations of state. One and two-dimensional numerical results provide a validation of the Asymptotic-Preserving ‘all-speed’ properties. 相似文献
3.
We consider interface flows where compressibility and capillary forces (surface tension) are significant. These flows are described by a non-conservative, unconditionally hyperbolic multiphase model. The numerical approximation is based on finite-volume method for unstructured grids. At the discrete level, the surface tension is approximated by a volume force (CSF formulation). The interface physical properties are recovered by designing an appropriate linearized Riemann solver (Relaxation scheme) that prevents spurious oscillations near material interfaces. For low-speed flows, a preconditioning linearization is proposed and the low Mach asymptotic is formally recovered. Numerical computations, for a bubble equilibrium, converge to the required Laplace law and the dynamic of a drop, falling under gravity, is in agreement with experimental observations. 相似文献
4.
5.
K.R. Arun M. Kraft M. Luká?ová-Medvid’ová Phoolan Prasad 《Journal of computational physics》2009,228(2):565-590
We present a generalization of the finite volume evolution Galerkin scheme [M. Luká?ová-Medvid’ová, J. Saibertov’a, G. Warnecke, Finite volume evolution Galerkin methods for nonlinear hyperbolic systems, J. Comp. Phys. (2002) 183 533– 562; M. Luká?ová-Medvid’ová, K.W. Morton, G. Warnecke, Finite volume evolution Galerkin (FVEG) methods for hyperbolic problems, SIAM J. Sci. Comput. (2004) 26 1–30] for hyperbolic systems with spatially varying flux functions. Our goal is to develop a genuinely multi-dimensional numerical scheme for wave propagation problems in a heterogeneous media. We illustrate our methodology for acoustic waves in a heterogeneous medium but the results can be generalized to more complex systems. The finite volume evolution Galerkin (FVEG) method is a predictor–corrector method combining the finite volume corrector step with the evolutionary predictor step. In order to evolve fluxes along the cell interfaces we use multi-dimensional approximate evolution operator. The latter is constructed using the theory of bicharacteristics under the assumption of spatially dependent wave speeds. To approximate heterogeneous medium a staggered grid approach is used. Several numerical experiments for wave propagation with continuous as well as discontinuous wave speeds confirm the robustness and reliability of the new FVEG scheme. 相似文献
6.
We prove an almost sure invariance principle that is valid for general classes of nonuniformly expanding and nonuniformly hyperbolic dynamical systems. Discrete time systems and flows are covered by this result. In particular, the result applies to the planar periodic Lorentz flow with finite horizon.Statistical limit laws such as the central limit theorem, the law of the iterated logarithm, and their functional versions, are immediate consequences. 相似文献
7.
Using a scheme given by Marco, we prove that partially hyperbolic tori along resonant surfaces of near-integrable Hamiltonian systems possess the obstruction property in Arnold's terminology. The proof is based on a specific lambda lemma for these tori. 相似文献
8.
《Journal of Nonlinear Mathematical Physics》2013,20(3):225-266
Abstract The family of simple quasilinear systems in one space variable is partitioned into classes of commuting flows, i.e., symmetry classes. The systems in a symmetry class have the same zeroth order conserved densities and the same Hamiltonian structure. The zeroth and first order conservation laws and the Hamiltonian structure of the systems in a complete symmetry class are described. If such a system has a degenerate characteristic speed, then it has conservation laws of arbitrarily high order. Symmetry classes of 2-component hyperbolic systems correspond to coframes on the plane. The invariants of 2-component Hamiltonian hyperbolic symmetry classes are given. An exact symmetry class of 2-component hyperbolic systems is characterized by its canonical representative, and the first order conservation laws of the canonical system correspond to the infinitesimal automorphisms of the coframe. The normal forms of the rank 0 and rank 1 exact classes are listed. A simple symmetry class is tri-Hamiltonian if and only if the metric of its coframe has constant curvature. The normal forms of the tri-Hamiltonian simple classes are listed. 相似文献
9.
基于非结构四边形网格发展求解双曲守恒律的三阶加权基本无振荡(WENO)格式.针对任意非结构四边形网格选取重构模板,并给出基于线性多项式的三阶线性重构.但对于一般的非结构四边形网格,会出现非常大的线性权和负权,使得非线性重构的WENO格式对光滑问题也不稳定.本文给出一个处理非常大的线性权的优化重构方法,对优化后得到的负线性权采用分裂方法进行处理.对于非线性权,提出一种考虑局部网格和物理量间断的新光滑度量因子.采用优化重构方法和新的非线性权,当前的三阶WENO格式在质量很差的网格上也具有很好的稳定性.理论的三阶精度在数值精度测试算例中得到验证,同时一范数和无穷范数的误差绝对值不依赖于网格质量;具有强间断的数值结果证明了当前格式的有效性. 相似文献
10.
Satoshi Ii Kazuyasu Sugiyama Shintaro Takeuchi Shu Takagi Yoichiro Matsumoto Feng Xiao 《Journal of computational physics》2012,231(5):2328-2358
An interface capturing method with a continuous function is proposed within the framework of the volume-of-fluid (VOF) method. Being different from the traditional VOF methods that require a geometrical reconstruction and identify the interface by a discontinuous Heaviside function, the present method makes use of the hyperbolic tangent function (known as one of the sigmoid type functions) in the tangent of hyperbola interface capturing (THINC) method [F. Xiao, Y. Honma, K. Kono, A simple algebraic interface capturing scheme using hyperbolic tangent function, Int. J. Numer. Methods Fluids 48 (2005) 1023–1040] to retrieve the interface in an algebraic way from the volume-fraction data of multi-component materials. Instead of the 1D reconstruction in the original THINC method, a multi-dimensional hyperbolic tangent function is employed in the present new approach. The present scheme resolves moving interface with geometric faithfulness and compact thickness, and has at least the following advantages: (1) the geometric reconstruction is not required in constructing piecewise approximate functions; (2) besides a piecewise linear interface, curved (quadratic) surface can be easily constructed as well; and (3) the continuous multi-dimensional hyperbolic tangent function allows the direct calculations of derivatives and normal vectors. Numerical benchmark tests including transport of moving interface and incompressible interfacial flows are presented to validate the numerical accuracy for interface capturing and to show the capability for practical problems such as a stationary circular droplet, a drop oscillation, a shear-induced drop deformation and a rising bubble. 相似文献
11.
We give a general method for deducing statistical limit laws in situations where rapid decay of correlations has been established.
As an application of this method, we obtain new results for time-one maps of hyperbolic flows.
In particular, using recent results of Dolgopyat, we prove that many classical limit theorems of probability theory, such
as the central limit theorem, the law of the iterated logarithm, and approximation by Brownian motion (almost sure invariance
principle), are typically valid for such time-one maps.
The central limit theorem for hyperbolic flows goes back to Ratner 1973 and is always valid, irrespective of mixing hypotheses.
We give examples which demonstrate that the situation for time-one maps is more delicate than that for hyperbolic flows, illustrating
the need for rapid mixing hypotheses.
Received: 4 January 2002 / Accepted: 16 February 2002?Published online: 24 July 2002 相似文献
12.
B. K. Shivamoggi 《Czechoslovak Journal of Physics》1987,37(5):596-600
A solution for two-dimensional steady MHD flows in a nearly hyperbolic magnetic field is given. This solution exhibits the existence of a rectangular hyperbolic flow in the resistive region near the magnetic neutral point and is confirmed by recent laboratory experiments. 相似文献
13.
Dong Wang Nianyu Zou Gaofeng Cui Yi Yang Yoshinori Namihira Yinghai Zhang 《Optical Review》2012,19(6):371-375
A companding method for peak-to-average power ratio (PAPR) reduction in optical orthogonal frequency division multiplexing systems has been proposed and simulated. The proposed scheme is based on the modified hyperbolic tangent transform, which can enlarge the small signals and compress the large signals while keeping the average power invariant. Simulation results verify that the proposed companding scheme can markedly decrease the PAPR, and a good bit error rate performance is obtained. 相似文献
14.
在移动网格上构造一种反应流的动理学格式.首先利用BGK模型推导含化学反应的流体力学方程组,并利用其积分形式构造移动网格上离散格式,再利用自适应移动网格方法得到网格速度,最后利用时间精确的动理学数值方法构造数值通量,得到移动网格单元上新的物理量.一维与二维的数值实验表明这种格式同时具有高精度、高分辨率的特点. 相似文献
15.
We study Hamiltonian systems which depend slowly on time. We show that if the corresponding frozen system has a uniformly
hyperbolic invariant set with chaotic behaviour, then the full system has orbits with unbounded energy growth (under very
mild genericity assumptions). We also provide formulas for the calculation of the rate of the fastest energy growth. We apply
our general theory to non-autonomous perturbations of geodesic flows and Hamiltonian systems with billiard-like and homogeneous
potentials. In these examples, we show the existence of orbits with the rates of energy growth that range, depending on the
type of perturbation, from linear to exponential in time. Our theory also applies to non-Hamiltonian systems with a first
integral. 相似文献
16.
17.
Integrable systems are derived from inelastic flows of timelike, spacelike, and null curves in 2– and 3– dimensional Minkowski space. The derivation uses a Lorentzian version of a geometrical moving frame method which is known to yield the modified Korteveg-de Vries (mKdV) equation and the nonlinear Schrödinger (NLS) equation in 2– and 3– dimensional Euclidean space, respectively. In 2–dimensional Minkowski space, timelike/spacelike inelastic curve flows are shown to yield the defocusing mKdV equation and its bi-Hamiltonian integrability structure, while inelastic null curve flows are shown to give rise to Burgers’ equation and its symmetry integrability structure. In 3–dimensional Minkowski space, the complex defocusing mKdV equation and the NLS equation along with their bi-Hamiltonian integrability structures are obtained from timelike inelastic curve flows, whereas spacelike inelastic curve flows yield an interesting variant of these two integrable equations in which complex numbers are replaced by hyperbolic (split-complex) numbers. 相似文献
18.
For hyperbolic flows over basic sets we study the asymptotic of the number of closed trajectories γ with periods T
γ
lying in exponentially shrinking intervals ${(x - e^{-\delta x}, x + e^{-\delta x}), \; \delta > 0, \; x \to + \infty.}${(x - e^{-\delta x}, x + e^{-\delta x}), \; \delta > 0, \; x \to + \infty.} A general result is established which concerns hyperbolic flows admitting symbolic models whose corresponding Ruelle transfer
operators satisfy some spectral estimates. This result applies to a variety of hyperbolic flows on basic sets, in particular
to geodesic flows on manifolds of constant negative curvature and to open billiard flows. 相似文献
19.
Dinshaw S. Balsara 《Journal of computational physics》2010,229(6):1970-1993
In this work we present a general strategy for constructing multidimensional HLLE Riemann solvers, with particular attention paid to detailing the two-dimensional HLLE Riemann solver. This is accomplished by introducing a constant resolved state between the states being considered, which introduces sufficient dissipation for systems of conservation laws. Closed form expressions for the resolved fluxes are also provided to facilitate numerical implementation. The Riemann solver is proved to be positively conservative for the density variable; the positivity of the pressure variable has been demonstrated for Euler flows when the divergence in the fluid velocities is suitably restricted so as to prevent the formation of cavitation in the flow.We also focus on the construction of multidimensionally upwinded electric fields for divergence-free magnetohydrodynamical (MHD) flows. A robust and efficient second order accurate numerical scheme for two and three-dimensional Euler and MHD flows is presented. The scheme is built on the current multidimensional Riemann solver and has been implemented in the author’s RIEMANN code. The number of zones updated per second by this scheme on a modern processor is shown to be cost-competitive with schemes that are based on a one-dimensional Riemann solver. However, the present scheme permits larger timesteps.Accuracy analysis for multidimensional Euler and MHD problems shows that the scheme meets its design accuracy. Several stringent test problems involving Euler and MHD flows are also presented and the scheme is shown to perform robustly on all of them. 相似文献
20.
迎风紧致格式求解Hamilton-Jacobi方程 总被引:1,自引:1,他引:0
基于Hamilton-Jacobi(H-J)方程和双曲型守恒律之间的关系,将三阶和五阶迎风紧致格式推广应用于求解H-J方程,建立了高精度的H-J方程求解方法.给出了一维和二维典型数值算例的计算结果,其中包括一个平面激波作用下的Richtmyer Meshkov界面不稳定性问题.数值试验表明,在解的光滑区域该方法具有高精度,而在导数不连续的不光滑区域也获得了比较好的分辨效果.相比于同阶精度的WENO格式,本方法具有更小的数值耗散,从而有利于多尺度复杂流动的模拟中H-J方程的求解. 相似文献