半离散Jacobi-球面调和谱格式用于流体低马赫数流动

本文提出了一种用于解决流体在球内以低马赫数流动问题的半离散Jacobi-球面调和谱格式,并证明了它的稳定性和收敛性.所用技巧也可应用于球形区域上其它非线性问题.     

三维可压缩Boltzmann模型及其在低Mach数湍流中的应用

改进了有限差分格子Boltzmann方法(FDLBM),以直接数值模拟气动噪声.基于LB求解器特性,采用动力学方程中的恒定对流速度以实施高阶迎风差分,提高了声波和湍流的分辨率.通过建立一个新的三维粒子模型,计算得到了任意比热容的三维可压缩Navier-Stokes系统.此外,利用Bhatnagar-Gross-Krook (BGK)碰撞算子,通过引入热流量修正,实现了Prandtl数的可变性.在激波管内弱声波以及伴随有温度梯度的Taylor-Couette层流的验证计算中,提出的新方法结果良好.此外也对NACA0012翼型绕流进行了三维模拟.其中,Reynolds数、Mach数和攻角分别取2× 105,8.75×10-2以及9°.计算发现,在机翼前缘附近的分离气流位置,以及表面压力波动强度的Maeh数依赖性方面,数值计算结果与实验结果相吻合.     

可压缩流动的Fourier谱-有限元解法

本文考虑n维(n=2,3)可压缩流动的带有单向周期边值条件问题的数值解.我们在周期方向采用Fourier谱方法,在非周期方向采用有限元方法,从而构造了一类谱-有限元格式.文中严格分析了计算误差,得到了收敛阶的估计.     

Efficient Solution of the Compressible Euler Equations for Low Mach Numbers

This paper investigates the benefits of local preconditioning for the compressible Euler equations to predict nearly incompressible fluid flow. The AUSMDV(P) upwind method by Edwards and Liou is employed to maintain the spatial accuracy of the method for low Mach numbers. The results indicate excellent solution quality and fast convergence to steady state for compressible as well as nearly incompressible fluid flow. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Asymptotic Error Expansions for Numerical Solutions of Integral Equations

A general theorem dealing with asymptotic error expansions fornumerical solutions of linear operator equations is proved.This is applied to the Nystr?m, collocation, and Galerkin methodsfor second kind, Fredholm integral equations. For example, weshow that when piecewise polynomials of degree m–1 areused, the iterated Galerkin solution admits an error expansionin even powers of the step-size h, beginning with a term inh^2m.     

The Zero Mach Number Limit of the Three-Dimensional Compressible Viscous Magnetohydrodynamic Equations

This paper is concerned with the zero Mach number limit of the three-dimension- al compressible viscous magnetohydrodynamic equations. More precisely, based on the local existence of the three-dimensional compressible viscous magnetohydrodynamic equations, first the convergence-stability principle is established. Then it is shown that, when the Mach number is sufficiently small, the periodic initial value problems of the equations have a unique smooth solution in the time interval, where the incompressible viscous magnetohydrodynamic equations have a smooth solution. When the latter has a global smooth solution, the maximal existence time for the former tends to infinity as the Mach number goes to zero. Moreover, the authors prove the convergence of smooth solutions of the equations towards those of the incompressible viscous magnetohydrodynamic equations with a sharp convergence rate.     

Numerical Prediction of Aerodynamic Noise Generated from an Aircraft in Low Mach Number Flight

The paper describes numerical prediction of aerodynamic noise generated from an Aircraft. Simulation of turbulent flow is done solving the incompressible Navier-Stokes equation, where turbulence is modeled applying the orthogonal subgrid scale (OSGS) method with dynamical subscales. Because of comparison, the same simulation is done using the LES (Large Eddy simulation). It is shown how simulation of turbulent flow affects the prediction of acoustic sources calculated using Lighthill's analogy. Translation from the time to frequency domain is done through DFT (Direct Fourier Transform), which gives smaller usage of memory. Acoustic sources are used in the inhomogeneous Helmholtz equation to simulate pressure wave propagation in the domain. It is shown that OSGS with dynamical subscales gives better representation of the spectrum. Overall, better prediction of energy transfer across large and small eddies will give better allocation and presentation of acoustics sources. These sources will change wave propagation of the pressure in the acoustic field. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multiscale Considerations for Sound Generation in Low Mach Number Flows

Classical approaches in aeroacoustics are mainly based on analytical solutions of the linear wave equations which are valid in the far field. The sound generation is approximated by source terms obtained from a flow simulation. This procedure designated as the ‘acoustic analogy’ was initiated in the classical work of Lighthill. In order to tackle the sound generation problem at low Mach numbers, we consider a multiple scale asymptotic analysis. As we deal with a fluid flow generating the sound itself, the asymptotic ansatz uses one time scale given by the flow convection, but two space scales due to the difference in fluid and sound velocity. The insight given by this analysis is used to obtain source terms describing the sound generation and perturbation equations for the sound propagation. Numerical results are shown for the example of a co‐rotating vortex pair.     

Asymptotic Analysis of Steady and Nonsteady Navier-Stokes Equations for Barotropic Compressible Flow

We study the asymptotic behavior of solutions to steady and nonsteady Navier-Stokes equations for barotropic compressible fluids with slip boundary conditions in small channels whose diameters converge to zero. We also derive the corresponding asymptotic one-dimensional equations and we analyze the sets, where L ¹-weak convergence of the pressure terms fails.     

Adaptive Runge-Kutta Discontinuous Galerkin Methods with Modified Ghost Fluid Method for Simulating the Compressible Two-Medium Flow

In this paper, we investigate using the adaptive Runge-Kutta discontinuous Galerkin (RKDG) methods with the modified ghost fluid method (MGFM) in conjunction with the adaptive RKDG methods for solving the level set function to simulate the compressible two-medium flow in one and two dimensions. A shock detection technique (KXRCF method) is adopted as an indicator to identify the troubled cell, which serves for further numerical limiting procedure which uses a modified TVB limiter to reconstruct different degrees of freedom and an adaptive mesh refinement procedure. If the computational mesh should be refined or coarsened, and the detail of the implementation algorithm is presented on how to modulate the hanging nodes and redefine the numerical solutions of the two-medium flow and the level set function on such adaptive mesh. Extensive numerical tests are provided to illustrate the proposed adaptive methods may possess the capability of enhancing the resolutions nearby the discontinuities inside of the single medium flow region and material interfacial vicinities of the two-medium flow region.     

Modeling and Numerical Simulation of Cavitation for Compressible Liquid Flow

A method for the numerical simulation of cavitation phenomena based on the thermodynamic properties of liquid and steam is described. Thereby, a homogeneous cavitation model using a fully compressible discretization technique is considered. The ability of the scheme is proven by numerical experiments.     

On Low Mach Number Preconditioning of Finite Volume Schemes

A finite volume method for inviscid unsteady flows at low Mach numbers is studied. The method uses a preconditioning of the dissipation term within the numerical flux function only. It can be observed by numerical experiments, as well as by analysis, that the preconditioned scheme yields a physically corrected pressure distribution and combined with an explicit time integrator it is stable if the time step Δt satisfies the requirement to be 𝒪(M ²) as the Mach number M tends to zero, whereas the corresponding standard method remains stable up to Δt = 𝒪(M ),M → 0, though producing unphysical results. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Uniform Asymptotic Expansions for Meixner Polynomials

Meixner polynomials m _n (x;β,c) form a postive-definite orthogonal system on the positive real line x > 0 with respect to a distribution step function whose jumps are Unlike classical orthogonal polynomials, they do not satisfy a second-order linear differential equation. In this paper, we derive two infinite asymptotic expansions for m _n (nα;β,c) as . One holds uniformly for , and the other holds uniformly for , where a and b are two small positive quantities. Both expansions involve the parabolic cylinder function and its derivative. Our results include all five asymptotic formulas recently given by W. M. Y. Goh as special cases. April 16, 1996. Date revised: October 30, 1996.     

Asymptotic Expansions for Two-Dimensional Hypersingular Integrals

Summary. We define and examine two-dimensional hypersingular integrals on [0,1)² and on [0,)² and relate their Hadamard finite-part (HFP) values to Mellin transforms. These integrands have algebraic singularities of a possibly unintegrable nature on the axes and at the origin. Extending our work on one-dimensional integrals reported in 1998, we obtain variants of the classical Euler-Maclaurin expansion for various two-dimensional integrals. In many cases, the constant term in the expansion (which is not necessarily the leading term) provides the value of the HFP integral. These expansions may be used as the basis for the numerical evaluation of a class of HFP integrals by extrapolation.Mathematics Subject Classification (2000): 65D30, 65B15, 65R10This author was supported in part by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, Office of Science, U.S. Department of Energy, under Contract W-31-109-Eng 38. Part of this work was performed while this author was visiting professor at the Politecnico di Torino, under the sponsorship of the Italian C.N.R.-Gruppo Nazionale per lInformatica Matematica.This author was supported by the Ministero dellUniversitá e della Ricerca Scientifica e Tecnologica of Italy, and by the C.N.R.-Comitato n.11.     

Complete Asymptotic Expansions for Altomare Operators

In the present paper, we study an approximation process by a sequence of operators with a prescribed asymptotic behavior. The method of construction of these operators is due to Altomare and Amiar. The operators have several applications in semigroup theory. Our investigation provides an insight in their asymptotic behaviour. Finally, we apply our results to concrete examples of approximation operators recently defined and used by Altomare and Milella for the study of semigroups.     

Appell Polynomials and Asymptotic Expansions

Some properties of the Appell polynomials are studied and analyzed. Various formulas and expressions for the Appell quotient are derived and connection with asymptotic expansions is presented.     

Complete Asymptotic Expansions for the Chlodovsky Polynomials

The purpose of this article is to study the local rate of convergence of the Chlodovsky operators (C_nf)(x). As the main results, we investigate their asymptotic behaviour and derive the complete asymptotic expansions of these operators. All the coefficients of n^?k (k = 1, 2,…) are calculated in terms of the Stirling numbers of first and second kind. We mention that analogous results for the Bernstein polynomials can be found in Lorentz [2 G. G. Lorentz ( 1953 ). Bernstein Polynomials . University of Toronto Press , Toronto . [Google Scholar]].     

Uniform Asymptotic Expansions for Pricing European Options

Starting with a stochastic volatility model, in which the volatility depends on a nonlinear function of a fast varying diffusion, and assuming the fast diffusion is mean reverting, the problem of pricing European options is considered in this paper. Uniform asymptotic expansions of the option price are obtained. The formal expansions are justified and the uniform error bounds are derived using outer and inner expansions of the option prices.     

有关调和数的更多渐近展开公式

基于指数型完全Bell多项式,建立了一个一般调和数渐近展开式,并给出展开式中系数的相应递推关系.由生成函数方法进一步推导出这些系数的具体表达式.另外,我们建立了两个在对数项里只含有奇数或偶数次幂项的lacunary调和数渐近展开式,     

可压磁流体方程组弱解轨迹的渐近行为(英文)

研究可压磁流体力学方程组弱解轨迹的渐近行为,流体受任意外力作用且流经的区域为三维有界区域.对绝热指数进行适当限制,得到了有限能量弱解的轨迹的渐近行为.