新型上风格式(AUSM+)的性能分析及其应用

研究了新型上风格式AUSM+的分辨率、效率等性能,并用它与Roe、vanLeer上风格式数值模拟了前向台阶激波反射流动,通过对激波、膨胀波、接触间断及其间相互干扰的复杂波系的模拟对比,分析探讨了AUSM+格式的低数值耗散、间断高分辨率等特性。     

一种基于AUSM思想的通量分裂方法

根据对流迎风分裂(AUSM)思想提出一种通量分裂方法,称为K-CUSP格式.它与传统H-CUSP和E-CUSP格式的最大差异在于总能量的分裂:K-CUSP格式将无粘守恒通量中所有的运动学量分裂到对流项,所有的热力学量分裂到压力项,即总能量被分裂成动能和静焓.对于压力项的数值通量,采用一种新的界面构造方法.数值测试表明:①K-CUSP格式继承了FVS格式的简单性和稳健性.在激波后不易出现压力过冲,在膨胀区域没有振荡,优于AUSM和WPS格式;②K-CUSP格式继承了FDS格式的分辨率.激波间断的分辨率和H-CUSP、E-CUSP格式基本相同,接触间断的分辨率高于FVS格式,低于Roe、AUSM和WPS格式.AUSM和WPS格式在计算运动接触间断时,速度存在很大振荡,而新格式不存在振荡.     

高分辨率激波捕捉格式及其CFD应用

在曲线坐标下将高分辨率AUSMPW激波捕捉格式扩展到三维问题。为了提高计算精度,采用三阶MUSCL格式,将AUSMPW格式与隐械时间推进法LU－SGS方法结合,应用于可压缩无粘和有粘流动的数散模拟,计算结果与文献中计算结果和实验数据相符,并将该格式与CD、TVD、FVS和FD格式进行了比较。     

涡流数值模拟中的计算格式粘性分辨率探讨

采用理论分析和三角翼数值模拟实验相结合的方法,研究了目前常用的CFD计算格式——Jameson中心格式、RoeFDS格式、VanLeerFVS格式、迎风TVD格式等的粘性分辨率,论述了Jameson中心格式和RoeFDS格式在粘性分辨率上具有的优势,以及VanLeerFVS格式和迎风TVD格式在此方面的不足     

混合通量差分格式的比较

系统研究了几种混合通量差分格式的构造方法和耗散模型,分别对低速平板绕流、二维跨音速喷管流动和高超音速钝头体无粘绕流进行了数值模拟,结合先进的EASM湍流模型对格式的粘性分辨率和激波稳定性进行了细致的比较分析.结果表明混合通量差分格式兼顾了FDS和FVS格式的优点,具有较高的间断分辨率和数值稳定性.     

A comparative study of the performance of high-resolution non-oscillating advection schemes in the context of the motion induced by mixed region in a stratified fluid

The problem of a two-dimensional fully mixed region collapsing in continuously density-stratified medium is considered. This article deals with the numerical treatment of the advective terms in the Navier-Stokes equations in the Oberbeck-Boussinesq approximation. Comparisons are performed between the upwind scheme, flux-limiter schemes, namely, Minmod, Superbee, Van Leer, and Monotonized Centred (MC), the monotone adaptive stencil schemes, namely, ENO3 and SMIF, and weighted stencil scheme WENO5. We used laboratory experimental data of Wu as a benchmark test to compare performance of different numerical approaches. It is found that the flux-limiter schemes have the smallest numerical diffusion. The WENO5 scheme describes more accurately the width of collapse region variation with time. All considered schemes give a realistic pattern of internal gravity waves generated by collapse region.     

守恒律方程组的大时间步长叠波格式

大时间步长叠波格式最初思想为LeVeque提出的大时间步长Godunov格式,通过叠加间断分解发出的强波来构造数值格式.原方法只给出了间断强波的穿越叠加方法,文章对其进行了完善,并推广到多维.针对膨胀波提出了一种网格单元分解法可以自动满足熵条件,避免出现非物理解.给出了格式的具体计算公式,并用单个守恒律方程、一维/多维Euler方程组进行了数值计算.计算结果表明,新格式除了可以采用大时间步长的优点外,在一定范围内随CFL数增加其耗散反而更低,因而对激波接触间断膨胀波的分辨率更高.     

Robust HLLC Riemann solver with weighted average flux scheme for strong shock

Many researchers have reported failures of the approximate Riemann solvers in the presence of strong shock. This is believed to be due to perturbation transfer in the transverse direction of shock waves. We propose a simple and clear method to prevent such problems for the Harten–Lax–van Leer contact (HLLC) scheme. By defining a sensing function in the transverse direction of strong shock, the HLLC flux is switched to the Harten–Lax–van Leer (HLL) flux in that direction locally, and the magnitude of the additional dissipation is automatically determined using the HLL scheme. We combine the HLLC and HLL schemes in a single framework using a switching function. High-order accuracy is achieved using a weighted average flux (WAF) scheme, and a method for v-shear treatment is presented. The modified HLLC scheme is named HLLC–HLL. It is tested against a steady normal shock instability problem and Quirk’s test problems, and spurious solutions in the strong shock regions are successfully controlled.     

一个二阶单调迎风格式及对不定常激波反射的计算

本文介绍了Van Leer提出的一个二阶单调迎风格式。此格式有效地克服了通常二阶穿行法格式的激波后过跳现象,同时保持较窄的间断过渡区。本文主要算例是黎曼问题及平面一维强爆炸波遇固壁后正反射问题。我们改进了单调化的算法,给出了适当处理某种固壁条件的方法,因此得到了较好的数值结果。本文更正了Van Leer文章中一个主要公式及稳定性条件等的不妥之处。     

Finite difference computation of acoustic scattering by small surface inhomogeneities and discontinuities

The use of finite difference schemes to compute the scattering of acoustic waves by surfaces made up of different materials with sharp surface discontinuities at the joints would, invariably, result in the generations of spurious reflected waves of numerical origin. Spurious scattered waves are produced even if a high-order scheme capable of resolving and supporting the propagation of the incident wave is used. This problem is of practical importance in jet engine duct acoustic computation. In this work, the basic reason for the generation of spurious numerical waves is first examined. It is known that when the governing partial differential equations of acoustics are discretized, one should only use the long waves of the computational scheme to represent or simulate the physical waves. The short waves of the computational scheme have entirely different propagation characteristics. They are the spurious numerical waves. A method by which high wave number components (short waves) in the wave scattering process is intentionally removed so as to minimize the scattering of spurious numerical waves is proposed. This method is implemented in several examples from computational aeroacoustics to illustrate its effectiveness, accuracy and efficiency. This method is also employed to compute the scattering of acoustic waves by scatterers, such as rigid wall acoustic liner splices, with width smaller than the computational mesh size. Good results are obtained when comparing with computed results using much smaller mesh size. The method is further extended for applications to computations of acoustic wave reflection and scattering by very small surface inhomogeneities with simple geometries.     

MUSCL格式TV性质的非线性分析

分析求解非线性双曲型守恒律的MUSCL类格式的TV性质。首先从该类格式的一般形式出发,提出和证明了该类格式实现TVD的需求。所提TVD需求直接表示为对变量变差符号和量值限制,体现了双曲型方程解的依赖域原理,为分析MUSCL格式的TV性质提供了理论工具。同时提出了基于TVD需求再构数值解分布,以降低数值耗散从而提高接触面及膨胀波头/波尾分辨率的基本思路。     

双曲型守恒律的一种三阶半离散中心迎风格式

对一维双曲型守恒律,给出了一种具有较小数值耗散的三阶半离散中心迎风格式.该格式以Liu和Tadmor提出的三阶无振荡重构为基础,同时考虑了波传播的单侧局部速度.时间离散用保持强稳定性的三阶Runge-Kutta方法.由于不需用Riemann解算器,避免了特征分解过程,保持了中心格式简单的优点.数值算例验证本方法可进一步减小数值耗散,提高分辨率.     

A class of finite difference schemes with low dispersion and controllable dissipation for DNS of compressible turbulence

In this paper, a class of finite difference schemes which achieves low dispersion and controllable dissipation in smooth region and robust shock-capturing capabilities in the vicinity of discontinuities is presented. Firstly, a sufficient condition for semi-discrete finite difference schemes to have independent dispersion and dissipation is derived. This condition enables a novel approach to separately optimize the dissipation and dispersion properties of finite difference schemes and a class of schemes with minimized dispersion and controllable dissipation is thus obtained. Secondly, for the purpose of shock-capturing, one of these schemes is used as the linear part of the WENO scheme with symmetrical stencils to constructed an improved WENO scheme. At last, the improved WENO scheme is blended with its linear counterpart to form a new hybrid scheme for practical applications. The proposed scheme is accurate, flexible and robust. The accuracy and resolution of the proposed scheme are tested by the solutions of several benchmark test cases. The performance of this scheme is further demonstrated by its application in the direct numerical simulation of compressible turbulent channel flow between isothermal walls.     

A high-order discontinuous Galerkin method for wave propagation through coupled elastic–acoustic media

We introduce a high-order discontinuous Galerkin (dG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in coupled elastic–acoustic media. A velocity–strain formulation is used, which allows for the solution of the acoustic and elastic wave equations within the same unified framework. Careful attention is directed at the derivation of a numerical flux that preserves high-order accuracy in the presence of material discontinuities, including elastic–acoustic interfaces. Explicit expressions for the 3D upwind numerical flux, derived as an exact solution for the relevant Riemann problem, are provided. The method supports h-non-conforming meshes, which are particularly effective at allowing local adaptation of the mesh size to resolve strong contrasts in the local wavelength, as well as dynamic adaptivity to track solution features. The use of high-order elements controls numerical dispersion, enabling propagation over many wave periods. We prove consistency and stability of the proposed dG scheme. To study the numerical accuracy and convergence of the proposed method, we compare against analytical solutions for wave propagation problems with interfaces, including Rayleigh, Lamb, Scholte, and Stoneley waves as well as plane waves impinging on an elastic–acoustic interface. Spectral rates of convergence are demonstrated for these problems, which include a non-conforming mesh case. Finally, we present scalability results for a parallel implementation of the proposed high-order dG scheme for large-scale seismic wave propagation in a simplified earth model, demonstrating high parallel efficiency for strong scaling to the full size of the Jaguar Cray XT5 supercomputer.     

有限差分格式的一个通用色散-耗散条件

通过分析显式有限差分格式的数值色散和数值耗散,导出一个适于有限差分格式的通用色散-耗散条件.根据群速度和耗散率之间的物理关系,确定了用以抑制数值解中伪高波数波所需要的适度耗散.在以往发展的低耗散加权基本无振荡格式WENO-CU6-M2上的应用表明,该条件可用作优化线性或非线性有限差分格式的色散和耗散的通用指导准则.此外,满足色散-耗散条件的改进WENO-CU6-M2格式还可选作低分辨率数值模拟,以三维Taylor-Green涡向湍流转捩和自相似能量衰减问题展现了它的这种能力.与经典的动态Smagorinsky亚网格尺度模型相比,在Reynolds数Re=400~3000条件下,无黏和黏性Taylor-Green涡的数值模拟结果均得到明显改善.在保持激波捕捉特性同时,与最新的隐式大涡模拟模型的计算效果相当.      

低阶格式在大涡模拟计算中的适用性

采用三维Taylor-Green涡作为研究对象,利用工程中常用的低阶数值格式,研究格式本身的数值误差对大涡模拟计算的影响.结果表明:三种数值格式的数值耗散行为都与亚格子模型行为类似,即在小雷诺数下,流场比较光滑时,耗散很小,当雷诺数增加,流动转捩为湍流,流场梯度增大,耗散显著增大.对于MUSCL格式和二阶有界中心格式,在高雷诺数下,亚格子尺度模型没有明显改善计算结果,但也没有使计算结果恶化.中心格式相比其它两种格式,数值耗散最小,但是在高雷诺数湍流情况下,中心格式的数值耗散仍然主导了能量的耗散,再添加亚格子模型,计算结果反而变得稍差.对于工程中的低阶格式而言,采用中心格式计算大涡模拟是比较好的选择,而且在计算不存在稳定性问题时,采用不添加亚格子模型的隐式大涡模拟效果更好.     

Method of adaptive artificial viscosity

A new finite-difference method for the numerical solution of gas dynamics equations is proposed. This method is a uniform monotonous finite-difference scheme of second-order approximation on time and space outside of domains of shock and compression waves. This method is based on inputting adaptive artificial viscosity (AAV) into gas dynamics equations. In this paper, this method is analyzed for 2D geometry. The testing computations of the movement of contact discontinuities and shock waves and the breakup of discontinuities are demonstrated.     

基于气动声学问题的高阶非线性紧致格式

文章基于线性中心紧致差分格式, 通过非线性加权插值的方法来求解网格中心处的函数值.这类格式保持了原有中心紧致差分格式的高阶精度和低耗散特性, 同时其分辨率也非常高, 由于其非线性插值的机制, 使得这类格式能够捕捉强激波, 所以这类新的高阶非线性紧致格式是一种较好的模拟湍流和气动声学等多尺度问题的方法.      

Modified kinetic flux vector splitting schemes for compressible flows

We investigate the traditional kinetic flux vector splitting (KFVS) and BGK schemes for the compressible Euler equations. First, based on a careful study of the behavior of the discrete physical variables across the contact discontinuity, we analyze quantitatively the mechanism of inducing spurious oscillations of the velocity and pressure in the vicinity of the contact discontinuity for the first-order KFVS and BGK schemes. Then, with the help of this analysis, we propose a first-order modified KFVS (MKFVS) scheme which is oscillation-free in the vicinity of the contact discontinuity, provided certain consistent conditions are satisfied. Moreover, by using piecewise linear reconstruction and van Leer’s limiter, the first-order MKFVS scheme is extended to a second-order one, consequently, a nonoscillatory second-order MKFVS scheme is constructed. Finally, by combing the MKFVS schemes with the γ-model, we successfully extend the MKFVS schemes to multi-flows, and propose therefore a first- and second-order MKFVS schemes for multi-fluid computations, which are nonoscillatory across fluid interfaces. A number of numerical examples presented in this paper validate the theoretic analysis and demonstrate the good performance of the MKFVS schemes in simulation of contact discontinuities for both single- and multi-fluids.     

迎风紧致格式求解Hamilton-Jacobi方程

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.