一种基于AUSM分裂的真正多维HLL格式

文章给出了一种真正多维的HLL Riemann解算器.采用AUSM分裂将通量分解成为对流通量和压力通量, 其中对流通量的计算采用迎风格式, 压力通量的计算采用HLL格式, 且将HLL格式的耗散项中的密度差用压力差代替, 从而使得格式能够分辨接触间断.为了实现数值格式真正多维的特性, 分别计算了网格界面中点和角点上的数值通量, 并且采用Simpson公式加权组合中点和角点上的数值通量得到网格界面的数值通量.为了减少重构角点处状态时的模板宽度, 计算中采用基于SDWLS梯度的线性重构获得2阶空间精度, 而时间离散采用2阶保强稳Runge-Kutta方法.数值实验表明, 相比于传统的一维HLL格式, 文章的真正多维HLL格式具有能够分辨接触间断, 以及更大的时间步长等优点.与其他能够分辨接触间断的格式(例如HLLC格式)不同, 真正多维的HLL格式在计算二维问题时不会出现激波不稳定现象.      

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。     

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.     

基于样条逼近有限体积法的通量分裂算法

研究了任意曲线坐标系中求解双曲型守恒律的高精度、无波动样条逼近有限体积方法,比较了三种不同的通量分裂技术在这种方法中的应用。数值实验表明,在不同的通量分裂技术下,该方法对流场中的激波和接触间断都有很高的分辨率。     

一类新型激波捕捉格式的耗散性与稳定性分析

高超声速流动是高复杂性的可压缩黏性流动, 其中存在激波、剪切层、激波/激波干扰、激波/边界层干扰、旋涡与分离流动等复杂流场结构. 对其进行准确模拟需要使用低耗散、强鲁棒性的激波捕捉方法. 本文基于一类新型的通量项分裂方法, 提出了一种耗散低且鲁棒性好的激波捕捉格式K-CUSP-X. 对该格式的耗散性和激波稳定性进行了详细的理论分析, 得到了格式激波稳定的数值条件. 推论认为, 迎风格式激波稳定的充分条件为速度扰动量具有衰减性, 数值实验验证了该推论. 研究表明, 该格式与Toro提出的通量分裂格式K-CUSP-T相比, 在保证精确捕捉接触间断的同时, 又具有更好的稳定性, 在激波处不会产生“红玉”现象.     

求解双曲守恒律方程的高分辨率熵相容格式

为提高熵相容格式的精度,利用限制器机制构造高分辨率格式,将构造的通量限制器插入熵相容格式,得到一类高分辨率熵相容格式.构造Euler方程高分辨率熵相容格式时,对熵相容格式中的几个参数做简单调整,提高了接触间断处的分辨率.将所得格式的数值结果与熵相容格式的数值结果比较表明,构造的高分辨率熵相容格式具有稳健和基本无振荡等特性.     

利用通量限制思想改进紧致格式

利用通量限制思想改进紧致格式计算有间断流场的性能,并设计出一种限制器,该限制器被运用在一系列3至8阶的紧致格式上.数值实验表明,通量限制型紧致格式不仅具有较高的精度和分辨率,而且还能有效地抑制非物理振荡,适用于各种高低Mach数的流动,捕捉到的流场间断所占网格点数少.     

ρ-VOF:一种可清晰模拟自由界面的两相流方法

文章通过对EFM(effective field modeling)模型进行简化, 消除了原模型的非守恒性项和非双曲性特性项, 发展了一种基于密度的气液两相流模拟方法: ρ-VOF方法.利用体积分数信息对控制单元内的自由界面进行重构, 得到了控制单元内流体的空间分布, 并采用AUSM+-up格式获得考虑气液流体接触间断信息的对流通量.新方法可统一处理激波间断和接触间断的相互作用, 保持自由界面的尖锐性, 并且其计算量与自由界面的空间复杂度无关.最后, 数值模拟了液体激波管气液激波管和气体激波跨二维液滴传播等问题, 并与文献结果进行对比, 验证了本方法在气液两相流模拟中的准确性.      

多介质五方程简化模型及界面捕捉的人工压缩算法

根据两介质五方程简化模型的基本假设,发展了适用于任意多种介质的体积分数方程。为了捕捉多介质界面,将HLLC-HLLCM混合型数值通量的计算格式推广应用于二维平面和柱几何的多介质复杂流动问题,在高阶精度的数据重构过程中采用斜率修正型人工压缩方法ACM。通过一维、二维多介质黎曼问题算例测试,结果表明：发展的计算格式能够较好地分辨接触间断和激波,间断附近物理量无振荡;对于添加了初始扰动的激波问题,能够有效抑制激波数值不稳定性;使用二维柱球SOD问题和接触间断型黎曼问题检验计算格式对多介质复杂流动问题的适应性。     

两类差分格式在锋生数值模拟中的应用比较

在二维理想锋生数值模式的基础上,用两类差分格式进行数值试验比较.计算结果表明,无论是在大气数值模拟中广泛使用的总能量守恒型差分格式,还是在高速流中捕捉接触间断较好的反扩散格式,对锋生过程均有较好的模拟能力,反扩散格式的效果更好一些.     

Hybrid Flux-Splitting Schemes for a Two-Phase Flow Model

In this paper we deal with the construction of hybrid flux-vector-splitting (FVS) schemes and flux-difference-splitting (FDS) schemes for a two-phase model for one-dimensional flow. The model consists of two mass conservation equations (one for each phase) and a common momentum equation. The complexity of this model, as far as numerical computation is concerned, is related to the fact that the flux cannot be expressed in terms of its conservative variables. This is the motivation for studying numerical schemes which are not based on (approximate) Riemann solvers and/or calculations of Jacobian matrix. This work concerns the extension of an FVS type scheme, a Van Leer type scheme, and an advection upstream splitting method (AUSM) type scheme to the current two-phase model. Our schemes are obtained through natural extensions of corresponding schemes studied by Y. Wada and M.-S. Liou (1997, SIAM J. Sci. Comput.18, 633–657) for Euler equations. We explore the various schemes for flow cases which involve both fast and slow transients. In particular, we demonstrate that the FVS scheme is able to capture fast-propagating acoustic waves in a monotone way, while it introduces an excessive numerical dissipation at volume fraction contact (steady and moving) discontinuities. On the other hand, the AUSM scheme gives accurate resolution of contact discontinuities but produces oscillatory approximations of acoustic waves. This motivates us to propose other hybrid FVS/FDS schemes obtained by removing numerical dissipation at contact discontinuities in the FVS and Van Leer schemes.     

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.     

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     

An unconditionally stable rotational velocity-correction scheme for incompressible flows

We present an unconditionally stable splitting scheme for incompressible Navier–Stokes equations based on the rotational velocity-correction formulation. The main advantages of the scheme are: (i) it allows the use of time step sizes considerably larger than the widely-used semi-implicit type schemes: the time step size is only constrained by accuracy; (ii) it does not require the velocity and pressure approximation spaces to satisfy the usual inf–sup condition: in particular, the equal-order finite element/spectral element approximation spaces can be used; (iii) it only requires solving a pressure Poisson equation and a linear convection–diffusion equation at each time step. Numerical tests indicate that the computational cost of the new scheme for each time step, under identical time step sizes, is even less expensive than the semi-implicit scheme with low element orders. Therefore, the total computational cost of the new scheme can be significantly less than the usual semi-implicit scheme.     

气相爆轰高阶中心差分-WENO组合格式自适应网格方法

研究一种高阶中心差分-WENO组合格式,并采用自适应网格方法进行二维和三维气相爆轰波的数值模拟.采用ZND爆轰模型的控制方程为包含化学反应源项的Euler方程组.组合格式在大梯度区采用WENO格式捕捉间断,在光滑区采用高阶中心差分格式提高计算效率.采用一种基于流场结构特征的自适应网格.计算结果,表明这种方法同时具有高精度、高分辨率和高效率的特点.     

改进的三阶WENO-Z+格式及其应用

为改善三阶WENO格式的耗散特性,提高其对流场结构的分辨率,在三阶WENO-Z+格式（WENO-Z+3）基础上,构造不同形式的全局光滑因子,提出一种改进的WENO-Z+3格式（NWENO-Z+3）.选取Sod激波管、双爆轰波碰撞、激波与熵波相互作用、双马赫反射等经典算例,考察该格式的计算性能,结果表明：NWENO-Z+3格式具有更低耗散性和更高的分辨率.数值研究柱形高压气体爆炸波在单舱室和连通舱室内部的传播过程及波系演化.结果表明：改进格式NWENO-Z+3能够较好地模拟包含高压比、高密度比的爆炸波系结构.     

Nonlinear spectral-like schemes for hybrid schemes

In spectral-like resolution-WENO hybrid schemes,if the switch function takes more grid points as discontinuity points,the WENO scheme is often turned on,and the numerical solutions may be too dissipative.Conversely,if the switch function takes less grid points as discontinuity points,the hybrid schemes usually are found to produce oscillatory solutions or just to be unstable.Even if the switch function takes less grid points as discontinuity points,the final hybrid scheme is inclined to be more stable,provided the spectral-like resolution scheme in the hybrid scheme has moderate shock-capturing capability.Following this idea,we propose nonlinear spectral-like schemes named weighted group velocity control(WGVC)schemes.These schemes show not only high-resolution for short waves but also moderate shock capturing capability.Then a new class of hybrid schemes is designed in which the WGVC scheme is used in smooth regions and the WENO scheme is used to capture discontinuities.These hybrid schemes show good resolution for small-scales structures and fine shock-capturing capabilities while the switch function takes less grid points as discontinuity points.The seven-order WGVC-WENO scheme has also been applied successfully to the direct numerical simulation of oblique shock wave-turbulent boundary layer interaction.     

Numerical solution of under-resolved detonations

A new fractional-step method is proposed for the numerical solution of high speed reacting flows, where the chemical time scales are often much smaller than the fluid dynamical time scales. When the problem is stiff, because of insufficient spatial/temporal resolution, a well-known spurious numerical phenomenon occurs in standard finite volume schemes: the incorrect calculation of the speed of propagation of discontinuities. The new method is first illustrated considering a one-dimensional scalar hyperbolic advection/reaction equation with stiff source term, which may be considered as a model problem to under-resolved detonations. During the reaction step, the proposed scheme replaces the cell average representation with a two-value reconstruction, which allows us to locate the discontinuity position inside the cell during the computation of the source term. This results in the correct propagation of discontinuities even in the stiff case. The method is proved to be second-order accurate for smooth solutions of scalar equations and is applied successfully to the solution of the one-dimensional reactive Euler equations for Chapman–Jouguet detonations.     

一种具有较小数值耗散的对称TVD格式

为了减小TVD格式的数值粘性,提高TVD格式的分辨度,提出了一种具有较小数值耗散的Harten型TVD格式.数值模拟结果表明,这种Harten型TVD格式比原来的Harten格式^[1]及其改进形式Harten-Yee^[2]的TVD格式能更好地模拟出边界层及涡流.