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1.
使用Roe格式计算多维流动问题时,在强激波附近会出现数值激波不稳定现象。带有剪切粘性的HLLEC格式不仅可以捕捉接触间断,而且表现出很好的稳定性。混合Roe格式和HLLEC格式来消除数值激波不稳定性。在强激波附近,通过激波面法向和网格界面法向的夹角来定义开关函数,使得数值通量在激波面横向切换成HLLEC格式。在其余地方,数值通量依然使用Roe格式来计算。数值试验表明,混合格式不仅消除了Roe格式的数值激波不稳定性,还最大程度地减少了HLLEC格式所带来的剪切耗散,保留了Roe格式高分辨率的优点。  相似文献   

2.
针对欧拉方程三种流行的对流-压力通量分裂方法(Liou-Steffen,Zha-Bilgen和Toro-Vázquez)进行特征分析,进而提出一种新的对流-压力通量分裂格式。采用Zha-Bilgen分裂方法将欧拉方程的通量分裂成对流项和压力项两部分,使用TV格式来计算这两部分的数值通量。利用压力比构造激波探测函数,并且在强激波附近的亚声速区域增加TV格式的剪切粘性来克服数值模拟中的激波不稳定性。数值算例的计算结果表明,新的对流-压力通量分裂格式不仅保留了原始TV格式精确分辨接触间断的优点,而且具有更好的鲁棒性,在数值模拟多维强激波问题时不会出现不稳定现象。因此,该格式是一种精确并且具有强鲁棒性的数值方法,可以广泛地应用于可压缩流体的数值计算中。  相似文献   

3.
传统的Roe格式不满足熵条件并且在计算激波问题时会遭遇不同形式的不稳定现象,如慢行激波的波后振荡和红玉(carbuncle)现象.基于Zha-Bilgen对流-压力通量分裂方法,构造一种新型的通量差分裂格式.利用约旦标准型理论,通过添加广义特征向量构造通量差分裂方法来计算对流子系统.压力子系统具有一组完备的线性无关特征向量,因此可以构造传统的通量差分裂格式进行计算.为了提高接触间断的分辨率,利用界面变差下降(BVD)算法来重构对流通量耗散项中的密度差.激波稳定性分析表明,新格式可以有效地衰减数值误差,从而抑制不稳定现象的发生.一系列数值实验证明了本文构造的新型通量差分裂格式比Roe格式具有更高的分辨率和更好的鲁棒性.  相似文献   

4.
基于Godunov型数值格式的有限体积法是求解双曲型守恒律系统的主流方法,其中用来计算界面数值通量的黎曼求解器在很大程度上决定了数值格式在计算中的表现。单波的Rusanov求解器和双波的HLL求解器具有简单、高效和鲁棒性好等优点,但是在捕捉接触间断时耗散太大。全波的HLLC格式能够精确捕捉接触间断,但是在计算中出现的激波不稳定现象限制了其在高马赫数流动问题中的应用。本文利用双曲正切函数和五阶WENO格式来重构界面两侧的密度值,并且结合边界变差下降算法来减小Rusanov格式耗散项中的密度差,从而提高格式对于接触间断的分辨率。研究表明,相比于全波的HLLC求解器,本文构造的黎曼求解器不仅具有更高的接触分辨率,而且还具有更好的激波稳定性。  相似文献   

5.
传统的一维通量分裂格式在计算界面数值通量时,只考虑网格界面法向的波系。采用传统的TV格式分别求解对流通量和压力通量。通过求解考虑了横向波系影响的角点数值通量来构造一种真正二维的TV通量分裂格式。在计算一维数值算例时,该格式与传统的TV格式具有相同的数值通量计算公式,因此其保留了传统的TV格式精确捕捉接触间断和膨胀激波的优点。在计算二维算例时,该格式比传统的TV格式具有更高的分辨率;在计算二维强激波问题时,消除了传统TV格式的非物理现象,表现出更好的鲁棒性;此外,该格式大大提高了稳定性CFL数,从而具有更高的计算效率。因此,本文方法是一种精确、高效并且具有强鲁棒性的数值方法,在可压缩流的数值模拟中具有广阔的应用前景。  相似文献   

6.
G.H.Miller等把高压金属中的粘性激波作为强间断面处理,解析推论出:在大粘性系数条件下小扰动激波是不稳定的,物质粘性是导致失稳的因素。本文中针对平面正激波,认为高压金属中的粘性激波的物理量是连续变化的,利用线性稳定性理论,用数值解推论出:在有粘性条件下小扰动激波都是稳定的,物质粘性是致稳的因素。指出G.H.Miller等获得错误结论的原因在于:从无粘流动解推出的小扰动边界条件导致粘性激波小扰动增长。给出实验确定的小扰动速度梯度的边界条件,这样既可以把粘性正激波作为强间断面处理,也能够保证粘性正激波的稳定性。  相似文献   

7.
粘性及热传导对于爆轰波的影响   总被引:6,自引:0,他引:6  
武丹  王健平 《应用力学学报》2012,29(6):630-635,769
对在满足化学当量比的氢氧混合气体中传播的一维和二维连续旋转爆轰波进行了数值模拟,以此检验粘性和热传导对爆轰波发展和结构的影响。模拟分别基于NS和Euler控制方程,采用二步化学反应模型,对流项采用5阶MPWENO格式求解,时间方向采用3阶TVD Runge-Kutta法,粘性项采用中心差分格式进行离散。结果表明:粘性和热传导不会对爆轰波流场的基本流场结构产生影响;在具体数值上,粘性和热传导的影响值在爆轰波、斜激波、接触间断等速度或温度剧烈变化处相对较大,但总体上其影响量均比爆轰波流场的步进值小三个量级。因此,在没有壁面效应的一维爆轰和二维连续旋转爆轰波流场中,粘性和热传导项作为很小的扰动存在,对爆轰波的流场结构和数值大小基本不会产生影响。  相似文献   

8.
基于HLL-HLLC的高阶WENO格式及其应用研究   总被引:1,自引:0,他引:1  
HLL-HLLC格式能够克服HLLC在强激波附近的激波不稳定现象,并且保持了HLLC的低耗散特性,是一种适合更大马赫数范围的近似黎曼求解器。本文从RANS方程出发,将HLL-HLLC近似黎曼求解器结合五阶WENO重构,实现了对无粘通量的高阶离散;同时,采用完全守恒形式的四阶中心差分格式处理粘性项,建立了RANS 方程的高阶数值求解格式。通过对四个经典算例,钝头体、 ONERA M6机翼、DLR F6-WB翼身组合体和DLR F6-WBNP复杂外形的数值模拟,考察了两种WENO改进格式在复杂流场中的表现,研究了高阶格式的收敛特性;给出了在复杂流动中 WENO自由参数的推荐值,以增强求解的收敛性。算例结果表明,本文构造的高阶格式鲁棒性好,能够显著改善激波位置和激波强度,捕获更丰富的流场细节,满足复杂工程应用需求。  相似文献   

9.
HLL-HLLC格式能够克服HLLC在强激波附近的激波不稳定现象,并且保持了HLLC的低耗散特性,是一种适合更大马赫数范围的近似黎曼求解器。本文从RANS方程出发,将HLL-HLLC近似黎曼求解器结合五阶WENO重构,实现了对无粘通量的高阶离散;同时,采用完全守恒形式的四阶中心差分格式处理粘性项,建立了RANS方程的高阶数值求解格式。通过对四个经典算例,钝头体、ONERA M6机翼、DLR F6-WB翼身组合体和DLR F6-WBNP复杂外形的数值模拟,考察了两种WENO改进格式在复杂流场中的表现,研究了高阶格式的收敛特性;给出了在复杂流动中WENO自由参数的推荐值,以增强求解的收敛性。算例结果表明,本文构造的高阶格式鲁棒性好,能够显著改善激波位置和激波强度,捕获更丰富的流场细节,满足复杂工程应用需求。  相似文献   

10.
随着计算流体力学的快速发展,设计精确、高效并且健壮的数值格式变得尤为重要。Toro等[8]提出的TV通量分裂格式表现出简单、高效和精确分辨接触间断等优点,但是在计算一些多维算例时会出现数值激波不稳定现象。两波近似的HLL格式在计算中非常高效和健壮,但是不能分辨接触间断大大地限制了其应用。本文对TV通量分裂格式进行稳定性分析,据此提出一种混合格式来消除TV格式的数值激波不稳定性。数值试验表明,本文构造的混合格式不仅保留了原始TV格式的优点,而且具有更好的健壮性,在计算二维问题时不会出现数值激波不稳定现象。  相似文献   

11.
空腔流动存在剪切层运动、涡脱落与破裂,以及激波与激波、激波与剪切层、激波与膨胀波和激波/涡/剪切层相互干扰等现象,流动非常复杂,特别是高马赫数(M>2)时,剪切层和激波更强,激波与激波干扰更严重,对数值格式的要求更高,既需要格式耗散小,对分离涡等有很高的模拟精度,又需要格式在激波附近具有较大的耗散,可以很好地捕捉激波,防止非物理解的出现。Roe和HLLC等近似Riemann解格式在高马赫数强激波处可能会出现红玉现象,而HLLE++格式大大改善了这种缺陷,在捕捉高超声速激波时避免了红玉现象的发生,同时还保持在光滑区域的低数值耗散特性。本文在结构网格下HLLE++格式的基础上,通过改进激波探测的求解,建立了基于非结构混合网格的HLLE++计算方法,通过无粘斜坡算例,验证了HLLE++格式模拟高马赫数流动的能力,并应用于高马赫数空腔流动的数值模拟,开展了网格和湍流模型影响研究,验证了方法模拟高马赫数空腔流动的可靠性和有效性。  相似文献   

12.
The HLLEM scheme is a popular contact and shear preserving approximate Riemann solver that is known to be plagued by various forms of numerical shock instability. In this paper, we clarify that the shock instability exhibited by this scheme is primarily triggered by the spurious activation of the antidiffusive terms present in the first and third Riemann flux components on the transverse interfaces adjoining the shock front due to numerical perturbations. These erroneously activated terms are shown to counteract the favorable damping mechanism provided by its inherent HLL-type diffusive terms, causing an unphysical variation of the conserved quantity ρu both along and across the numerical shock. To prevent this, two distinct strategies are proposed termed as S elective W ave M odification and A nti D iffusion C ontrol. The former focuses on enhancing the quantity of the favorable HLL-type dissipation available on these critical flux components by carefully increasing the magnitudes of certain nonlinear wave speed estimates, while the latter focuses on directly controlling the magnitude of these critical antidiffusive terms. A linear perturbation analysis is performed to gauge the effectiveness of these cures and to estimate a von Neumann–type stability bounds on the CFL number associated with their use. Results from a variety of classic shock instability test cases show that the proposed strategies are able to provide excellent shock stable solutions even on grids that are highly elongated across the shock front without compromising the accuracy on inviscid contact or shear dominated viscous flows.  相似文献   

13.
Study on the numerical schemes for hypersonic flow simulation   总被引:1,自引:0,他引:1  
Hypersonic flow is full of complex physical and chemical processes, hence its investigation needs careful analysis of existing schemes and choosing a suitable scheme or designing a brand new scheme. The present study deals with two numerical schemes Harten, Lax, and van Leer with Contact (HLLC) and advection upstream splitting method (AUSM) to effectively simulate hypersonic flow fields, and accurately predict shock waves with minimal diffusion. In present computations, hypersonic flows have been modeled as a system of hyperbolic equations with one additional equation for non-equilibrium energy and relaxing source terms. Real gas effects, which appear typically in hypersonic flows, have been simulated through energy relaxation method. HLLC and AUSM methods are modified to incorporate the conservation laws for non-equilibrium energy. Numerical implementation have shown that non-equilibrium energy convect with mass, and hence has no bearing on the basic numerical scheme. The numerical simulation carried out shows good comparison with experimental data available in literature. Both numerical schemes have shown identical results at equilibrium. Present study has demonstrated that real gas effects in hypersonic flows can be modeled through energy relaxation method along with either AUSM or HLLC numerical scheme.  相似文献   

14.
We investigate the linearized response of two elastic half-spaces sliding past one another with constant Coulomb friction to small three-dimensional perturbations. Starting with the assumption that friction always opposes slip velocity, we derive a set of linearized boundary conditions relating perturbations of shear traction to slip velocity. Friction introduces an effective viscosity transverse to the direction of the original sliding, but offers no additional resistance to slip aligned with the original sliding direction. The amplitude of transverse slip depends on a nondimensional parameter η=csτ0/μv0, where τ0 is the initial shear stress, 2v0 is the initial slip velocity, μ is the shear modulus, and cs is the shear wave speed. As η→0, the transverse shear traction becomes negligible, and we find an azimuthally symmetric Rayleigh wave trapped along the interface. As η→∞, the inplane and antiplane wavesystems frictionally couple into an interface wave with a velocity that is directionally dependent, increasing from the Rayleigh speed in the direction of initial sliding up to the shear wave speed in the transverse direction. Except in these frictional limits and the specialization to two-dimensional inplane geometry, the interface waves are dissipative. In addition to forward and backward propagating interface waves, we find that for η>1, a third solution to the dispersion relation appears, corresponding to a damped standing wave mode. For large-amplitude perturbations, the interface becomes isotropically dissipative. The behavior resembles the frictionless response in the extremely strong perturbation limit, except that the waves are damped. We extend the linearized analysis by presenting analytical solutions for the transient response of the medium to both line and point sources on the interface. The resulting self-similar slip pulses consist of the interface waves and head waves, and help explain the transmission of forces across fracture surfaces. Furthermore, we suggest that the η→∞ limit describes the sliding interface behind the crack edge for shear fracture problems in which the absolute level of sliding friction is much larger than any interfacial stress changes.  相似文献   

15.
G. J. Ball 《Shock Waves》1996,5(5):311-325
A Free-Lagrange numerical procedure for the simulation of two-dimensional inviscid compressible flow is described in detail. The unsteady Euler equations are solved on an unstructured Lagrangian grid based on a density-weighted Voronoi mesh. The flow solver is of the Godunov type, utilising either the HLLE (2 wave) approximate Riemann solver or the more recent HLLC (3 wave) variant, each adapted to the Lagrangian frame. Within each mesh cell, conserved properties are treated as piece-wise linear, and a slope limiter of the MUSCL type is used to give non-oscillatory behaviour with nominal second order accuracy in space. The solver is first order accurate in time. Modifications to the slope limiter to minimise grid and coordinate dependent effects are described. The performances of the HLLE and HLLC solvers are compared for two test problems; a one-dimensional shock tube and a two-dimensional blast wave confined within a rigid cylinder. The blast wave is initiated by impulsive heating of a gas column whose centreline is parallel to, and one half of the cylinder radius from, the axis of the cylinder. For the shock tube problem, both solvers predict shock and expansion waves in good agreement with theory. For the HLLE solver, contact resolution is poor, especially in the blast wave problem. The HLLC solver achieves near-exact contact capture in both problems. Received May 25, 1995 / Accepted September 11, 1995  相似文献   

16.
A hybrid numerical flux scheme is proposed by adapting the carbunclefree modified Harten-Lax-van Leer contact(HLLCM) scheme to smoothly revert to the Harten-Lax-van Leer contact(HLLC) scheme in regions of shear. This hybrid scheme, referred to as the HLLCT scheme, employs a novel, velocity-based shear sensor. In contrast to the non-local pressure-based shock sensors often used in carbuncle cures, the proposed shear sensor can be computed in a localized manner meaning that the HLLCT scheme can be easily introduced into existing codes without having to implement additional data structures. Through numerical experiments, it is shown that the HLLCT scheme is able to resolve shear layers accurately without succumbing to the shock instability.  相似文献   

17.
This paper explores the potential of a newly developed conjugate filter oscillation reduction (CFOR) scheme for shock‐capturing under the influence of natural high‐frequency oscillations. The conjugate low‐ and high‐pass filters are constructed based on the principle of the discrete singular convolution (DSC), a local spectral method. The accuracy and resolution of the DSC basic algorithm are accessed with a one‐dimensional advection equation. Two Euler systems, the advection of an isotropic vortex flow and the interaction of shock–entropy wave are utilized to demonstrate the utility of the CFOR scheme. Computational accuracy and order of approximation are examined and compared with the literature. Some of the best numerical results are obtained for the shock–entropy wave interaction. Numerical experiments indicate that the CFOR scheme is stable, conservative and reliable for the numerical simulation of hyperbolic conservation laws. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

18.
针对复杂管系内可压缩流体,基于有限体积法,采用HLLC(Harten-Lax-vanLeerContact)格式和黎曼求解器构建了有限控制体数值离散方法,引入虚拟节点用于连接有限控制体,借助虚拟节点给出控制体之间数值通量的计算格式,发展了一种管道内一维流动数值建模方法。针对含有分支管路的管系,在管道连接部位构建了分支管路拟一维流动数值计算模型。基于所发展的一维流动数值方法,建立了变径管道和含60°分支管道内流动计算模型,验证了该方法的收敛性和有效性;基于虚拟节点的数值格式处理变径管激波问题具有一定精度优势。研究了变径管和分支管模型中可压缩流体激波、稀疏波等的传播机理,分析了管径对相邻支管压力的影响,为工程管路设计提供了参考。  相似文献   

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