基于非结构网格的不可压流动耦合求解器

采用非结构化网格有限容积法求解了不可压N-S方程组,对流项采用GAMMA格式,扩散项采用二阶中心差分格式建立离散方程,用SOAR算法处理压力与速度的耦合关系,得到了一种求解不可压N-S方程的非结构网格耦合求解器。通过方腔顶盖驱动流、后台阶绕流以及方腔自然对流等几个典型的算例,考察了求解器的计算精度及收敛特性,并与SIMPLE算法进行了比较,结果表明该求解器是有效可行的。     

径向对称非线性Schrodinger方程的守恒差分格式

对径向对称的非线性Ｓｃｈｒｏｄｉｎｇｅｒ方程提出了一个新的守恒差分格式,这是一个三层格式,它不需迭代求解因此提高了计算速度,同时也较好地保持了方程的两上守恒律。文中证明了格式的收敛性与稳定性,数值计算结果表明,该差分格式是有效的。     

二维不可压流函数N-S方程的多重网格方法

通过对二维不可压缩N-S方程的涡量-流函数方程组消去涡量而得到仅以流函数为求解变量的控制方程,从而 使不可压N-S方程的求解个数减到最少。求解方法采用本文提出的二阶精度的九节点紧致差分格式,因此无须对靠近边 界的网格点作特殊处理。为了加快迭代收敛速度,采用多重网格加速技术。数值实验结果验证了方法的精确性和可靠性。     

低展弦比跨音速轴流风扇转子流场三维数值模拟

应用基于时间推进的有限差分法求解跨音速压气机风扇转子内部三维粘性流场．该方法以新型ＬＵ隐式格式和改良型 ＭＵＳＣＬ ＴＶＤ格式为基础,对三维可压缩雷诺平均 Ｎａｖｉｅ－Ｓｔｏｋｅｓ方程和低雷诺数ｑ－ω双方程湍流模型进行求解．计算得到了ＮＡＳＡ Ｌｅｗｉｓ ６７跨音速、低展弦比轴流风扇转子的性能曲线并重点分析了近最高效率点工况和近失速工况下的内部流场．计算与实验结果的对比表明此方法能够得到三维粘性流场的流动特性且计算精度较高,可用来模拟跨音速风扇转子内部流动．     

二阶STC格式及其对跨音速湍流流动的数值模拟

ＳＴＣ格式是一种求解积分形式物理守恒律的计算方法,具有守恒性好,精度高的特点。目前求解Ｅｕｌｅｒ方程的ＳＴＣ格式已经建立起来,但求解Ｎ－Ｓ方程的ＳＴＣ格式尚在发展之中。为了使ＳＴＣ格式能够有效地求解粘性流动的问题,本文构造出了求解曲线坐标系下的二维Ｎ－Ｓ方程的二阶ＳＴＣ格式。用该格式对跨音速湍流流动问题进行了计算。     

振荡机翼跨音速非定常粘性绕流的数值计算

以非定常Ｎ－Ｓ方程为主管方程，采用ＬＵ－ＮＮＤ混合差分格式，Ｃ和Ｃ－Ｈ型贴体运动网格，Ｂ－Ｌ双层代数紊流模型，求解绕振荡翼型和三维机翼的跨音速非定常粘性流场，分别计算了ＮＡＣＡ００１２翼型和Ｍ６机翼作俯仰振荡时跨音速非定常粘性绕流流场。研究了非定常绕流的气动特性，部分计算结果和风洞实验值作了比较。     

多级轴流压气机全工况特性数值模拟

采用一种快速求解三维粘性流场的计算方法求解某多级轴流压气机内部流场及全工况特性。该方法以ＬＵ－ＳＧＳ－ＧＥ隐式格式和 ＭＵＳＣＬ ＴＶＤ迎风格式为基础，结合壁面函数方法和简单的混合长度湍流模型，使用多重网格迭代加速收敛技术对三维可压缩雷诺平均Ｎａｖｉｅ－Ｓｔｏｋｅｓ方程进行求解．叶列间参数的传递采用混合平面方法并应用了微机网络并行计算技术．首先对一个五排压气机（进口导叶加两级）进行了全工况特性计算，并对计算结果做了详细分析．然后对前三排（进口导叶加一级）进行了全工况特性计算并与五排联赛的计算结果进行了对比，对多级环境对单级性能的影响机理做了初步探讨。     

非线性Schrodinger方程的守恒数值格式

对非线性Ｓｃｈｒｏｄｉｎｇｅｒ方程提出了一种新的守恒差分格式,并证明了该格式的收性与稳定性。通过数值计算,对非线性Ｓｃｈｒｏｄｉｎｇｅｒ方程中非线性项的离散进行了讨论,获得如下结论在取适当的参数后,所提出孤差分格式工上好于作为该格式特例的文（７）中的格式。     

透平级非设计工况气动性能的数值模拟

采用新型 ＬＵ隐式格式和改良型高阶 ＭＵＳＣＬ ＴＶＤ格式求解全三维雷诺平均的 Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程和 ｑ－ｗ低雷诺数双方程湍流模型,对一台ＮＡＳＡ跨音单级透平在不同工况下的内部流场进行了详细的数值模拟,并与可能得到的实验结果进行了对比。总结了小流量工况下动叶内部流动的分离模式。     

振动叶栅中三维振荡粘性流场的压力密度消去法

1前言三维非定常流场的求解是目前国内外的一个热点研究课题山。文献［2］完成了三维可压非定常欧拉流场的求解,这一方法在求解三维非定常欧拉流场时,应用了四阶fringe－Kutta方法对控制方程进行积分,用中心差分进行空间离散,采用了四阶人工粘性项来保证计算格式稳定,计算稳定性要求严格,时间步长不能大,计算时间长。本文从非定常三维粘性N－S方程组出发,通过合理的数学方法,消去压力及密度项,得到只包含振荡速度矢量项对空间的偏微分方程组,在已知定常速度场后,这一方程组很容易求解。2基本方程在以角速度为n作旋转的相对坐…     

Adaptive multiscale finite-volume method for nonlinear multiphase transport in heterogeneous formations

In the previous multiscale finite-volume (MSFV) method, an efficient and accurate multiscale approach was proposed to solve the elliptic flow equation. The reconstructed fine-scale velocity field was then used to solve the nonlinear hyperbolic transport equation for the fine-scale saturations using an overlapping Schwarz scheme. A coarse-scale system for the transport equations was not derived because of the hyperbolic character of the governing equations and intricate nonlinear interactions between the saturation field and the underlying heterogeneous permeability distribution. In this paper, we describe a sequential implicit multiscale finite-volume framework for coupled flow and transport with general prolongation and restriction operations for both pressure and saturation, in which three adaptive prolongation operators for the saturation are used. In regions with rapid pressure and saturation changes, the original approach, with full reconstruction of the velocity field and overlapping Schwarz, is used to compute the saturations. In regions where the temporal changes in velocity or saturation can be represented by asymptotic linear approximations, two additional approximate prolongation operators are proposed. The efficiency and accuracy are evaluated for two-phase incompressible flow in two- and three-dimensional domains. The new adaptive algorithm is tested using various models with homogeneous and heterogeneous permeabilities. It is demonstrated that the multiscale results with the adaptive transport calculation are in excellent agreement with the fine-scale solutions. Furthermore, the adaptive multiscale scheme of flow and transport is much more computationally efficient compared with the previous MSFV method and conventional fine-scale reservoir simulation methods.     

An Asymptotic-Preserving all-speed scheme for the Euler and Navier–Stokes equations

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.     

A coupled pressure-based computational method for incompressible/compressible flows

Pressure-based flow solvers couple continuity and linearized truncated momentum equations to derive a Poisson type pressure correction equation and use the well known SIMPLE algorithm. Momentum equations and the pressure correction equation are typically solved sequentially. In many cases this method results in slow and often difficult convergence. The current paper proposes a novel computational algorithm, solving for pressure and velocity simultaneously within a pressure-correction coupled solution approach using finite volume method on structured and unstructured meshes. The method can be applied to both incompressible and subsonic compressible flows. For subsonic compressible flows, the energy equation is also coupled with flow field and the density of fluid is obtained by equation of state. The procedure eliminates the pressure correction step, the most expensive component of the SIMPLE-like algorithms. The proposed coupled continuity-momentum-energy equation method can be used to simulate steady state or transient flow problems. The method has been tested on several CFD benchmark cases with excellent results showing dramatically improved numerical convergence and significant reduction in computational time.     

用涡方法数值模拟运动物体非定常流场

采用涡方法对静止圆柱绕流、简谐振动圆柱、静止NACA0012翼型绕流和运动扑翼的非定常流场进行了数值模拟和数值验证,对比验证结果较好.控制方程采用二维不可压缩N-S方程,根据算子分裂法,对流和扩散分别采用不同的时间步长.涡方法基于Lagrange坐标系的特点使其方便模拟运动物体的非定常流场.本文的工作为今后的翼型动态失...     

Efficient kinetic schemes for steady and unsteady flow simulations on unstructured meshes

This paper presents efficient second-order kinetic schemes on unstructured meshes for both compressible unsteady and incompressible steady flows. For compressible unsteady flows, a time-dependent gas distribution function with a discontinuous particle velocity space at a cell interface is constructed and used for the evaluations of both numerical fluxes and conservative flow variables. As a result, a compact scheme on the unstructured meshes is developed. For incompressible steady flows, a continuous second-order gas-kinetic BGK type scheme is presented, for which the time-dependent gas distribution function with a continuous particle velocity is used on unstructured meshes. The efficiency of the schemes lies in the fact that the slopes of the flow variables inside each cell can be constructed using values of the flow variables within that cell only without involving neighboring cells. Therefore, even with the stencil of a first-order scheme, a high resolution method is constructed. Numerical examples are presented which are compared with the benchmark solutions and the experimental measurements.     

A hybrid scheme for computing incompressible two-phase flows

We propose a hybrid scheme for computations of incompressible two-phase flows. The incompressible constraint has been replaced by a pressure Poisson-like equation and then the pressure is updated by the modified marker and cell method. Meanwhile, the moment equations in the incompressible Navier-Stokes equations are solved by our semidiscrete Hermite central-upwind scheme, and the interface between the two fluids is considered to be continuous and is described implicitly as the 0.5 level set of a smooth function being a smeared out Heaviside function. It is here named the hybrid scheme. Some numerical experiments are successfully carried out, which verify the desired efficiency and accuracy of our hybrid scheme.     

A numerical study on the flow and sound fields of centrifugal impeller located near a wedge

Centrifugal fans are widely used and the noise generated by these machines causes one of the serious problems. In general, the centrifugal fan noise is often dominated by tones at blade passage frequency and its higher harmonics. This is a consequence of the strong interaction between the flow discharged from the impeller and the cut-off in the casing. However, only a few researches have been carried out on predicting the noise because of the difficulty in obtaining detailed information about the flow field and considering the scattering effect of the casing. The objective of this study is to understand the generation mechanism of sound and to develop a prediction method for the unsteady flow field and the acoustic pressure field of the centrifugal impeller. A discrete vortex method is used to model the centrifugal impeller and a wedge and to calculate the flow field. The force of each element on the blade is calculated by the unsteady Bernoulli equation. Lowson's method is used to predict the acoustic source. In order to consider the scattering and diffraction effects of the casing, Kirchhoff-Helmholtz boundary element method (BEM) is developed. The source of Kirchhoff-Helmholtz BEM is newly developed, so the sound field of the centrifugal fan can be obtained. A centrifugal impeller and wedge are used in the numerical calculation and the results are compared with the experimental data. Reasonable results are obtained not only for the peak frequencies but also for the amplitudes of the tonal sound. The radiated acoustic field shows the diffraction and scattering effect of the wedge.     

A multi-block ADI finite-volume method for incompressible Navier–Stokes equations in complex geometries

An efficient second-order accurate finite-volume method is developed for a solution of the incompressible Navier–Stokes equations on complex multi-block structured curvilinear grids. Unlike in the finite-volume or finite-difference-based alternating-direction-implicit (ADI) methods, where factorization of the coordinate transformed governing equations is performed along generalized coordinate directions, in the proposed method, the discretized Cartesian form Navier–Stokes equations are factored along curvilinear grid lines. The new ADI finite-volume method is also extended for simulations on multi-block structured curvilinear grids with which complex geometries can be efficiently resolved. The numerical method is first developed for an unsteady convection–diffusion equation, then is extended for the incompressible Navier–Stokes equations. The order of accuracy and stability characteristics of the present method are analyzed in simulations of an unsteady convection–diffusion problem, decaying vortices, flow in a lid-driven cavity, flow over a circular cylinder, and turbulent flow through a planar channel. Numerical solutions predicted by the proposed ADI finite-volume method are found to be in good agreement with experimental and other numerical data, while the solutions are obtained at much lower computational cost than those required by other iterative methods without factorization. For a simulation on a grid with O(10⁵) cells, the computational time required by the present ADI-based method for a solution of momentum equations is found to be less than 20% of that required by a method employing a biconjugate-gradient-stabilized scheme.     

Multiscale finite-volume method for parabolic problems arising from compressible multiphase flow in porous media

The multiscale finite-volume (MSFV) method was originally developed for the solution of heterogeneous elliptic problems with reduced computational cost. Recently, some extensions of this method for parabolic problems have been proposed. These extensions proved effective for many cases, however, they are neither general nor completely satisfactory. For instance, they are not suitable for correctly capturing the transient behavior described by the parabolic pressure equation. In this paper, we present a general multiscale finite-volume method for parabolic problems arising, for example, from compressible multiphase flow in porous media. Opposed to previous methods, here, the basis and correction functions are solutions of full parabolic governing equations in localized domains. At the same time, to enhance the computational efficiency of the scheme, the basis functions are kept pressure independent and do not have to be recalculated as pressure evolves. This general approach requires no additional assumptions and its good efficiency and high accuracy is demonstrated for various challenging test cases. Finally, to improve the quality of the results and also to extend the scheme for highly anisotropic heterogeneous problems, it is combined with the iterative MSFV (i-MSFV) method for parabolic problems. As one iterates, the i-MSFV solutions of compressible multiphase problems (parabolic problems) converge to the corresponding fine-scale reference solutions in the same way as demonstrated recently for incompressible cases (elliptic problems). Therefore, the proposed MSFV method can also be regarded as an efficient linear solver for parabolic problems and studies of its efficiency are presented for many test cases.     

A consistent and conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part III: On a staggered mesh

The consistent and conservative scheme developed on a rectangular collocated mesh [M.-J. Ni, R. Munipalli, N.B. Morley, P. Huang, M.A. Abdou, A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part I: on a rectangular collocated grid system, Journal of Computational Physics 227 (2007) 174–204] and on an arbitrary collocated mesh [M.-J. Ni, R. Munipalli, P. Huang, N.B. Morley, M.A. Abdou, A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part II: on an arbitrary collocated mesh, Journal of Computational Physics 227 (2007) 205–228] has been extended and specially designed for calculation of the Lorentz force on a staggered grid system (Part III) by solving the electrical potential equation for magnetohydrodynamics (MHD) at a low magnetic Reynolds number. In a staggered mesh, pressure (p) and electrical potential (φ) are located in the cell center, while velocities and current fluxes are located on the cell faces of a main control volume. The scheme numerically meets the physical conservation laws, charge conservation law and momentum conservation law. Physically, the Lorentz force conserves the momentum when the magnetic field is constant or spatial coordinate independent. The calculation of current density fluxes on cell faces is conducted using a scheme consistent with the discretization for solution of the electrical potential Poisson equation, which can ensure the calculated current density conserves the charge. A divergence formula of the Lorentz force is used to calculate the Lorentz force at the cell center of a main control volume, which can numerically conserve the momentum at constant or spatial coordinate independent magnetic field. The calculated cell-center Lorentz forces are then interpolated to the cell faces, which are used to obtain the corresponding velocity fluxes by solving the momentum equations. The “conservative” is an important property of the scheme, which can guarantee computational accuracy of MHD flows at high Hartmann number with a strongly non-uniform mesh employed to resolve the Hartmann layers and side layers. 2D fully developed MHD flows with analytical solutions available have been conducted to validate the scheme at a staggered mesh. 3D MHD flows, with the experimental data available, at a constant magnetic field in a rectangular duct with sudden expansion and at a varying magnetic field in a rectangular duct are conducted on a staggered mesh to verify the computational accuracy of the scheme. It is expected that the scheme for the Lorentz force can be employed together with a fully conservative scheme for the convective term and the pressure term [Y. Morinishi, T.S. Lund, O.V. Vasilyev, P. Moin, Fully conservative higher order finite difference schemes for incompressible flow, Journal of Computational Physics 143 (1998) 90–124] for direct simulation of MHD turbulence and MHD instability with good accuracy at a staggered mesh.