采用Power限制器的PNND和PWNND格式

为高精度捕捉激波等流场结构,引入一种Power限制器,对NND格式和WNND格式进行改进,分别得到二阶PNND(Power NND)格式和三阶PWNND(Power WNND)格式.该Power类型格式通过Power限制器对相邻待选模板上的一阶导数进行限制,改善了NND格式和WNND格式在间断附近的耗散效应.对各种格式的分析表明,在间断附近采用Power限制器的格式比原格式的表现要好,耗散小且捕捉间断精度高,其中PNND格式虽然只有二阶精度,但在所有算例中与三阶WNND格式的计算结果比较接近,在个别算例中甚至优于WNND格式.最后将PWNND格式应用到二维NACA0012翼型的强迫俯仰振动的数值模拟,计算结果与实验值、参考计算值吻合较好.     

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 improved monotone finite volume scheme for diffusion equation on polygonal meshes

We construct a new nonlinear monotone finite volume scheme for diffusion equation on polygonal meshes. The new scheme uses the cell-edge unknowns instead of cell-vertex unknowns as the auxiliary unknowns in order to improve the accuracy of monotone scheme. Our scheme is locally conservative and has only cell-centered unknowns. Numerical results are presented to show how our scheme works for preserving positivity on various distorted meshes. Specially, numerical results show that the new scheme is robust, and more accurate than the existing monotone scheme on some kinds of meshes.     

Multisymplectic Euler Box Scheme for the KdV Equation

We investigate the multisymplectic Euler box scheme for the Korteweg-de Vries （KdV） equation. A new completely explicit six-point scheme is derived. Numerical experiments of the new scheme with comparisons to the Zabusky-Kruskal scheme, the multisymplectic 12-point scheme, the narrow box scheme and the spectral method are made to show nice numerical stability and ability to preserve the integral invariant for long-time integration.     

A high-order accurate hybrid scheme using a central flux scheme and a WENO scheme for compressible flowfield analysis

A high-order accurate hybrid central-WENO scheme is proposed. The fifth order WENO scheme [G.S. Jiang, C.W. Shu, Efficient implementation of weighted ENO schemes, J. Comput. Phys. 126 (1996) 202–228] is divided into two parts, a central flux part and a numerical dissipation part, and is coupled with a central flux scheme. Two sub-schemes, the WENO scheme and the central flux scheme, are hybridized by means of a weighting function that indicates the local smoothness of the flowfields. The derived hybrid central-WENO scheme is written as a combination of the central flux scheme and the numerical dissipation of the fifth order WENO scheme, which is controlled adaptively by a weighting function. The structure of the proposed hybrid central-WENO scheme is similar to that of the YSD-type filter scheme [H.C. Yee, N.D. Sandham, M.J. Djomehri, Low-dissipative high-order shock-capturing methods using characteristic-based filters, J. Comput. Phys. 150 (1999) 199–238]. Therefore, the proposed hybrid scheme has also certain merits that the YSD-type filter scheme has. The accuracy and efficiency of the developed hybrid central-WENO scheme are investigated through numerical experiments on inviscid and viscous problems. Numerical results show that the proposed hybrid central-WENO scheme can resolve flow features extremely well.     

二维扩散方程的局部二阶线性保极值节点计算方法及应用

对一般四边形网格设计一种优化的节点控制体, 并构造了一种扩散方程的保极值二阶收敛的局部线性节点计算格式(优化控制体节点格式, VOC格式)。在网格不出现异常节点的情况下, 证明VOC格式是保极值、线性精确和二阶收敛的。而且在均匀的矩形网格上, 修正的逆距离加权格式与VOC格式等价, 从而对间断系数问题也是局部二阶收敛的。VOC格式可以用于单元中心型线性扩散格式和保正格式的节点值计算。数值算例表明对扭曲网格上的间断系数问题, VOC格式是二阶收敛的。采用VOC格式计算节点值的线性九点格式具有线性精确性和二阶收敛性, 采用VOC格式的保正格式也具有二阶收敛性。     

Analysis and optimization of chirp-compensation OPCPA scheme

We present general guidelines for the chirp-compensation optical parametric chirped pulse amplification scheme, where maximization of both conversion efficiency and signal-to-noise ratio and simultaneous overcoming of the gain-narrowing effect are required. Using numerical simulation, we find that the crystal length, the ratio of signal and pump durations, and the pump chirp are the critical parameters for the chirp-compensation scheme. We compare the chirp-compensation scheme with the usual collinear or noncollinear schemes, and find that the chirp-compensation scheme can obtain both higher conversion efficiency and signal-to-noise ratio, and overcome the gain-narrowing effect simultaneously. We also compare the linear-chirp-compensation scheme with the nonlinear-chirp-compensation scheme and find that the linear-chirp-compensation scheme is a good approximation for the nonlinear-chirp-compensation scheme when the signal bandwidth is not very broad.     

A high-resolution,hybrid compact-WENO scheme with minimized dispersion and controllable dissipation

In this paper,a high-resolution,hybrid compact-WENO scheme is developed based on the minimized dispersion and controllable dissipation reconstruction technique.Firstly,a suffcient condition for a family of tri-diagonal compact schemes to have independent dispersion and dissipation is derived.Then,a specific 4th order compact scheme with low dispersion and adjustable dissipation is constructed and analyzed.Finally,the optimized compact scheme is blended with the WENO scheme to form the hybrid scheme.Moreover,the approximation dispersion relation approach is employed to optimize the spectral properties of the nonlinear scheme to yield the true wave propagation behavior of the finite difference scheme.Several test cases are carried out to verify the highresolution as well as the robust shock-capturing capabilities of the proposed scheme.     

径向对称非线性Schrdinger方程的守恒差分格式

对径向对称的非线性Schrdinger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个守恒律。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。     

分辨率优化的混合WENO格式

为提高有限差分格式的分辨率,利用傅里叶分析对WENO格式进行色散及耗散优化,并给出优化的线性权重.用优化后的WENO格式与保单调格式（MP）进行加权混合,得到新的加权混合WENO格式（H-WENO）.通过一维激波管问题、Shu-Osher问题及二维双Mach反射问题及R-T不稳定性问题对格式进行数值测试.结果显示,新格式具有强健的激波捕捉能力和对小尺度波结构的高分辨率,与原WENO格式相比改进明显.     

多介质流体力学计算的守恒型高分辨率格式

应用Lagrange坐标系下的守恒型格式计算多介质流体力学问题,在物质交界面附近采用一阶格式的数值通量,而在其余部分采用高分辨率格式的数值通量,不仅保持了高分辨率的良好性质,而且消除了一般的守恒型格式在界面附近所产生的震荡.     

保持对称性的新积分梯度格式

针对柱坐标系下拉氏流体力学的动量方程,提出一种积分梯度格式IGTSP(Integral Gradient Total Symmetry-Preserving),它具备现有积分梯度格式IGA(Integral Gradient Average)和IGT(Integral Gradient Total)的优点,不仅克服了IGT格式不能保持柱坐标系下的一维球对称性的缺点,而且系统的总动量守恒误差为O(h),比IGA格式更好地保持系统的总动量守恒.数值试验进一步显示了该格式理论分析的优点.     

A 5th order monotonicity-preserving upwind compact difference scheme

Based on an upwind compact difference scheme and the idea of monotonicity-preserving, a 5th order monotonicity-preserving upwind compact difference scheme (m-UCD5) is proposed. The new difference scheme not only retains the advantage of good resolution of high wave number but also avoids the Gibbs phenomenon of the original upwind compact difference scheme. Compared with the classical 5th order WENO difference scheme, the new difference scheme is simpler and small in diffusion and computation load. By emplo...     

A Fifth-Order Low-Dissipative Conservative Upwind Compact Scheme Using Centered Stencil

In this paper, a conservative fifth-order upwind compact scheme using centered stencil is introduced. This scheme uses asymmetric coefficients to achieve the upwind property since the stencil is symmetric. Theoretical analysis shows that the proposed scheme is low-dissipative and has a relatively large stability range. To maintain the convergence rate of the whole spatial discretization, a proper non-periodic boundary scheme is also proposed. A detailed analysis shows that the spatial discretization implemented with the boundary scheme proposed by Pirozzoli [J. Comput. Phys., 178 (2001), pp. 81-117] is approximately fourth-order. Furthermore, a hybrid methodology, coupling the compact scheme with WENO scheme, is adopted for problems with discontinuities. Numerical results demonstrate the effectiveness of the proposed scheme.     

QUICK与多种差分方案的比较和计算

本文用QUICK和多种差分方案计算了四个流动与换热问题．计算结果表明。对于强制流动问题,QUICK用较粗网格就能得到其他差分方案用较细网格才能得到的结果。对稳态自然对流,QUICK与其他差分方案的计算结果相近,但QUICK方案能预测出所计算的低Pr数流体自然对流的物理振荡,而其他几种方案不能．     

Spray algorithm without interface construction

This research is aimed to create a new and robust family of convective schemes to capture the interface between the dispersed and the carrier phases in a spray without the need to build up the interface boundary. The selection of the Weighted Average Flux (WAF) scheme is due to this scheme being designed to deal with random flux scheme which is second-order accurate in space and time. The convective flux in each cell face utilizes the WAF scheme blended with Switching Technique for Advection and Capturing of Surfaces (STACS) scheme for high resolution flux limiters. In the next step, the high resolution scheme is blended with the WAF scheme to provide the sharpness and boundedness of the interface by using switching strategy. In this work, the Eulerian–Eulerian framework of non-reactive turbulent spray is set in terms of theoretical proposed methodology namely spray moments of drop size distribution, presented by Beck and Watkins [1]. The computational spray model avoids the need to segregate the local droplet number distribution into parcels of identical droplets. The proposed scheme is tested on capturing the spray edges in modelling hollow cone sprays without need to reconstruct two-phase interface. A test is made on simple comparison between TVD scheme and WAF scheme using the same flux limiter on convective flow hollow cone spray. Results show the WAF scheme gives a better prediction than TVD scheme. The only way to check the accuracy of the presented models is by evaluating the spray sheet thickness.     

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.     

Evaluation of the applicability of a retrospective scheme based on comparison with several difference schemes

The evaluation of the applicability of a retrospective multi-time-level scheme (RT scheme) is carried out on the basis of comparison with the common leapfrog scheme (LF scheme) and its derivatives, and modified BOTT‘s positive-definite schemes used in atmospheric models. Two rational flow field tests confirm that at least the BOTT scheme tested may be applied, but apparently the best results are obtained by the RT scheme. The results of wavelet analysisshow that the RT scheme can better extract the useful information from the initial fields, i.e. to memorize many main initial characteristics, such as periods, thus offering a new approach to the short-term climate numerical prediction.     

Explicit and implicit finite difference schemes for fractional Cattaneo equation

In this paper, the numerical solution of fractional (non-integer)-order Cattaneo equation for describing anomalous diffusion has been investigated. Two finite difference schemes namely an explicit predictor–corrector and totally implicit schemes have been developed. In developing each scheme, a separate formulation approach for the governing equations has been considered. The explicit predictor–corrector scheme is the fractional generalization of well-known MacCormack scheme and has been called Generalized MacCormack scheme. This scheme solves two coupled low-order equations and simultaneously computes the flux term with the main variable. Fully implicit scheme however solves a single high-order undecomposed equation. For Generalized MacCormack scheme, stability analysis has been studied through Fourier method. Through a numerical test, the experimental order of convergency of both schemes has been found. Then, the domain of applicability and some numerical properties of each scheme have been discussed.     

Numerical Simulation of Electromagnetic Waves Scattering by Discrete Exterior Calculus

We show how to construct discrete Maxwell equations by discrete exterior calculus. The new scheme has many virtues compared to the traditional Yee＇s scheme： it is a multisymplectic scheme and keeps geometric properties. Moreover, it can be applied on triangular mesh and thus is more adaptive to handle domains with irregular shapes. We have implemented this scheme on a Java platform successfully and our experimental results show that this scheme works well.