Computational Stability of the Explicit Difference Schemes of the Forced Dissipative Nonlinear Evolution Equations

The computational stability of the explicit difference schemes of the forced dissipative nonlinear evolution equations is analyzed and the computational quasi-stability criterion of explicit difference schemes of the forced dissipative nonlinear atmospheric equations is obtained on account of the concept of computational quasi-stability, Therefore, it provides the new train of thought and theoretical basis for designing computational stable difference scheme of the forced dissipative nonlinear atmospheric equations. Key words Computational quasi-stability - Computational stability - Forced dissipative nonlinear evolution equation - Explicit difference scheme This work was supported by the National Outstanding Youth Scientist Foundation of China (Grant No. 49825109), the Key Innovation Project of Chinese Academy of Sciences (KZCX1-10-07), the National Natural Science Foundation of China (Grant Nos, 49905007 and 49975020) and the Outstanding State Key Laboratory Project (Grant No. 40023001).

Construction of Explicit Quasi-complete Square Conservative Difference Schemes of Forced Dissipative Nonlinear Evolution Equations

Based on the forced dissipetive nonlinear evolution equations for describing the motion of atmosphere and ocean, the computational stability of the explicit difference schemes of the forced dissipotive nonlinear atmospheric and oceanic equations is analyzed and the computationally stable explicit complete square conservative difference schemes are constructed. The theoretical analysis and numerical experiment prove that the explicit complete square conservative difference schemes are computationally stable and deserve to be disseminated.

DISSIPATIVE SCHEMES WITH PROPERTY OF INHERITING HOMOCLINIC ORBITS FOR 2N-DIMENSIONAL HAMILTONIAN SYSTEMS

In this paper we develop a kind of dissipative discrete scheme for the computation of homoclinic orbits near TB-point in Hamiltonian systems. It is proved by using continuation method that when the dissipative term and its coefficient are suitably chosen, this scheme possesses discrete homoclinic orbits, which approximate the continuous homoclinic orbits with second order accuracy w.r. to time-step size.

Optimization of a global seventh-order dissipative compact finite-difference scheme by a genetic algorithm

A global seventh-order dissipative compact finite-difference scheme is optimized in terms of time stability. The dissipative parameters appearing in the boundary closures are assumed to be different, resulting in an optimization problem with several parameters determined by applying a generic algorithm. The optimized schemes are analyzed carefully from the aspects of the eigenvalue distribution, the ε-pseudospectra, the short time behavior, and the Fourier analysis. Numerical experiments for the Euler equations are used to show the effectiveness of the final recommended scheme.

GROUP VELOCITY CONTROL SCHEME WITH LOW DISSIPATION

In order to prevent smearing the discontinuity, a modified term is added to the third order Upwind Compact Difference scheme to lower the dissipation error. Moreover, the dispersion error is controled to hold back the non physical oscillation by means of the group velocity control. The scheme is used to simulate the interactions of shock density stratified interface and the disturbed interface developing to vortex rollers. Numerical results are satisfactory.

High velocity flow simulation using lattice Boltzmann method with no-free-parameter dissipation scheme

A finite difference lattice Boltzmann method of second-order accuracy in time is developed based on non-oscillatory scheme with no-free-parameter dissipation （NND） difference scheme in this paper. The NND lattice Boltzmann method is used to simulate high-speed flows by constructing a new equilibrium distribution function of the lattice Boltzmann method. Compared with a variation of lattice Boltzmann method developed by Qu, et al., the present method can capture shock waves and handle oscillations of high velocity flows accurately in larger time steps and in shorter computing time. Numerical results indicate the correctness and capability of simulating shock wave interactions of the NND lattice Boltzmann method.

APPLICATION OF WEIGHTED NONOSCILLATORY AND NON-FREE-PARAMETER DISSIPATION DIFFERENCE SCHEME IN CALCULATING THE FLOW OF VIBRATING FLAT CASCADE

A dual-time method is introduced to calculate the unsteady flow in a certain vibrating flat cascade. An implicit lower-upper symmetric-gauss-seidel scheme（LU-SGS） is applied for time stepping in pseudo time domains, and the convection items are discretized with the spatial three-order weighted non-oscillatory and non-free-parameter dissipation difference （WNND） scheme. The turbulence model adopts q-co low-Reynolds-number model. The frequency specmuns of lift coefficients and the unsteady pressure-difference coefficients at different spanwise heights as well as the entropy contours at blade tips on different vibrating instants, are obtained. By the analysis of frequency specmuns of lift coefficients at three spanwise heights, it is considered that there exist obvious non-linear perturbations in the flow induced by the vibrating, and the perturbation frequencies are higher than the basic frequency. The entropy contours at blade tips at different times display an intensively unsteady attribute of the flow under large amplitudes.

Fifth-Order A-WENO Schemes Based on the Adaptive Diffusion Central-Upwind Rankine-Hugoniot Fluxes

We construct new fifth-order alternative WENO(A-WENO)schemes for the Euler equations of gas dynamics.The new scheme is based on a new adaptive diffusion centralupwind Rankine-Hugoniot(CURH)numerical flux.The CURH numerical fluxes have been recently proposed in[Garg et al.J Comput Phys 428,2021]in the context of secondorder semi-discrete finite-volume methods.The proposed adaptive diffusion CURH flux contains a smaller amount of numerical dissipation compared with the adaptive diffusion central numerical flux,which was also developed with the help of the discrete RankineHugoniot conditions and used in the fifth-order A-WENO scheme recently introduced in[Wang et al.SIAM J Sci Comput 42,2020].As in that work,we here use the fifth-order characteristic-wise WENO-Z interpolations to evaluate the fifth-order point values required by the numerical fluxes.The resulting one-and two-dimensional schemes are tested on a number of numerical examples,which clearly demonstrate that the new schemes outperform the existing fifth-order A-WENO schemes without compromising the robustness.

某新建高位水池消能改造方案及应急措施研究

某新建高位水池建成运行后,产生了两种恶劣流态:一是通气孔出口发生喷水,二是下游水厂出现掺气。该文通过水工模型试验演示了新建高位水池内部水流运行流态及掺气状况,探究了池内水流紊动及掺气机理,验证并提出了憋阀运行时的堰后“临界水位”消能方案,短期可消除高位水池内恶劣流态;在比较了堰板中部、及底部开孔等多个消能改造方案后,提出的优化方案池内流态平稳、无掺气,消能效果良好,可作为水池结构改造的可行实施方案,试验研究成果可为类似工程设计提供参考。

迎风格式在接触间断的数值耗散及其诱导误差

在不同流场参数条件下对三种迎风格式在接触间断中的数值耗散问题进行了数值实验,并对数值耗散产生的机理进行了分析。数值计算结果和理论分析表明,矢通量分裂格式计算接触间断问题时,若流场静止或流场内存在亚声速区域,密度耗散的产生会诱导出以特征速度运动的数值扰动误差,该误差对数值耗散的大小无影响,但会影响流场的速度及压力参数分布,从而改变流场的结构。在二维问题中,诱导误差相互干扰会产生大量的复杂小尺度结构,给流场结构分析带来困难。同时,在密度参数线性分布的流场中,若空间离散格式重构的对象为对流通量,使用矢通量分裂格式计算流场会产生数值误差,使计算精度难以到达二阶。

黏滞与金属阻尼器协同工作于加固工程的减震性能研究

文章基于现有黏滞阻尼器和金属阻尼器的研究,以安徽某住院门诊楼实际加固项目为研究对象,提出单独布置黏滞阻尼器、单独布置金属阻尼器、混合布置黏滞与金属阻尼器的3种加固方案;开展各方案在多遇和罕遇地震下的动力时程分析,综合减震前后层间位移、最大加速度等参数,研究黏滞阻尼器和金属阻尼器协同工作减震性能的优劣;基于协同工作方案进一步分析加固后的能量耗散情况以及阻尼器滞回曲线,研究其在实际工程中的具体减震效果。结果表明:2种阻尼器同时应用于加固工程时,合理的混合布置方案对结构的减震效果有显著提升,并且可以利用2种阻尼器的耗能特性实现分阶段耗能,耗能表现优异。

HLLCE格式构造及其在气动热计算中应用

飞行器表面热环境是临近空间高超声速飞行器研究中的一个重点问题,它对飞行器的气动、热环境和安全性有重要影响。受试验手段的限制,风洞试验无法准确模拟真实飞行条件,数值计算是研究气动加热问题的重要手段。格式的耗散性、网格尺度是影响气动热模拟的两个重要因素。气动热计算要求格式耗散越小越好,但低耗散性会引起激波不稳定现象。构造了兼具HLLE格式稳定性和HLLC格式低耗散性的HLLCE格式,该格式在较低马赫数下表现出HLLC的性质,是一种低耗散性格式,在高马赫数下则具有HLLE格式的性质,能够克服激波不稳定现象。针对气动热计算中最小网格尺度的选取,提出以边界层线性底层厚度为参考尺度,以特征长度计算的边界层线性底层厚度的1/10作为热环境计算的壁面最小网格尺度参考值。基于这一尺度确定了高超声速球头算例气动力热计算网格,计算结果验证了低耗散格式在临近空间高超声速气动力热计算中的良好性能。

A CLASS OF EXPLICIT FORWARD TIME-DIFFERENCE SQUARE CONSERVATIVE SCHEMES

In the present paper, a class of explicit forward time-difference schemes are established from a geometric view with strict analytical deductions. This class includes the schemes with a constant time interval and with adjustable time intervals, which is proved to be effective and remarkably time-saving in numerical tests and applications.

DISSIPATION-BASED CONSISTENT RATE-DEPENDENT MODEL FOR CONCRETE

An energy-dissipation based viscoplastic consistency model is presented to describe the performance of concrete under dynamic loading. The development of plasticity is started with the thermodynamic hypotheses in order that the model may have a sound theoretical background. Independent hardening and softening and the rate dependence of concrete are described separately for tension and compression. A modified implicit backward Euler integration scheme is adopted for the numerical computation. Static and dynamic behavior of the material is illustrated with certain numerical examples at material point level and structural level, and compared with existing experimental data. Results validate the effectiveness of the model.

Constructions and Applied Examinations of a Kind of Square-Conservative Schemes in High Precision in the Time Direction

In order to meet the needs of work in numerical weather forecast and in numerical simulations for climate change and ocean current, a kind of difference scheme in high precision in the time direction developed from the completely square-conservative difference scheme in explicit way is built by means of the Taylor expansion. A numerical test with 4-wave Rossby-Haurwitz waves on them and an application of them on the monthly mean current the of South China Sea are carried out, from which, it is found that not only do the new schemes have high harmony and approximate precision but also can the time step of the schemes be lengthened and can much computational time be saved. Therefore, they are worth generalizing and applying.

Mesoscale Numerical Simulation Study of Warm Fog Dissipation by Salt Particles Seeding

Based on the dynamic framework of WRF and Morrison 2-moment explicit cloud scheme, a salt-seeding scheme was developed and used to simulate the dissipation of a warm fog event during 6–7 November 2009 in the Beijing and Tianjin area. The seeding effect and its physical mechanism were studied. The results indicate that when seeding fog with salt particles sized 80 μm and at a quantity of 6 gm^（-2） at the fog top, the seeding effect near the ground surface layer is negative in the beginning period, and then a positive seeding effect begins to appear at 18 min, with the best effect appearing at 21 min after seeding operation. The positive effect can last about 35 min. The microphysical mechanism of the warm fog dissipation is because of the evaporation due to the water vapor condensation on the salt particles and coalescence with salt particles.The process of fog water coalescence with salt particles contributed mostly to this warm fog dissipation. Furthermore, two series of sensitivity experiments were performed to study the seeding effect under different seeding amounts and salt particles sizes. The results show that seeding fog with salt particles sized of 80 μm can have the best seeding effect, and the seeding effect is negative when the salt particle size is less than 10 μm. For salt particles sized 80 μm, the best seeding effect, with corresponding visibility of 380 m, can be achieved when the seeding amount is 30 g m^（-2）.

BRB加固对高层砼框-剪结构减震影响

根据防屈曲耗能支撑的工作原理与力学性能,进行既有高层框-剪结构布置防屈曲耗能支撑研究.以BRB承担层剪力占比为设计依据,使用SAP2000结构非线性有限元软件研究了单斜式和倒V式两种不同布置形式下,各3种竖向不同楼层布置方案结构动力时程响应、BRB耗能占比、剪力墙应力分布等特点.分析表明:在结构下部布置防屈曲耗能支撑具有减震作用;罕遇地震作用下,结构下部布置防屈曲耗能支撑不仅能够承担较大耗能,也对结构峰值响应下的剪力墙应力的减幅最大,该布置方案可为高层框-剪结构布置防屈曲耗能支撑的工程实践提供参考.

水电水利工程导流隧洞建设经验总结与设计探讨

结合十余年来国内导流隧洞的建设经验和教训,对导流隧洞的设计标准、结构设计、环保安全、施工方案等新出现的问题进行了深入探讨,得到以下结论:导流隧洞的结构设计标准和耐久性标准可结合工程的长远规划要求适当提高;底板抗冲耐磨、出口消能防冲设计、衬砌结构设计、封堵设计等可参考已建工程的成功经验;导流隧洞的设计应满足环保要求;进出口边坡设计可借鉴交通行业经验,更新设计理念,优化施工方案。

公路工程绿色低碳施工方案评价——基于“碳中和”与造价双目标

公路工程绿色低碳施工能够有效减少环境污染,但是建设工程中某一单位工程的施工方案无法实现“碳中和”,只能面向“碳中和”的低碳排放形成施工方案,同时也必须坚持合理造价控制下的绿色低碳施工方案。笔者从碳中和理念以及施工方案的造价成本双目标研究公路工程施工方案,将公路工程施工系统类比为耗散系统,根据“碳中和”理念,引入正负熵值模型,根据对施工系统的影响类型,将碳排放和造价成本解释为施工系统正熵值,将碳吸收解释为施工系统负熵值;根据模型公式运用PSR模型建立了基于“碳中和”理念的公路工程绿色低碳施工评价指标体系,得到正负熵值模型所需权重,从而计算施工系统总熵值,对比不同施工方案的施工系统熵值大小,综合分析比较施工方案的造价成本以及绿色低碳两方面的影响,设立3个情景对施工方案进行评价进而选出总体占优的施工方案。研究结果表明:使用生态砌块预制件的施工方案的施工总熵值小于使用传统预制件的施工总熵值,前者施工方案更加契合“碳中和”与造价双目标。

Developing Hybrid cell-edge and cell-node Dissipative Compact Scheme for Complex Geometry Flows

Developing high resolution finite difference scheme and enabling the use of this scheme on complex geometry are the aims of this study.High resolution has been achieved by Dissipative Compact Schemes(DCS),however,according to the recent research,applications of DCS on complex geometry may have serious problem for that the Geometric Conservation Law(GCL)is not satisfied,and this may cause numerical instability.To cope with this problem,a new scheme named Hybrid cell-edge and cell-node Dissipative Compact Scheme(HDCS)has been formulated.The formulation of the HDCS contains two steps.First,a new central compact scheme is formulated for the purpose of conveniently fulfilling the GCL,and then dissipation is added on the central scheme by high-order dissipative interpolation of cell-edge variables.The solutions of Euler and Navier-Stokes equations show that the HDCS can be applied successfully on complex geometry,while the DCS may suffer numerical instabilities.Moreover,high resolution of the HDCS may be observed in the test of scattering of acoustic waves by multiple cylinders.