High Order Central Schemes Applied to Relativistic Multi-Component Flow Models

The dynamics of inviscid multi-component relativistic fluids may be modeled by the relativistic Euler equations, augmented by one (or more) additional species equation(s). We use the high-resolution staggered central schemes to solve these equations. The equilibrium states for each component are coupled in space and time to have a common temperature and velocity. The current schemes can handle strong shocks and the oscillations near the interfaces are negligible, which usually happens in the multi-component flows. The schemes also guarantee the exact mass conservation for each component, the exact conservation of total momentum, and energy in the whole particle system. The central schemes are robust, reliable, compact and easy to implement. Several one- and two-dimensional numerical test cases are included in this paper, which validate the application of these schemes to relativistic multi-component flows.

A MOVING WATER EQUILIBRIA PRESERVING NONSTAGGERED CENTRAL SCHEME ACHIEVED VIA FLUX GLOBALIZATION FOR THE RIPA MODEL

In this paper,we propose a second-order moving-water equilibria preserving nonstaggered central scheme to solve the Ripa model via flux globalization.To maintain the moving-water steady states,we use the discrete source terms proposed by Britton et al.(J Sci Comput,2020,82(2):Art 30)by incorporating the expression of the source terms as a whole into the flux gradient,which directly avoids the discrete complexity of the source terms in order to maintain the well-balanced properties of the scheme.In addition,since the nonstaggered central scheme requires re-projecting the updated values of the nonstaggered cells onto the staggered cells,we modify the calculation of the global variables by constructing ghost cells and alternating the values of the global variables with the water depths obtained from the solution through the nonlinear relationship between the global flux and the water depth.In order to maintain the second-order accuracy of the scheme on the time scale,we incorporate a new Runge-Kutta type time discretization in the evolution of the numerical solution for the nonstaggered cells.Meanwhile,we introduce the"draining"time step technique to ensure that the water depth is positive and that it satisfies mass conservation.Numerical experiments verify that the scheme is well-balanced,positivity-preserving and robust.

SOLUTION OF 2D SHALLOW WATER EQUATIONS BY GENUINELY MULTIDIMENSIONAL SEMI-DISCRETE CENTRAL SCHEME

A numerical two-dimensional shallow water method was based on method for solving the equations was presented. This the third-order genuinely multidimensional semi-discrete central scheme for spatial discretization and the optimal third-order Strong Stability Preserving （SSP） Runge-Kutta method for time integration. The third-order compact Central Weighted Essentially Non-Oscillatory （CWENO） reconstruction was adopted to guarantee the non-oscillatory behavior of the presented scheme and improve the resolution. Two kinds of source terms were considered in this work. They were evaluated using different approaches. The resulting scheme does not require Riemann solvers or characteristic decomposition, hence it retains all the attractive features of central schemes such as simplicity and high resolution. To evaluate the performance of the presented scheme, several numerical examples were tested. The results demonstrate that our method is efficient, stable and robust.

Well-Balanced Central Scheme for the System of MHD Equations with Gravitational Source Term

A well-balanced second order finite volume central scheme for the magnetohydrodynamic(MHD)equations with gravitational source term is developed in this paper.The scheme is an unstaggered central scheme that evolves the numerical solution on a single grid and avoids solving Riemann problems at the cell interfaces using ghost staggered cells.A subtraction technique is used on the conservative variables with the support of a known steady state in order to manifest the well-balanced property of the scheme.The divergence-free constraint of themagnetic field is satisfied after applying the constrained transport method(CTM)for unstaggered central schemes at the end of each time-step by correcting the components of the magnetic field.The robustness of the proposed scheme is verified on a list of numerical test cases from the literature.

Central Schemes and Second Order Boundary Conditions for 1D Interface and Piston Problems in Lagrangian Coordinates

We study high-resolution central schemes in Lagrangian coordinates for the one-dimensional system of conservation laws describing the evolution of two gases in slab geometry separated by an interface.By using Lagrangian coordinates,the interface is transformed to a fixed coordinate in the computational domain and,as a consequence,the movement of the interface is obtained as a byproduct of the numerical solution.The main contribution is the derivation of a special equation of state to be imposed at the interface in order to avoid non-physical oscillations.Suitable boundary conditions at the piston that guarantee second order convergence are described.We compare the solution of the piston problem to other results available in the literature and to a reference solution obtained within the adiabatic approximation.A shock-interface interaction problem is also treated.The results on these tests are in good agreement with those obtained by other methods.

HIGH-RESOLUTION SEMI-DISCRETE CENTRAL SCHEME FOR DAM-BREAK PROBLEMS

A numerical model for simulating the dambreak problems was presented. The model was based on a high-resolution semi-discrete central-upwind difference scheme. In order to reduce spurious oscillation, the uniformly non-oscillatory limiter was employed. A third-order total variation diminishing Runge-Kutta method is used for time integration. The main feature of the presented method is its simplicity. It requires no Riemann solvers, no flux splitting and no flux limiter. It is explicit and does not require dimensional splitting for two dimensions. The Simpson quadrature rule was employed to compute the source term. To verify the effectiveness and accuracy of the proposed method, the 1D dambreak, circular dam-break and partial dam-break problems were simulated. The results are shown to be in good agreement with analytical solution and numerical results obtained by other methods.

High-resolution central difference scheme for the shallow water equations

A two-dimensional nonoscillatory central difference scheme was extended to the shallow water equations. A high-resolution numerical method for solving the shallow water equations was presented. In order to prevent oscillation, the nonlinear limiter is employed to approximate the discrete slopes. The main advantage of the presented method is simplicity comparable with the upwind schemes. This method does not require Riemann solvers or some form of flux difference splitting methods. Furthermore, the discrete derivatives of flux can be approximated by the component-wise approach and thus the computation of Jacobian can be avoided. The method retains high resolution and high accuracy similar to the upwind results. It is applied to simulating several tests, including circular dam-break problem, shock focusing problem and partial dam-break problem. The results are in good agreement with the numerical results obtained by other methods. The simulated results also demonstrate that the presented method is stable and efficient.

Central Upwind Scheme for Solving Multivariate Cell Population Balance Models

Microbial cultures are comprised of heterogeneous cells that differ according to their size and intracellular concentrations of DNA, proteins and other constituents. Because of the included level of details, multi-variable cell population balance models (PBMs) offer the most general way to describe the complicated phenomena associated with cell growth, substrate consumption and product formation. For that reason, solving and understanding of such models are essential to predict and control cell growth in the processes of biotechnological interest. Such models typically consist of a partial integro-differential equation for describing cell growth and an ordinary integro-differential equation for representing substrate consumption. However, the involved mathematical complexities make their numerical solutions challenging for the given numerical scheme. In this article, the central upwind scheme is applied to solve the single-variate and bivariate cell population balance models considering equal and unequal partitioning of cellular materials. The validity of the developed algorithms is verified through several case studies. It was found that the suggested scheme is more reliable and effective.

Bidding Scheme Design of Central Recreational Area for Xiaogan Linkong Economic Zone

This paper elaborated the bidding scheme design of the Central Recreational Area in Linkong Economic Zone from the perspectives of site analysis, determination of properties, design theme and principle, scheme layout and conception, in order to explore the potential enlightenments of the scheme design process, and disclose significance of site analysis and its close relationship with the scheme design.

Comments on Three-point explicit compact difference scheme with arbitrary order of accuracy and its application in CFD

The explicit compact difference scheme, proposed in Three-point explicit compact difference scheme with arbitrary order of accuracy and its application in CFD by Lin et al., published in Applied Mathematics and Mechanics （English Edition）, 2007, 28（7）, 943-953, has the same performance as the conventional finite difference schemes. It is just another expression of the conventional finite difference schemes. The proposed expression does not have the advantages of a compact difference scheme. Nonetheless, we can more easily obtain and implement compared with the conventional expression in which the coefficients can only be obtained by solving equations, especially for higher accurate schemes.

Changing central-local relationin post-reform China:a geographical perspective

This study examines the evolution of fiscal relations between the central state and local governments in China since the founding of the People's Republic The emphasis is placed on the changing arrangement for the central state's collection of taxes and allocation of capital among provinces The central local relation has experienced constant reorganization since 1949, but the tax division scheme introduced in the early 1990s represents the most significant change Prior to the 1990s, the central local fiscal relation was shaped by a highly centralized administrative and economic system without rational and scientific design for revenue collection and expenditure The financial responsibility system established after the reforms contributed to regional economic development during the first decade of reforms, but it was a temporary and transitional arrangement that does not meet the requirement of rational resources arrangement according to free market forces The implementation of the tax division scheme has stopped the decline of the ratio of fiscal revenue to gross domestic product, raised the percentage of central revenue in total national income, and strengthened the central function for macro economic control The mechanism for tax refund under the tax division scheme required further improvements Several proposals are made in this study: 1) tax classification should be adjusted according to administration; 2) a scientific and standardized system for regional transfer payment should be developed; and 3) the power for tax legislation should be delineated according to the rational division of administration between the central and local government

A Gas-Kinetic Scheme for Six-Equation Two-Phase Flow Model

A kinetic flux-vector splitting (KFVS) scheme is applied for solving a reduced six-equation two-phase flow model of Saurel et al. [1]. The model incorporates single velocity, two pressures and relaxation terms. An additional seventh equation, describing the total mixture energy, is added to the model to guarantee the correct treatment of shocks in the single phase limit. Some salient features of the model are that it is hyperbolic with only three wave propagation speeds and the volume fraction remains positive. The proposed numerical scheme is based on the direct splitting of macroscopic flux functions of the system of equations. The second order accuracy of the scheme is achieved by using MUSCL-type initial reconstruction and Runge-Kutta time stepping method. Moreover, a pressure relaxation procedure is used to fulfill the interface conditions. For validation, the results of suggested scheme are compared with those from the high resolution central upwind and HLLC schemes. The central upwind scheme is also applied for the first time to this model. The accuracy, efficiency and simplicity of the KFVS scheme demonstrate its potential for modeling two-phase flows.

Negotiation-Based TDMA Scheme for Ad Hoc Networks from Game Theoretical Perspective

This paper proposes a negotiation-based TDMA scheme for ad hoc networks, which was modeled as an asynchronous myopic repeated game. Compared to the traditional centralized TDMA schemes, our scheme operates in a decentralized manner and is scalable to topology changes. Simulation results show that, with respect to the coloring quality, the performance of our scheme is close to that of the classical centralized algorithms with much lower complexity.

有色金属板带加工企业公辅设备集控中心方案设计

文章设计了一套完善的监视、控制一体化集控中心,通过公辅设备的集中监控,减少操作人员数量,合理优化运维人员配置,实现有色金属板带加工企业公辅系统高效运行、集约化管控的目标。

组串式及集中式逆变器方案比选及应用场景分析

为研究光伏组件中逆变器的选型,对存在的直流电压转交流电压存在大量的波形失真度问题进行有效分析解决,开展对组串式逆变器与集中式逆变器的技术方案比较分析,以得出在特定光伏应用场景下的最为合适的逆变器选用方案;其次为解决逆变器的使用能效最大化问题,引入光伏阵列因素,对光照资源进行数据整合分析,得出在大型光伏发电场区中进行光伏组件安装方法的最佳搭配模式。分析结果表明:集中式逆变器具有在大型平坦且光照充足的场景中进行工程建设的突出优势。

Revisting High-Resolution Schemes with van Albada Slope Limiter

Slope limiters play an essential role in maintaining the non-oscillatory behavior of high-resolution methods for nonlinear conservation laws.The family of minmod limiters serves as the prototype example.Here,we revisit the question of non-oscillatory behavior of high-resolution central schemes in terms of the slope limiter proposed by van Albada et al.(Astron Astrophys 108:76–84,1982).The van Albada(vA)limiter is smoother near extrema,and consequently,in many cases,it outperforms the results obtained using the standard minmod limiter.In particular,we prove that the vA limiter ensures the one-dimensional Total-Variation Diminishing(TVD)stability and demonstrate that it yields noticeable improvement in computation of one-and two-dimensional systems.

基于箱流波动的集装箱中心站直达班列开行方案优化

研究一类契合箱流波动的铁路集装箱中心站直达班列开行方案优化问题。以班列始发集结车小时和沿途改编车小时消耗最小为目标,考虑中心站改编能力和箱流组织方案唯一等限制,利用统计时段内集装箱流日均值,构建基于箱流日均数据的中心站直达班列开行方案优化模型。进而直接利用集装箱流波动数据,构建基于箱流动态数据的中心站直达班列开行方案优化模型。然后开发概率约束的确定性转化方法,并设计基于车流序列优选-更新-接续的元启发式求解过程。最后,设计实验场景对箱流日均数据模型和箱流动态数据模型的中心站直达班列开行方案进行比对。结果表明:集装箱流在±10%、±15%、±20%和±25%波动区间,日均数据模型的稳定性分别为77.2%、72.4%、68.4%和51.6%,动态数据模型的稳定性分别为96.0%、92.8%、88.2%和77.2%,动态数据模型适应性更强。

缓倾斜薄矿体溜井布置与集中运输方案研究

某磷矿属于沉积型矿床,矿体倾角较缓,厚度不大,属于缓倾斜薄矿体,开采时,采用溜井集矿,然后集中运输到主提升系统,而后通过主提升系统运输到地表;文章结合矿体的具体赋存条件,研究溜井布置与集中运输方案。

动车段(所)控制集中系统智能化研究及设计

为适应智能铁路的快速发展,动车段(所)控制集中系统面临着智能化升级的迫切需求。以中国智能铁路总体架构为指导,研究智能动车段(所)控制集中系统(iCCS)设计方案,采用企业级系统通用的分层架构设计方法,将iCCS的系统应用逻辑归入感知、传输、数据资源、决策、应用等5个层次中协同工作,实现智能化目标。提出iCCS系统设计方案:在硬件上增加作业计划服务器、综合数据服务器、智能化接口平台、控制集中综合仿真平台等设备;在软件方面,增加作业计划智能管理、列车按计划自动行车、综合数据应用、作业综合管控、控制集中综合仿真等功能。对系统实现中将涉及的作业计划智能管理、按计划自动行车、无线进路预告、综合数据应用、综合仿真平台等若干项关键技术进行探讨,并提出相应的技术实现方法。iCCS系统设计方案是在既有控制集中系统基本软硬件结构的基础上,通过增加硬件设备和软件功能的方式,实现控制集中系统从自动化向智能化的平滑升级。

典型缺水地区国家中心城市供水方案——以郑州市为例

水资源是经济社会发展的基础性、先导性、控制性要素,水资源的承载能力直接决定城市的发展空间和建设效果。从郑州市国家中心城市建设任务出发,全面梳理郑州市作为典型缺水地区国家中心城市所面临的主要水问题,通过构建多水源联合配置模型,提出不同阶段南水北调中线工程作为主力供水水源向郑州市增加供水方案,并分析方案效果、存在问题和相应措施建议。研究可为构建缺水地区国家中心城市供水保障体系提供参考。