Gas kinetic flux solver based finite volume weighted essentially non-oscillatory scheme for inviscid compressible flows

A high-order gas kinetic flux solver(GKFS)is presented for simulating inviscid compressible flows.The weighted essentially non-oscillatory(WENO)scheme on a uniform mesh in the finite volume formulation is combined with the circular function-based GKFS(C-GKFS)to capture more details of the flow fields with fewer grids.Different from most of the current GKFSs,which are constructed based on the Maxwellian distribution function or its equivalent form,the C-GKFS simplifies the Maxwellian distribution function into the circular function,which ensures that the Euler or Navier-Stokes equations can be recovered correctly.This improves the efficiency of the GKFS and reduces its complexity to facilitate the practical application of engineering.Several benchmark cases are simulated,and good agreement can be obtained in comparison with the references,which demonstrates that the high-order C-GKFS can achieve the desired accuracy.

Numerical Simulation of Diffusion Type Traffic Flow Model Using Second-Order Lax-Wendroff Scheme Based on Exponential Velocity Density Function

In order to control traffic congestion, many mathematical models have been used for several decades. In this paper, we study diffusion-type traffic flow model based on exponential velocity density relation, which provides a non-linear second-order parabolic partial differential equation. The analytical solution of the diffusion-type traffic flow model is very complicated to approximate the initial density of the Cauchy problem as a function of x from given data and it may cause a huge error. For the complexity of the analytical solution, the numerical solution is performed by implementing an explicit upwind, explicitly centered, and second-order Lax-Wendroff scheme for the numerical solution. From the comparison of relative error among these three schemes, it is observed that Lax-Wendroff scheme gives less error than the explicit upwind and explicit centered difference scheme. The numerical, analytical analysis and comparative result discussion bring out the fact that the Lax-Wendroff scheme with exponential velocity-density relation of diffusion type traffic flow model is suitable for the congested area and shows a better fit in traffic-congested regions.

Lattice Boltzmann Flux Solver:An Efficient Approach for Numerical Simulation of Fluid Flows

A lattice Boltzmann flux solver(LBFS)is presented for simulation of fluid flows.Like the conventional computational fluid dynamics(CFD)solvers,the new solver also applies the finite volume method to discretize the governing differential equations,but the numerical flux at the cell interface is not evaluated by the smooth function approximation or Riemann solvers.Instead,it is evaluated from local solution of lattice Boltzmann equation(LBE)at cell interface.Two versions of LBFS are presented in this paper.One is to locally apply one-dimensional compressible lattice Boltzmann(LB)model along the normal direction to the cell interface for simulation of compressible inviscid flows with shock waves.The other is to locally apply multi-dimensional LB model at cell interface for simulation of incompressible viscous and inviscid flows.The present solver removes the drawbacks of conventional lattice Boltzmann method(LBM)such as limitation to uniform mesh,tie-up of mesh spacing and time interval,limitation to viscous flows.Numerical examples show that the present solver can be well applied to simulate fluid flows with non-uniform mesh and curved boundary.

A numerical study for WENO scheme-based on different lattice Boltzmann flux solver for compressible flows

In this paper,the finite difference weighted essentially non-oscillatory (WENO) scheme is incorporated into the recently developed four kinds of lattice Boltzmann flux solver (LBFS) to simulate compressible flows,including inviscid LBFS Ⅰ,viscous LBFS Ⅱ,hybrid LBFS Ⅲ and hybrid LBFS Ⅳ.Hybrid LBFS can automatically realize the switch between inviscid LBFS Ⅰ and viscous LBFS Ⅱ through introducing a switch function.The resultant hybrid WENO-LBFS scheme absorbs the advantages of WENO scheme and hybrid LBFS.We investigate the performance of WENO scheme based on four kinds of LBFS systematically.Numerical results indicate that the devopled hybrid WENO-LBFS scheme has high accuracy,high resolution and no oscillations.It can not only accurately calculate smooth solutions,but also can effectively capture contact discontinuities and strong shock waves.

High-precision nonisothermal transient wellbore drift flow model suitable for the full flow pattern domain and full dip range

A reliable multiphase flow simulator is an important tool to improve wellbore integrity and production decision-making.To develop a multiphase flow model with high adaptability and high accuracy,we first build a multiphase flow database with 3561 groups of data and developed a drift closure relationship with stable continuity and high adaptability.Second,a high-order numerical scheme with strong fault capture ability is constructed by effectively combining MUSCL technology,van Albada slope limiter and AUSMV numerical scheme.Finally,the energy equation is coupled into the AUSMV numerical scheme of the drift flow model in the form of finite difference.A transient non-isothermal wellbore multiphase flow model with wide applicability is formed by integrating the three technologies,and the effects of various factors on the calculation accuracy are studied.The accuracy of the simulator is verified by comparing the measurement results with the blowout experiment of a full-scale experimental well.

A high-order scheme based on lattice Boltzmann flux solver for viscous compressible flow simulations

In this paper,a high-order scheme based on the lattice Boltzmann flux solver(LBFS)is proposed to simulate viscous compressible flows.The flux reconstruction(FR)approach is adopted to implement the spatial discretization.The LBFS is employed to compute the inviscid flux by using the local reconstruction of the lattice Boltzmann equation solutions from macroscopic flow variables.Meanwhile,a switch function is used in LBFS to adjust the magnitude of the numerical viscosity.Thus,it is more beneficial to capture both strong shock waves and thin boundary layers.Moreover,the viscous flux is computed according to the local discontinuous Galerkin method.Some typical compressible viscous problems,including manufactured solution case,lid-driven cavity flow,supersonic flow around a cylinder and subsonic flow over a NACA0012 airfoil,are simulated to demonstrate the accuracy and robustness of the proposed FR-LBFS.

高焓流动中的可压缩颗粒两相流并行求解器:数值方法及其验证

在极端力学环境下可压缩点力颗粒两相流理论方程的基础上,提出一种基于动态链表数组的并行颗粒求解器,使其与可压缩流体求解器耦合。与基于欧拉坐标系的携带流体相不同,基于拉格朗日坐标系的求解器采用动态链表数组对弥散颗粒相进行内存分配,可以解决因使用全局数组解决拉格朗日/欧拉坐标系转换带来的弥散颗粒群内存利用率低和计算效率低下问题。最后对多物理效应的可压缩颗粒两相流求解器进行验证,并在马赫数渐进趋于零的情况下,对两个不可压缩槽道颗粒湍流标模进行验证。

客运需求局部缩减条件下列车开行方案调整研究

因疫情或其他特定事件导致局部客运需求缩减时,铁路各OD之间客流规模均发生相应变化。如何保证铁路运输生产连续性来调整列车开行方案是铁路运营企业面临的难题。归纳了应对不同客运需求缩减场景的列车开行方案调整策略,包括列车停运、列车编组调整、列车运行区段调整、列车停站办理客运作业调整及关联售票调整。以此为基础,构建列车开行方案调整模型,对列车停运、列车停站不办理客运作业和列车编组调整综合决策,其中列车停运考虑整交路以实现决策在实际中的适用性。通过算例证明了模型的有效性,在实际线路案例中的结果显示,通过优化列车开行方案运力配置,调整后结果在供需匹配的基础上可以控制运营成本,减少需求缩减带来的损失。

Transversal effects of high order numerical schemes for compressible fluid flows

Finite volume schemes for the two-dimensional(2D) wave system are taken to demonstrate the role of the genuine dimensionality of Lax-Wendroff flow solvers for compressible fluid flows. When the finite volume schemes are applied, the transversal variation relative to the computational cell interfaces is neglected, and only the normal numerical flux is used, thanks to the Gauss-Green formula. In order to offset such defects, the Lax-Wendroff flow solvers or the generalized Riemann problem(GRP) solvers are adopted by substituting the time evolution of flows into the spatial variation. The numerical results show that even with the same convergence rate, the error by the GRP2D solver is almost one ninth of that by the multistage Runge-Kutta(RK) method.

Analysis of Unsteady Flow over Offshore Wind Turbines in Combination with Different types of Foundations

Environmental effects have an important influence on Offshore Wind Turbine (OWT) power generation efficiency and the structural stability of such turbines. In this study, we use an in-house Boundary Element (BEM)-panMARE code-to simulate the unsteady flow behavior of a full OWT with various combinations of aerodynamic and hydrodynamic loads in the time domain. This code is implemented to simulate potential flows for different applications and is based on a three-dimensional first-order panel method. Three different OWT configurations consisting of a generic 5 MW NREL rotor with three different types of foundations (Monopile, Tripod, and Jacket) are investigated. These three configurations are analyzed using the RANSE solver which is carried out using ANSYS CFX for validating the corresponding results. The simulations are performed under the same environmental atmospheric wind shear and rotor angular velocity, and the wave properties are wave height of 4 m and wave period of 7.16 s. In the present work, wave environmental effects were investigated firstly for the two solvers, and good agreement is achieved. Moreover, pressure distribution in each OWT case is presented, including detailed information about local flow fields. The time history of the forces at inflow direction and its moments around the mudline at each OWT part are presented in a dimensionless form with respect to the mean value of the last three loads and the moment amplitudes obtained from the BEM code, where the contribution of rotor force is lower in the tripod case and higher in the jacket case and the calculated hydrodynamic load that effect on jacket foundation type is lower than other two cases.

Harten-Lax-van Leer-contact(HLLC)approximation Riemann solver with elastic waves for one-dimensional elastic-plastic problems

A Harten-Lax-van Leer-contact （HLLC） approximate Riemann solver is built with elastic waves （HLLCE） for one-dimensional elastic-plastic flows with a hypo- elastic constitutive model and the von Mises＇ yielding criterion. Based on the HLLCE, a third-order cell-centered Lagrangian scheme is built for one-dimensional elastic-plastic problems. A number of numerical experiments are carried out. The numerical results show that the proposed third-order scheme achieves the desired order of accuracy. The third-order scheme is used to the numerical solution of the problems with elastic shock waves and elastic rarefaction waves. The numerical results are compared with a reference solution and the results obtained by other authors. The comparison shows that the pre- sented high-order scheme is convergent, stable, and essentially non-oscillatory. Moreover, the HLLCE is more efficient than the two-rarefaction Riemann solver with elastic waves （TRRSE）

Application Progress of Computational Fluid Dynamic Techniques for Complex Viscous Flows in Ship and Ocean Engineering

Complex flow around floating structures is a highly nonlinear problem,and it is a typical feature in ship and ocean engineering.Traditional experimental methods and potential flow theory have limitations in predicting complex viscous flows.With the improvement of high-performance computing and the development of numerical techniques,computational fluid dynamics(CFD)has become increasingly powerful in predicting the complex viscous flow around floating structures.This paper reviews the recent progress in CFD techniques for numerical solutions of typical complex viscous flows in ship and ocean engineering.Applications to free-surface flows,breaking bow waves of high-speed ship,ship hull-propeller-rudder interaction,vortexinduced vibration of risers,vortex-induced motions of deep-draft platforms,and floating offshore wind turbines are discussed.Typical techniques,including volume of fluid for sharp interface,dynamic overset grid,detached eddy simulation,and fluid-structure coupling,are reviewed along with their applications.Some novel techniques,such as high-efficiency Cartesian grid method and GPU acceleration technique,are discussed in the last part as the future perspective for further enhancement of accuracy and efficiency for CFD simulations of complex flow in ship and ocean engineering.

A computational study on robust prediction of transition point over NACA0012 aerofoil surfaces from laminar to turbulent flows

Flow transition from laminar to turbulent is prerequisite to decide whereabouts to apply surface flow control techniques. This appears missing in a number of works in which the control effects were merely investigated without getting insight into alteration of transition position. The aim of this study is to capture the correct position of transition over NACA0012 aerofoil at different angles of attack. Firstly, an implicit, time marching, high resolution total variation diminishing （TVD） scheme was developed to solve the governing Navier-Stokes equations for compressible fluid flows around aerofoil sections to obtain velocity profiles around the aerofoil surfaces. Secondly, the linear instability solver based on the Orr-Sommerfeld equations and the eg methods were developed to calculate the onset of transition over the aerofoil surfaces. For the low subsonic Mach number of 0.16, the accuracy of the compressible solutions was assessed by some available experimental results of low speed incompressible flows. In all cases, transition positions were accurately predicted which shows applicability and superiority of the present work to be extended for higher Mach number compressible flows. Here, transition prediction methodology is described and the results of this analysis without active flow control or separation are presented.

DIFFERENCE SCHEME FOR TWO-PHASE FLOW

A numerical method for two-phase flow with hydrodynamics behavior was considered. The nonconservative hyperbolic governing equations proposed by Saurel and Gallout were adopted. Dissipative effects were neglected but they could be included in the model without major difficulties. Based on the opinion proposed by Abgrall that “a two phase system, uniform in velocity and pressure at t=0 will be uniform on the same variable during its temporal evolution", a simple accurate and fully Eulerian numerical method was presented for the simulation of multiphase compressible flows in hydrodynamic regime. The numerical method relies on Godunov-type scheme, with HLLC and Lax-Friedrichs type approximate Riemann solvers for the resolution of conservation equations, and nonconservative equation. Speed relaxation and pressure relaxation processes were introduced to account for the interaction between the phases. Test problem was presented in one space dimension which illustrated that our scheme is accurate, stable and oscillation free.

流体拓扑优化的方法及应用综述

流体拓扑优化是一项突破性技术,在航空航天、汽车、电子芯片等领域均有广泛的应用前景,然而其所设计出的复杂结构难以通过传统制造技术加工成型等因素制约了它的推广应用。增材制造(3D打印)技术的发展为进一步拓展流体拓扑优化的应用和研究提供了有效途径,对实现相关工业装备的结构轻量化、动力学优化、安全性优化以及性能提升,落实国家“节能降耗、碳达峰碳中和”战略具有重要意义。借助文献计量工具VOSviewer对Web of Science数据库中流体拓扑优化相关文献进行了梳理和总结,全面系统阐述了流体拓扑优化的理论体系、求解方法、优化方法以及工程应用,并对相关问题进行了探讨。首先,与固体拓扑优化相比,流体拓扑优化涉及领域更广、流态特征更多样、数学模型更复杂,因而求解更困难、计算时间更长、计算资源需求更大,这是制约流体拓扑优化工程应用的主要因素。其次,较系统阐述了流体拓扑优化的3个环节和关键技术:拓扑设计变量表述方法、CFD模型及求解方法、拓扑优化模型及求解方法,并分析了现有技术的特点和应用场景,同时,对流体拓扑优化的电子芯片热沉、飞机汽车、换热器等几个应用场景进行了简述。最后,对流体拓扑优化的发展趋势进行了预测和总结,建议进一步加大湍流、共轭传热、流-固-热耦合、流-固-热-质耦合等方面的多学科拓扑优化研究;拓展基于多目标函数的拓扑优化研究;进一步加强与人工智能的深度结合,开发更加稳健成熟的智能CFD求解器、智能优化求解器以及智能流体拓扑优化软件。

Modeling and Simulation of Real Gas Flow in a Pipeline

In this paper, a mathematical model that describes the flow of gas in a pipe is formulated. The model is simplified by making some assumptions. It is considered that the natural gas flowing in a long horizontal pipe, no heat source occurs inside the volume, transfer of heat due to heat conduction is dominated by heat exchange with the surrounding. The flow equations are coupled with equation of state. Different types of equations of state, ranging from the simple Ideal gas law to the more complex equation of state Benedict Webb Rubin Starling (BWRS), are considered. The flow equations are solved numerically using the Godunov scheme with Roe solver. Some numerical results are also presented.

基于自主开发求解器的蒸汽发生器二次侧流场分析

针对蒸汽发生器二次侧复杂流动传热现象,基于iconCFD开发了新的物理模型和求解器,采用多孔介质模型完成了对蒸汽发生器二次侧的流动和换热现象的数值模拟分析。计算模型中通过映射的方法实现了不同区域之间的数据的相互交换和更新,计算结果与ATHOS软件计算的结果相比对,通过比较一次侧出口温度、二次侧出口水蒸气质量流量和二次侧进口和出口处压力,此3项与ATHOS软件计算结果误差均小于1%,验证了新求解器的有效性和可靠性。

An Accurate and Scalable Direction-Splitting Solver for Flows Laden with Non-Spherical Rigid Bodies–Part 1:Fixed Rigid Bodies

Particle-resolved direct numerical flow solvers predominantly use a projection method to decouple the non-linear mass and momentum conservation equations.The computing performance of such solvers often decays beyond O(1000)cores due to the cost of solving at least one large three-dimensional pressure Poisson problem per time step.The parallelization may perform moderately well only or even poorly sometimes despite using an efficient algebraic multigrid preconditioner[38].We present an accurate and scalable solver using a direction splitting algorithm[12]to transform all three-dimensional parabolic/elliptic problems(and in particular the elliptic pressure Poisson problem)into a sequence of three one-dimensional parabolic sub-problems,thus improving its scalability up to multiple thousands of cores.We employ this algorithm to solve mass and momentum conservation equations in flows laden with fixed non-spherical rigid bodies.We consider the presence of rigid bodies on the(uniform or non-uniform)fixed Cartesian fluid grid by modifying the diffusion and divergence stencils on the impacted grid node near the rigid body boundary.Compared to[12],we use a higher-order interpolation scheme for the velocity field to maintain a secondorder stress estimation on the particle boundary,resulting in more accurate dimensionless coefficients such as drag C_(d)and lift C_(l).We also correct the interpolation scheme due to the presence of any nearby particle to maintain an acceptable accuracy,making the solver robust even when particles are densely packed in a sub-region of the computational domain.We present classical validation tests involving a single or multiple(up to O(1000))rigid bodies and assess the robustness,accuracy and computing speed of the solver.We further show that the Direction Splitting solver is∼5 times faster on 5120 cores than our solver[38]based on a classical projection method[5].

A Genuinely Two-Dimensional HLL-Type Approximate Riemann Solver for Hypo-Elastic Plastic Flow

In this work,a genuinely two-dimensional HLL-type approximate Riemann solver is proposed for hypo-elastic plastic flow.To consider the effects of wave interaction from both the x-and y-directions,a corresponding 2D elastic-plastic approximate solver is constructed with elastic-plastic transition embedded.The resultant numerical flux combines one-dimensional numerical flux in the central region of the cell edge and two-dimensional flux in the cell vertex region.The stress is updated separately by using the velocity obtained with the above approximate Riemann solver.Several numerical tests,including genuinely two-dimensional examples,are presented to test the performances of the proposed method.The numerical results demonstrate the credibility of the present 2D approximate Riemann solver.

利用规划求解拟合水位流量关系曲线探讨

控制条件稳定的测站水位流量关系也保持稳定,通常采用单一曲线法推求流量。利用Excel规划求解功能,建立指数函数模型,拟合水位流量关系曲线,通过检验分析,拟合结果满足水文资料整编规范要求。此方法易操作上手,能够提高工作效率和拟合精度,具有推广应用价值。