High Order Finite Difference WENO Methods for Shallow Water Equations on Curvilinear Meshes

A high order finite difference numerical scheme is developed for the shallow water equations on curvilinear meshes based on an alternative flux formulation of the weighted essentially non-oscillatory(WENO)scheme.The exact C-property is investigated,and comparison with the standard finite difference WENO scheme is made.Theoretical derivation and numerical results show that the proposed finite difference WENO scheme can maintain the exact C-property on both stationarily and dynamically generalized coordinate systems.The Harten-Lax-van Leer type flux is developed on general curvilinear meshes in two dimensions and verified on a number of benchmark problems,indicating smaller errors compared with the Lax-Friedrichs solver.In addition,we propose a positivity-preserving limiter on stationary meshes such that the scheme can preserve the non-negativity of the water height without loss of mass conservation.

A Third Order Conservative Lagrangian Type Scheme on Curvilinear Meshes for the Compressible Euler Equations

Based on the high order essentially non-oscillatory(ENO)Lagrangian type scheme on quadrilateral meshes presented in our earlier work[3],in this paper we develop a third order conservative Lagrangian type scheme on curvilinear meshes for solving the Euler equations of compressible gas dynamics.The main purpose of this work is to demonstrate our claim in[3]that the accuracy degeneracy phenomenon observed for the high order Lagrangian type scheme is due to the error from the quadrilateral mesh with straight-line edges,which restricts the accuracy of the resulting scheme to at most second order.The accuracy test given in this paper shows that the third order Lagrangian type scheme can actually obtain uniformly third order accuracy even on distorted meshes by using curvilinear meshes.Numerical examples are also presented to verify the performance of the third order scheme on curvilinear meshes in terms of resolution for discontinuities and non-oscillatory properties.

Energy-Minimizing Curve Fitting for High-Order Surface Mesh Generation

We investigate different techniques for fitting Bézier curves to surfaces in context of high-order curvilinear mesh generation. Starting from distance-based least-squares fitting we develop an incremental algorithm, which incorporates approximations of stretch and bending energy. In the process, the algorithm reduces the energy weight in favor of accuracy, leading to an optimized set of sampling points. This energy-minimizing fitting strategy is applied to analytically defined as well as triangulated surfaces. The results confirm that the proposed method straightens and shortens the curves efficiently. Moreover the method preserves the accuracy and convergence behavior of distance-based fitting. Preliminary application to surface mesh generation shows a remarkable improvement of patch quality in high curvature regions.

Explicit structure-preserving geometric particle-in-cell algorithm in curvilinear orthogonal coordinate systems and its applications to whole-device 6D kinetic simulations of tokamak physics

Explicit structure-preserving geometric particle-in-cell(PIC)algorithm in curvilinear orthogonal coordinate systems is developed.The work reported represents a further development of the structure-preserving geometric PIC algorithm achieving the goal of practical applications in magnetic fusion research.The algorithm is constructed by discretizing the field theory for the system of charged particles and electromagnetic field using Whitney forms,discrete exterior calculus,and explicit non-canonical symplectic integration.In addition to the truncated infinitely dimensional symplectic structure,the algorithm preserves exactly many important physical symmetries and conservation laws,such as local energy conservation,gauge symmetry and the corresponding local charge conservation.As a result,the algorithm possesses the long-term accuracy and fidelity required for first-principles-based simulations of the multiscale tokamak physics.The algorithm has been implemented in the Sym PIC code,which is designed for highefficiency massively-parallel PIC simulations in modern clusters.The code has been applied to carry out whole-device 6 D kinetic simulation studies of tokamak physics.A self-consistent kinetic steady state for fusion plasma in the tokamak geometry is numerically found with a predominately diagonal and anisotropic pressure tensor.The state also admits a steady-state subsonic ion flow in the range of 10 km s-1,agreeing with experimental observations and analytical calculations Kinetic ballooning instability in the self-consistent kinetic steady state is simulated.It is shown that high-n ballooning modes have larger growth rates than low-n global modes,and in the nonlinear phase the modes saturate approximately in 5 ion transit times at the 2%level by the E×B flow generated by the instability.These results are consistent with early and recent electromagnetic gyrokinetic simulations.

三峡工程大江截流流场的数值模拟

通过数值求解二维浅水方程组，模拟三峡工程大江截流过程中的流场，可快速获得任一口门宽度下的全域流场信息，计算结果合理，可为截流方案和施工决策提供依据．

二维流场多媒体动态仿真系统的实现

本文介绍了应用微机开发的二维流场多媒体动态仿真系统．通过建立数学模型，运用计算机图形学与多媒体的理论和方法，采用面向对象的ＶｉｓｕａｌＣ＋＋语言，解决了流场转换、像素点旋转、流场的连续性及背景音乐及解说的同步性等问题，并对动态图像演示文件进行了压缩编码．仿真了不同方案下海河口的流场的运动，生动形象地展示了其运动的全过程．

利用二、三维嵌套技术数值模拟复杂边界下的流场

通过数值模拟复杂几何区域和边界条件下二、三维嵌套紊流模型，获得了计算区域内任意一点的流场信息。这一方法克服了常规的单纯模拟二维或三维紊流控制方程组而无法获得准确的自由表面和三维紊流场的缺点，通过两者有机的结合，并采用动边界处理等先进的计算技术，得出了精度更高、更为合理的紊流场。该方法曾被用于三峡工程大江截流完成之后导流明渠通航的流场模拟中，计算结果合理可信，部分成果的精度也已得到了实测资料的验证。

曲线齿轮的成型原理及啮合特性分析

尽管近几十年来齿轮的设计制造技术已经大大提高,但在实际应用中边缘接触、过载和侧隙等问题仍然存在。因此,研究性能更为优越的齿轮十分必要,作为一种新型齿轮,曲线齿轮不仅具有传统齿轮传动的特点,还具有很多优势:承载能力强、抗弯强度好等。对曲线齿轮的成型原理及啮合运动进行了研究分析,并借助UG GRIP语言实现了曲线齿轮理论模型的参数化造型,且分析得出了曲线齿轮副正确啮合的条件:Re≥Ri;进而为该齿轮的设计提供了必要的理论依据。

铸件凝固过程数值模拟的曲线网格差分法

铸件凝固过程的数值模拟过去大多数采用规划网格差分法和有限元法．当铸件与铸型的边界是不规划，网格剖分需要在铸件与铸型的交界处加密时，加上热传导方程的大多数参数在凝固过程中随时间而变化的，以前常用的规划网格差分法不够理想。

应用多重网格法生成正交曲线网格

本文从势流理论出发,建立生成正交曲线网格的控制方程,应用多重网格法的FAS-FMG格式求解离散后的控制方程,不仅提高了收敛速度,而且提高了正交曲线网格的生成质量。

非正交曲线坐标下三维弯曲河流湍流数学模型

本文在水平方向采用非正交曲线坐标,在垂直方向采用笛卡尔坐标系统,结合实际河床地形实行堵塞技术以实现对实际地形的模拟,在河床表面使用壁面函数法模拟河底阻力,在自由水面采用改进的“刚盖假定”方法,研究开发了非正交三维曲线坐标下的k-ε双方程湍流模型。通过实验室弯道对模型进行了验证,计算结果与实测值吻合较好,将模型应用于天然连续弯曲河流的流场计算,给出了4层流速矢量图和4个断面二次流矢量图。

基于全齿宽啮合的弧齿圆柱齿轮参数化设计及接触特性

为了揭示全齿宽啮合弧齿圆柱齿轮齿面间的真实接触情况,根据齿轮啮合原理,推导了基于全齿宽啮合的渐开线弧齿圆柱齿轮的精确齿面和过渡曲面方程,通过MATLAB软件编程计算出弧齿圆柱齿轮的凹齿面、凸齿面及过渡曲面的坐标点,将计算得到的点云导入三维实体建模软件,经过简单处理生成精确弧齿圆柱齿轮的三维实体模型。最后,通过数值解法计算了渐开线弧齿圆柱齿轮的真实啮合情况,并用可视化界面显示齿面接触曲线。结果表明该齿轮是关于齿轮中间截面对称的全齿宽啮合弧齿圆柱齿轮;轮齿在进入和退出啮合时是部分齿面接触。

曲线网格下基于粘声分离方法的流噪声计算

在曲线网格下基于粘声分离方法对流场中的静止圆柱同声波和涡波的相互作用进行研究.首先推导了曲线坐标系下、适用于水流噪声的粘声分离方法(viscous acoustic splitting method,VASM)控制方程,并采用7点色散关系保持(dispersion-relation preserving,DRP)格式和四阶时间差分格式进行计算.然后将静止流场中圆柱壁面对声波反射的计算结果同理论值进行比较,验证了计算方法模拟水中物体对声波散射的准确性.进而模拟了旋涡行走发声的特性,并分析了流速等对声场特性的影响.

NUMERICAL SOLUTION OF THE UNSTEADYINCOMPRESSIBLE NAVIER-STOKES EQUATIONS ON THECURVILINEAR HALF-STAGGERED MESHNUMERICAL SOLUTION OF THE UNSTEADYINCOMPRESSIBLE NAVIER-STOKES EQUATIONS ON THECURVILINEAR HALF-STAGGERED MESH

In this paper, the Crank-Nicholson + component-consistent pressure correction method for the numerical solution of the unsteady incompressible Navier-Stokes equation of [1] on the rectangular half-Staggered mesh has been extended to the curvilinear half-Staggered mesh. The discrete projection, both for the projection step in the solution procedure and for the related differential-algebraic equations, has been carefully studied and verified. It is proved that the proposed method is also unconditionally (in t) nonlinearly stable on the curvilinear mesh, provided the mesh is not too skewed. It is seen that for problems with an outflow boundary, the half-Staggered mesh is especially advantageous. Results of preliminary numerical experiments support these claims.

面向制造的圆弧齿线圆柱齿轮建模及特性分析

齿轮是现代工业中最重要的传递动力的机械零件之一,开发受力状况良好的新型结构一直是这一领域的研究前沿。圆弧齿线圆柱齿轮是一种新型传动机构,首先阐述了其成型原理,在坐标变换和空间啮合理论的基础上,推导其齿面方程。运用UG/grip语言,开发了符合实际加工过程的圆弧齿线圆柱齿轮的自动生成程序,实现了圆弧齿线圆柱齿轮理论模型的参数化造型,且分析得出了圆弧齿线圆柱齿轮副正确啮合的条件。

NUMERICAL SOLUTION FOR UNSTEADY 2－D FLOW USING THE TRANSFORMED SHALLOW WATER EQUATIONS

This paper is concerned with the numerical solution of two-dimensional flow.The technique of boundary-fitted coordinate systems is used to overcome the difficulties resulting from the complicated shape of natural river boundaries; the method of fractional steps is used to solve the partial differential equations in the transformed plane; and the technique of moving boundary is used to deal with the river bed exposed to water surface. Comparison between computed and experimental data shows a satisfactory agreement.

弧齿圆柱齿轮两种加工方法工艺分析

以弧齿圆柱齿轮的两种加工方法的工艺过程为研究对象,对两种加工方法的工艺特点和优缺点进行了对比分析。同时,以加工原理为基础,采用三维建模软件按照实际加工过程对两种齿轮的加工进行模拟,得到了两种工艺下弧齿圆柱齿轮的三维模型。使用三维建模软件分别对两种弧齿圆柱齿轮进行啮合分析和干涉分析。分析结果表明,旋转刀盘法加工弧齿圆柱齿轮的工艺性能要比平行连杆法好,特别是可以进行磨齿、剃齿等精加工工艺。因此,采用旋转刀盘法加工弧齿圆柱齿轮更适用于工业推广应用。本文中的研究对弧齿圆弧齿轮的设计和选用有一定的参考作用。

Multiderivative Combined Dissipative Compact Scheme Satisfying Geometric Conservation Law III: Characteristic-Wise Hybrid Method

Based on newly developed weight-based smoothness detectors and non-linear interpolations designed to capture discontinuities for the multiderivative com-bined dissipative compact scheme(MDCS),hybrid linear and nonlinear interpolations are proposed to form hybrid MDCS.These detectors are derived from the weights used for the nonlinear interpolations and can provide suitable switches between the linear and the nonlinear schemes to realize the characteristics for the hybrid MDCS of capturing discontinuities and maintaining high resolution in the region without large discontinuities.To save computational cost,the nonlinear scheme with characteris-tic decomposition is only applied in the detected discontinuities region by specially designed hybrid strategy.Typical tests show that the hybrid MDCS is capable of cap-turing discontinuities and maintaining high resolution power for the smooth region at the same time.With the satisfaction of the geometric conservative law(GCL),the MDCS is further applied on curvilinear mesh to present its promising capability of handling pragmatic simulations.