A kind of extended Korteweg——de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system

This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters: the nonlinearity ratio $\varepsilon $, represented by the ratio of amplitude to depth, and the dispersion ratio $\mu $, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin {\it et al} in the study of the surface waves when considering the order up to $O(\mu ^2)$. As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin {\it et al} for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.     

温盐双扩散均衡场中的振荡现象

在一种简单的边界加密的坐标变换下,用高精度的差分法研究了温盐双扩散系统.为了保证求解的稳定性和精确性,对流项采用了四阶精度的迎风格式,扩散项和涡量方程的浮力项则采用四阶精度的中心差.首先针对温度占优(Rρ=032)和盐度占优(Rρ=168)的情形进行了计算,得到了与文献[2]和[12]一致的结果,从而验证方法的正确性.其次系统地给出了不同Lewis数下的流动形态,包括稳定的对称结构、周期性振荡结构和非周期非对称的随机运动形态 关键词： 温盐双扩散 高精度格式 周期性振荡结构     

非定常对流扩散方程的高精度多重网格方法

由已有的求解定常对流扩散方程的高阶紧致差分格式出发,直接推导出了数值求解非定常对流扩散方程的一种高阶隐式紧致差分格式,其时间为二阶精度,空间为四阶精度,并且是无条件稳定的。为了加快传统迭代法在求解隐格式时在每一个时间步上的迭代收敛速度,采用了多重网格加速技术。数值实验结果验证了本文方法的高阶精度、高效性及高稳定性。     

三维定常问题的高阶紧致差分格式向非定常问题的推广

将已经建立的求解三维定常对流扩散方程的高阶紧致差分格式直接推广到三维非定常对流扩散方程的数值求解,时间导数项利用二阶向后欧拉差分公式,所得到的高阶隐式紧致差分格式时间为二阶精度,空间为四阶精度,并且是无条件稳定的.数值实验结果验证了本文方法的精确性和稳健性.     

Numerical simulation of core convection by a multi-layer semi-implicit spherical spectral method

A semi-implicit multi-layer spherical spectral method for simulating stellar core convection is described. The fully compressible three-dimensional hydrodynamic equations with rotation and energy generation are solved. Prognostic variables are expressed as finite sums of spherical harmonics in the horizontal directions and handled by the finite difference method in the radial direction. The stratified approximation is used to simplify the nonlinearity to quadratic. A multi-layer scheme is employed to overcome the time step problem arising from shrinking grid sizes in the physical space near the center of the star. Despite of the different spectral truncations in different layers, round-off conservation of the total mass and total angular momentum of the whole domain can be maintained, and were confirmed numerically. The code is parallelized; with 12 processors the speedup factor is about 9. The solutions of model core convection with and without rotation are discussed.     

Numerical study on the gas-kinetic high-order schemes for solving Boltzmann model equation

The high-order compact finite difference technique is introduced to solve the Boltzmann model equation, and the gas-kinetic high-order schemes are developed to simulate the different kinetic model equations such as the BGK model, the Shakhov model and the Ellipsoidal Statistical (ES) model in this paper. The methods are tested for the one-dimensional unsteady shock-tube problems with various Knudsen numbers, the inner flows of normal shock wave for different Mach numbers, and the two-dimensional flows past ...     

An improved two-dimensional unstructured CE/SE scheme for capturing shock waves

In this paper, the accuracy of Chang’s unstructured space–time conservation element and solution element (CE/SE) scheme is analysed for the first time. Based on a redefinition of conservation elements and solution elements, an improved two-dimensional (2D) unstructured CE/SE scheme with an adjustable parameter β is proposed to accurately capture shock waves. The new scheme can be applied to any type of grid without special treatment. Compared with Chang’s original parameter α, larger β dose not cost extra computational resources. Numerical tests reveal that the new scheme is not only clear in physical concept, compact and highly accurate but also more capable of capturing shock waves than the popular fifth-order accurate weighted essentially non-oscillatory scheme.     

引射系统排气装置的数值模拟

为削弱引射系统尾气对光传输的影响,依据将尾气排放到光传输区域以外的设计思路,运用数值模拟的方法,对引射系统排气管道内的流场特性及尾气射流影响区域开展了研究。通过对直管道以及弯管道内流场特性的数值分析和比较,给出了一种排气管道的结构设计方式。在给定系统出口速度的情况下,运用多组分输运模型,分别对无自然风和有侧向自然风状态下的尾气影响范围进行了分析,初步确定了尾气射流排出系统后的影响区域,并依据尾气影响区域,对管道长度及布置方式进行了研究。     

引射系统排气装置的数值模拟

为削弱引射系统尾气对光传输的影响,依据将尾气排放到光传输区域以外的设计思路,运用数值模拟的方法,对引射系统排气管道内的流场特性及尾气射流影响区域开展了研究。通过对直管道以及弯管道内流场特性的数值分析和比较,给出了一种排气管道的结构设计方式。在给定系统出口速度的情况下,运用多组分输运模型,分别对无自然风和有侧向自然风状态下的尾气影响范围进行了分析,初步确定了尾气射流排出系统后的影响区域,并依据尾气影响区域,对管道长度及布置方式进行了研究。     

新型动态多光学目标模拟装置研究

介绍了多光学系统观测平台的检测方法现状,列举了现有检测用光电靶标的局限性。叙述了动态光学靶标的功能原理,提出一种新的检测设备,即双光源动态光电目标模拟装置的设计方案。并对其进行了理论分析和可行性论证。着重对坐标变换过程进行了演算,证明基准转换的正确性。结合理论基础和现有的工程设计经验,论述了该新型双光源动态光电目标模拟装置的工程化设计方案。最后对该设计方案的最终精度进行了分析,验证了该设计方案可以满足多光学系统观测平台的综合检测和标定需求。     

一维多介质可压缩流动数值方法

应用高精度界面追踪方法计算一般状态方程的多介质可压缩流动问题;应用LevelSet技术捕捉界面位置,在界面附近采用守恒数值离散,用双波近似求解一般状态方程Riemann问题,并采用统一高阶PPM格式进行内点和交界面点的计算.一维算例表明,该方法对于光滑区域以及多介质交界面具有二阶精度,能准确地模拟交界面的位置,交界面计算无数值振荡和数值耗散,并能处理一般状态方程的多介质可压缩流动问题.