激波和单列水柱、气水固多界面相互作用的数值模拟

研究可压缩多介质流场的激波和多介质界面相互作用问题.在Descartes固定网格采用level-set方法追踪界面,气/气界面边界条件处理采用OGFM方法,采用修正的rGFM方法提高气/水和气/固界面处构造Riemann问题精度,将Riemann近似解得到的界面参数外推到两侧真实和虚拟流体,采用五阶WENO方法求解流场Euler方程和界面level-set方程,给出不同时刻流场数值纹影图像.结果表明：在可压缩流场嵌入固体和水、气体等目标,本文方法可较精确地分辨平面运动激波和单列水柱及包含气/气、气/水和气/固等界面作用后产生的复杂激波结构.和传统的分区与贴体变换方法不同,为Descartes网格包含多介质界面复杂流场计算提供新途径.     

改进的三阶WENO-Z+格式及其应用

为改善三阶WENO格式的耗散特性,提高其对流场结构的分辨率,在三阶WENO-Z+格式（WENO-Z+3）基础上,构造不同形式的全局光滑因子,提出一种改进的WENO-Z+3格式（NWENO-Z+3）.选取Sod激波管、双爆轰波碰撞、激波与熵波相互作用、双马赫反射等经典算例,考察该格式的计算性能,结果表明：NWENO-Z+3格式具有更低耗散性和更高的分辨率.数值研究柱形高压气体爆炸波在单舱室和连通舱室内部的传播过程及波系演化.结果表明：改进格式NWENO-Z+3能够较好地模拟包含高压比、高密度比的爆炸波系结构.     

界面捕捉Level Set方法的(AMR)数值模拟

在流体力学方程的计算中采用高精度WENO格式,用AMR(adaptive mesh refinement)方法提高流场局部分辨率,在采用Level Set函数标定物质界面的计算中用GFM(ghost fluid method)方法进行界面处理,尝试将AMR技术与界面追踪技术相互融合并应用于数值模拟,对不同的模拟结果进行了比较.     

LWDG Method for a Multi-Class Traffic Flow Model on an Inhomogeneous Highway

In this paper, we apply the discontinuous Galerkin method with Lax-Wendroff type time discretizations (LWDG) using the weighted essentially non-oscillatory (WENO) limiter to solve a multi-class traffic flow model for an inhomogeneous highway, which is a kind of hyperbolic conservation law with spatially varying fluxes. The numerical scheme is based on a modified equivalent system which is written as a "standard" hyperbolic conservation form. Numerical experiments for both the Riemann problem and the traffic signal control problem are presented to show the effectiveness of these methods.     

Assessment of WENO-extended two-fluid modelling in compressible multiphase flows

The two-fluid modelling based on an advection-upwind-splitting-method (AUSM)-family numerical flux function, AUSM⁺-up, following the work by Chang and Liou [Journal of Computational Physics 2007;225: 840–873], has been successfully extended to the fifth order by weighted-essentially-non-oscillatory (WENO) schemes. Then its performance is surveyed in several numerical tests. The results showed a desired performance in one-dimensional benchmark test problems: Without relying upon an anti-diffusion device, the higher-order two-fluid method captures the phase interface within a fewer grid points than the conventional second-order method, as well as a rarefaction wave and a very weak shock. At a high pressure ratio (e.g. 1,000), the interpolated variables appeared to affect the performance: the conservative-variable-based characteristic-wise WENO interpolation showed less sharper but more robust representations of the shocks and expansions than the primitive-variable-based counterpart did. In two-dimensional shock/droplet test case, however, only the primitive-variable-based WENO with a huge void fraction realised a stable computation.     

基于WENO重构的熵稳定格式求解浅水方程

针对浅水方程,提出一种数值求解格式:空间方向采用满足熵稳定条件的数值通量,并在单元交界面处进行高阶WENO重构,时间上的推进采用强稳定的Runge-Kutta方法.模拟一维和二维经典问题,结果表明,该格式具有分辨率高、基本无振荡性等特点.     

求解双曲守恒律方程的三阶修正模板WENO格式北大核心CSCD

为了降低经典的三阶加权本质无振荡(WENO)格式的数值耗散,提出了一种新的三阶WENO格式的修正模板近似方法.改进了经典WENO-JS格式中各候选模板上数值通量的一阶多项式逼近,通过加入二次项使模板逼近达到三阶精度.计算了相应的候选通量,并且通过引入可调函数φ(x),使得新的格式具有ENO性质.最后给出了一系列数值算例,证明了该方法的有效性.     

无粘可压缩流动的改进高精度方法

为更准确捕捉复杂流场的流动细节,通过对WENO格式的光滑因子进行改进,发展了一种新的五阶WENO格式。对三阶ENO格式进行加权可以得到五阶WENO格式,但是不同的加权处理,WENO格式在极值处保持加权基本无振荡的效果不同,本文构造了二阶精度的局部光滑因子,及不含一阶二阶导数的高阶全局光滑因子,从而实现WENO格式在极值处有五阶精度。基于改进五阶WENO格式,对一维对流方程、一维和二维可压缩无粘问题进行算例验证,并与传统WENO-JS格式和WENO-Z格式进行比较。计算结果表明,改进五阶WENO格式有较高的精度和收敛速度,有较低的数值耗散,能有效捕捉间断、激波和涡等复杂流动。     

A high performance fifth-order multistep WENO scheme

Many efforts have been made to improve the accuracy of the conventional weighted essentially nonoscillatory (WENO) scheme at transition points (connecting a smooth region and a discontinuity point). This paper analyzes these works and further develops a more effective multistep WENO scheme. Theoretical analysis and numerical results show that the new scheme not only improves the accuracy by one order higher than the traditional fifth-order WENO schemes at transition point but also maintains the fifth-order accuracy in smooth regions even at critical point where the first derivative vanishes.     

A NUMERICAL STUDY FOR THE PERFORMANCE OF THE WENO SCHEMES BASED ON DIFFERENT NUMERICAL FLUXES FOR THE SHALLOW WATER EQUATIONS

In this paper we investigate the performance of the weighted essential non-oscillatory （WENO） methods based on different numerical fluxes, with the objective of obtaining better performance for the shallow water equations by choosing suitable numerical fluxes. We consider six numerical fluxes, i.e., Lax-Friedrichs, local Lax-Friedrichs, Engquist-Osher, Harten-Lax-van Leer, HLLC and the first-order centered fluxes, with the WENO finite volume method and TVD Runge-Kutta time discretization for the shallow water equations. The detailed numerical study is performed for both one-dimensional and two-dimensional shallow water equations by addressing the property, and resolution of discontinuities. issues of CPU cost, accuracy, non-oscillatory