期刊文献+
共找到7篇文章
< 1 >
每页显示 20 50 100
HERMITE WENO SCHEMES WITH LAX-WENDROFF TYPE TIME DISCRETIZATIONS FOR HAMILTON-JACOBI EQUATIONS 被引量:3
1
作者 Jianxian Qiu 《Journal of Computational Mathematics》 SCIE EI CSCD 2007年第2期131-144,共14页
In this paper, we use Hermite weighted essentially non-oscillatory (HWENO) schemes with a Lax-Wendroff time discretization procedure, termed HWENO-LW schemes, to solve Hamilton-Jacobi equations. The idea of the reco... In this paper, we use Hermite weighted essentially non-oscillatory (HWENO) schemes with a Lax-Wendroff time discretization procedure, termed HWENO-LW schemes, to solve Hamilton-Jacobi equations. The idea of the reconstruction in the HWENO schemes comes from the original WENO schemes, however both the function and its first derivative values are evolved in time and are used in the reconstruction. One major advantage of HWENO schemes is its compactness in the reconstruction. We explore the possibility in avoiding the nonlinear weights for part of the procedure, hence reducing the cost but still maintaining non-oscillatory properties for problems with strong discontinuous derivative. As a result, comparing with HWENO with Runge-Kutta time discretizations schemes (HWENO-RK) of Qiu and Shu [19] for Hamilton-Jacobi equations, the major advantages of HWENO-LW schemes are their saving of computational cost and their compactness in the reconstruction. Extensive numerical experiments are performed to illustrate the capability of the method. 展开更多
关键词 weno scheme Hermite interpolation Hamilton-Jacobi equation Lax-Wendroff type time discretization High order accuracy.
原文传递
Simulations of Shallow Water Equations by Finite Difference WENO Schemes with Multilevel Time Discretization
2
作者 Changna Lu Gang Li 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2011年第4期505-524,共20页
In this paper we study a class of multilevel high order time discretization procedures for the finite difference weighted essential non-oscillatory(WENO)schemes to solve the one-dimensional and two-dimensional shallow... In this paper we study a class of multilevel high order time discretization procedures for the finite difference weighted essential non-oscillatory(WENO)schemes to solve the one-dimensional and two-dimensional shallow water equations with source terms.Multilevel time discretization methods can make full use of computed information by WENO spatial discretization and save CPU cost by holding the former computational values.Extensive simulations are performed,which indicate that,the finite difference WENO schemes with multilevel time discretization can achieve higher accuracy,and are more cost effective than WENO scheme with Runge-Kutta time discretization,while still maintaining nonoscillatory properties. 展开更多
关键词 Multilevel time discretization weighted essentially non-oscillatory schemes shallow water equations runge-kutta method high order accuracy
原文传递
一种基于WENO格式的一维溃坝水流数值模拟研究 被引量:2
3
作者 樊新建 张卫勇 张人会 《河南科学》 2008年第8期952-954,共3页
采用一维Saint-Venant方程组,应用WENO格式和Runge-Kutta时间离散的思想,进行溃坝水流的数值模拟,得出了水位和流速的沿程分布,并与理论解比较,发现数值解在间断波附近没有出现数值振荡,水位和流速数值解与理论解吻合较好,表明WENO格式... 采用一维Saint-Venant方程组,应用WENO格式和Runge-Kutta时间离散的思想,进行溃坝水流的数值模拟,得出了水位和流速的沿程分布,并与理论解比较,发现数值解在间断波附近没有出现数值振荡,水位和流速数值解与理论解吻合较好,表明WENO格式是一种进行溃坝水流模拟的非常理想的差分格式. 展开更多
关键词 weno格式 Runge.Kutta时间离散 数值计算 溃坝
下载PDF
A NUMERICAL STUDY FOR THE PERFORMANCE OF THE WENO SCHEMES BASED ON DIFFERENT NUMERICAL FLUXES FOR THE SHALLOW WATER EQUATIONS 被引量:2
4
作者 Changna Lu Jianxian Qiu Ruyun Wang 《Journal of Computational Mathematics》 SCIE CSCD 2010年第6期807-825,共19页
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 equ... 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 展开更多
关键词 Numerical flux weno finite volume scheme Shallow water equations High order accuracy Approximate Riemann solver runge-kutta time discretization.
原文传递
基于加权本质无振荡格式的二维溃坝水流数值模拟 被引量:13
5
作者 魏文礼 郭永涛 《水利学报》 EI CSCD 北大核心 2007年第5期596-600,共5页
将加权本质无振荡WENO(Weighted essentially non-oscillatory)格式和Runge-Kutta时间离散的思想应用于二维浅水控制方程的求解中,建立了模拟大坝瞬间全溃或局部溃倒所致的洪水演进过程的数学模型。应用该模型对一维矩形明渠中大坝瞬间... 将加权本质无振荡WENO(Weighted essentially non-oscillatory)格式和Runge-Kutta时间离散的思想应用于二维浅水控制方程的求解中,建立了模拟大坝瞬间全溃或局部溃倒所致的洪水演进过程的数学模型。应用该模型对一维矩形明渠中大坝瞬间全溃所致的水流运动进行了数值计算,并与理论解进行了比较,证实了方法的可靠性。最后用该模型预测了矩形河道中大坝瞬间局部溃倒时的洪水演进过程,模拟结果与实际相符。算例表明采用WENO格式所建立的高分辨率溃坝模型能够很好地模拟溃坝波的演进过程。 展开更多
关键词 weno格式 溃坝 数值模拟
下载PDF
A class of the fourth order finite volume Hermite weighted essentially non-oscillatory schemes 被引量:7
6
作者 ZHU Jun QIU JianXian 《Science China Mathematics》 SCIE 2008年第8期1549-1560,共12页
In this paper,we developed a class of the fourth order accurate finite volume Hermite weighted essentially non-oscillatory(HWENO)schemes based on the work(Computers&Fluids,34:642-663(2005))by Qiu and Shu,with Tota... In this paper,we developed a class of the fourth order accurate finite volume Hermite weighted essentially non-oscillatory(HWENO)schemes based on the work(Computers&Fluids,34:642-663(2005))by Qiu and Shu,with Total Variation Diminishing Runge-Kutta time discretization method for the two-dimensional hyperbolic conservation laws.The key idea of HWENO is to evolve both with the solution and its derivative,which allows for using Hermite interpolation in the reconstruction phase,resulting in a more compact stencil at the expense of the additional work.The main difference between this work and the formal one is the procedure to reconstruct the derivative terms.Comparing with the original HWENO schemes of Qiu and Shu,one major advantage of new HWENOschemes is its robust in computation of problem with strong shocks.Extensive numerical experiments are performed to illustrate the capability of the method. 展开更多
关键词 finite volume Hweno scheme conservation laws Hermite polynomial TVD runge-kutta time discretization method 65M06 65M99 35L65
原文传递
Development and Comparison of Numerical Fluxes for LWDG Methods
7
作者 Jianxian Qiu 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2008年第4期435-459,共25页
The discontinuous Galerkin (DO) or local discontinuous Galerkin (LDG) method is a spatial discretization procedure for convection-diffusion equations, which employs useful features from high resolution finite volu... The discontinuous Galerkin (DO) or local discontinuous Galerkin (LDG) method is a spatial discretization procedure for convection-diffusion equations, which employs useful features from high resolution finite volume schemes, such as the exact or approximate Riemann solvers serving as numerical fluxes and limiters. The Lax- Wendroff time discretization procedure is an altemative method for time discretization to the popular total variation diminishing (TVD) Runge-Kutta time discretizations. In this paper, we develop fluxes for the method of DG with Lax-Wendroff time discretization procedure (LWDG) based on different numerical fluxes for finite volume or finite difference schemes, including the first-order monotone fluxes such as the Lax-Friedfichs flux, Godunov flux, the Engquist-Osher flux etc. and the second-order TVD fluxes. We systematically investigate the performance of the LWDG methods based on these different numerical fluxes for convection terms with the objective of obtaining better performance by choosing suitable numerical fluxes. The detailed numerical study is mainly performed for the one-dimensional system case, addressing the issues of CPU cost, accuracy, non-oscillatory property, and resolution of discontinuities. Numerical tests are also performed for two dimensional systems. 展开更多
关键词 Discontinuous Galerkin method Lax-Wendroff type time discretization numerical flux approximate Riemann solver timiter weno scheme high order accuracy.
下载PDF
上一页 1 下一页 到第
使用帮助 返回顶部