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Entropy convergence of new two-value scheme with slope relaxation for conservation laws

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Applied Mathematics and Mechanics(English Edition) 2016年第11期37卷 1551-1570页

作者： Yue WANG jiequan li Institute of Applied Physics and Computational Mathematics Beijing 100094China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100094China

This paper establishes the resolution finite volume scheme with slope entropy convergence of a new two-value high relaxation for conservation laws. This scheme, motivated by the general method of high resolution schemes that have high-order accuracy in smooth regions of solutions and are free of oscillations near discontinuities, unifies and evolves slopes directly with a slope relaxation equation that governs the evolution of slopes in both smooth and discontinuous regions. Proper choices of slopes are realized adaptively via a relaxation parameter. The scheme is shown to be total-variation-bounded （TVB） stable and satisfies cell-entropy inequalities.

关键词： conservation law slope relaxation two-value scheme

Regularity of Fluxes in Nonlinear Hyperbolic Balance Laws

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Communications on Applied Mathematics and Computation 2023年第3期5卷 1289-1298页

作者： Matania Ben-Artzi jiequan li Institute of Mathematics Hebrew University of Jerusalem91904 JerusalemIsrael Academy of Multidisciplinary Studies Capital Normal UniversityBeijing 100048China State Key Laboratory for Turbulence Research and Complex System Peking UniversityBeijing 100871China

This paper addresses the issue of the formulation of weak solutions to systems of nonlinear hyperbolic conservation laws as integral balance *** basic idea is that the“meaningful objects”are the fluxes,evaluated across domain boundaries over time *** fundamental result in this treatment is the regularity of the flux trace in the multi-dimensional *** implies that a weak solution indeed satisfies the balance *** fact,it is shown that the flux is lipschitz continuous with respect to suitable perturbations of the *** should be emphasized that the weak solutions considered here need not be entropy ***,the assumption imposed on the flux f(u)is quite minimal-just that it is locally bounded.

关键词： Balance laws Hyperbolic conservation laws Multi-dimensional Discontinuous solutions Finite-volume schemes Flux Trace on boundary

Two-stage fourth order: temporal-spatial coupling in computational fluid dynamics (CFD)

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Advances in Aerodynamics 2019年第1期1卷 39-74页

作者： jiequan li Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijingPeople’s Republic of China Center for Applied Physics and Technology Peking UniversityBeijingPeople’s Republic of China

With increasing engineering demands,there need high order accurate schemes embedded with precise physical information in order to capture delicate small scale structures and strong waves with correct“physics”.There are two families of high order methods:One is the method of line,relying on the Runge-Kutta(R-K)*** building block is the Riemann solution labeled as the solution element“1”.Each step in R-K just has first order *** order to derive a fourth order accuracy scheme in time,one needs four stages labeled as“1111=4”.The other is the one-stage Lax-Wendroff(LW)type method,which is more compact but is complicated to design numerical fluxes and hard to use when applied to highly nonlinear *** recent years,the pair of solution element and dynamics element,labeled as“2”,are taken as the building *** direct adoption of the dynamics implies the inherent temporal-spatial *** this type of building blocks,a family of two-stage fourth order accurate schemes,labeled as“22=4”,are designed for the computation of compressible fluid *** resulting schemes are compact,robust and *** paper contributes to elucidate how and why high order accurate schemes should be so *** some extent,the“22=4”algorithm extracts the advantages of the method of line and one-stage LW *** a core part,the pair“2”is expounded and LW solver is *** generalized Riemann problem(GRP)solver,as the discontinuous and nonlinear version of LW flow solver,and the gas kinetic scheme(GKS)solver,the microscopic LW solver,are all *** compact Hermite-type data reconstruction and high order approximation of boundary conditions are ***,the computational performance and prospective discussions are presented.

关键词： Compressible fluid dynamics Hyperbolic balance laws High order methods Temporal-spatial coupling Multi-stage two-derivative methods Lax-Wendroff type flow solvers GRP solver

Accuracy of the Adaptive GRP Scheme and the Simulation of 2-D Riemann Problems for Compressible Euler Equations

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Communications in Computational Physics 2011年第8期10卷 577-606页

作者： Ee Han jiequan li Huazhong Tang IAN Department of MathematicsMagdeburg UniversityD-39106Germany School of Mathematical Science Beijing Normal UniversityBeijing 100875China CAPT and LMAM School of Mathematical SciencesPeking UniversityBeijing 100871China

The adaptive generalized Riemann problem(GRP)scheme for 2-D compressible fluid flows has been proposed in[***.,229(2010),1448–1466]and it displays the capability in overcoming difficulties such as the start-up error for a single shock,and the numerical instability of the almost stationary *** this paper,we will provide the accuracy study and particularly show the performance in simulating 2-D complex wave configurations formulated with the 2-D Riemann problems for compressible Euler *** this purpose,we will first review the GRP scheme briefly when combined with the adaptive moving mesh technique and consider the accuracy of the adaptive GRP scheme via the comparison with the explicit formulae of analytic solutions of planar rarefaction waves,planar shock waves,the collapse problem of a wedge-shaped dam and the spiral formation *** we simulate the full set of wave configurations in the 2-D four-wave Riemann problems for compressible Euler equations[SIAM ***.,21(1990),593–630],including the interactions of strong shocks(shock reflections),vortex-vortex and shock-vortex *** study combines the theoretical results with the numerical simulations,and thus demonstrates what Ami Harten observed"for computational scientists there are two kinds of truth:the truth that you prove,and the truth you see when you compute"[***.,31(2007),185–193].

关键词： Adaptive GRP scheme 2-D Riemann problems collapse of a wedge-shaped dam spiral formation shock reflections vortex-shock interaction

Remapping-Free Adaptive GRP Method for Multi-Fluid Flows I:One Dimensional Euler Equations

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Communications in Computational Physics 2014年第4期15卷 1029-1044页

作者： Jin Qi Yue Wang jiequan li School of Mathematical Sciences Beijing Normal UniversityBeijing 100875China Institute of Applied Physics and Computational Mathematics Beijing 100094China

In this paper,a remapping-free adaptive GRP method for one dimensional(1-D)compressible flows is *** on the framework of finite volume method,the 1-D Euler equations are discretized on moving volumes and the resulting numerical fluxes are computed directly by the GRP *** the remapping process in the earlier adaptive GRP algorithm[17,18]is *** adopting a flexible moving mesh strategy,this method could be applied for multi-fluid *** interface of two fluids will be kept at the node of computational grids and the GRP solver is extended at the material interfaces of multi-fluid flows *** typical numerical tests show competitive performances of the new method,especially for contact discontinuities of one fluid cases and the material interface tracking of multi-fluid cases.

关键词： The GRP method multi-fluid flows the Euler equations the adaptive mesh method

Preface to the Focused Issue in Honor of Professor Tong Zhang on the Occasion of His 90th Birthday

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Communications on Applied Mathematics and Computation 2023年第3期5卷 965-966页

作者： jiequan li Wancheng Sheng Chi-Wang Shu Ping Zhang Yuxi Zheng Academy of Multidisciplinary Studies Capital Normal UniversityBeijing 100048China Department of Mathematics Shanghai UniversityShanghai 200444China Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA Institute of Mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Department of Mathematics The Pennsylvania State UniversityUniversity ParkPA 16802USA

December 9,2022 is the 90th birthday of Tong Zhang,a mathematician in Institute of Mathematics,Chinese Academy of Sciences where he was always working on the Riemann problem for gas dynamics in his mathematical *** celebrate his 90th birthday and great contributions to this specifc feld,we organize this focused issue in the journal Communications on Applied Mathematics and Computation,since the Riemann problem has been proven to be a building block in all felds of theory,numerics and applications of hyperbolic conservation laws.

关键词： Riemann hyperbolic Focus

计算流体力学的时空观:模型的时空关联性及算法的时空耦合性

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空气动力学学报 2021年第1期39卷 92-110页

作者：李杰权北京应用物理与计算数学研究所计算物理重点实验室北京100088 北京大学应用物理与技术中心北京100871

流体力学中波的有限传播、粒子的碰撞、各种力之间相互作用,无不体现时空关联效应。本文从计算方法的视角探讨计算流体力学的时空观,即流体力学模型的时空关联性和计算方法的时空耦合性。从流体力学微团法建模出发,明确模型时空关联性... 详细信息

流体力学中波的有限传播、粒子的碰撞、各种力之间相互作用,无不体现时空关联效应。本文从计算方法的视角探讨计算流体力学的时空观,即流体力学模型的时空关联性和计算方法的时空耦合性。从流体力学微团法建模出发,明确模型时空关联性的涵义,建立有限体积格式的基本原理,阐述算法时空耦合的必要性,实现流体力学基本控制方程物理建模与有限体积格式数学原理的统一。在实践中,给出时空耦合高精度数值方法设计思路,利用算例比较它与时空解耦方法的差别。期望通过时空观的建立,对未来计算流体力学的算法研究提供帮助。

关键词：计算流体力学时空关联模型时空耦合算法积分平衡律有限体积方法时间区间通量广义黎曼问题解法器

A high order discontinuous Galerkin scheme based on the GRP method for compressible Euler equations

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A high order discontinuous Galerkin scheme based on the GRP ...

2016海峡两岸流体力学研讨会

作者： Yue Wang jiequan li Zhifang Du Institute of Applied Physics and Computational Mathematics School of Mathematical Science Beijing Normal University

In this paper,the GRP method is introduced into the DG framework in order to obtain a high order DG scheme both in time and *** the so-called GRP-DG scheme have second order time accuracy without the Runge-Kutta metho...

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地震作用下裂缝高切坡稳定性极限上限分析

工程勘察 2019年第2期47卷 21-25,30页

作者：李结全广西瑞宇建筑科技有限公司南宁530031 广西大学土木建筑工程学院南宁530004

本文基于极限上限分析法与拟静力法,考虑了高切坡中裂缝的存在,建立了地震荷载作用下高切坡稳定性二维计算模型。通过算例计算,对不同参数影响下边坡安全系数的变化规律进行了研究。研究结果表明:随着水平地震荷载的增大,安全系数显著减... 详细信息

本文基于极限上限分析法与拟静力法,考虑了高切坡中裂缝的存在,建立了地震荷载作用下高切坡稳定性二维计算模型。通过算例计算,对不同参数影响下边坡安全系数的变化规律进行了研究。研究结果表明:随着水平地震荷载的增大,安全系数显著减小;当水平地震荷载保持不变时,地震效应比例系数的变化对安全系数的影响并不显著;随着开挖处与坡脚距离的增大,安全系数逐渐减小,但随着水平地震荷载的增大,这一影响逐渐减弱;开挖处与坡脚距离不变时,开挖角度越小,安全系数越小;随着坡角的增大,裂缝对高切坡稳定性的不利影响逐渐增大。

关键词：高切坡裂缝地震极限分析拟静力法安全系数