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| 一维守恒的Lagrangian ADER格式 | |
| 引用本文： | 程军波,Eleuterio F. Toro. 一维守恒的Lagrangian ADER格式[J]. 计算物理, 2013, 30(4): 501-508 |
| 作者姓名： | 程军波 Eleuterio F. Toro |
| 作者单位： | 1. 北京应用物理与计算数学研究所, 北京 100094;2. Laboratory of Applied Mathematics Trento University, Trento, Italy |
| 基金项目： | 国家自然科学基金(11172050);中国工程物理研究院科学发展基金重点基金(2009A0202014)资助项目 |
| 摘 要： | 基于欧拉框架下ADER格式,构造一维守恒只有一个时间步的、高精度中心型拉格朗日ADER(LADER)格式.构造r阶LADER格式包括:从欧拉方程出发推导拉格朗日框架下积分形式的方程、采用WENO方法高精度重构节点处守恒量和从1阶到r-1阶的空间导数、求拉氏框架下这些变量的Godunov值,并计算1阶到r-1阶的时间全导数,最后高精度离散积分形式的流通量函数.对光滑流场的模拟表明,LADER格式达到设计的精度;对含强间断的流场模拟表明,数值解在间断附近基本无振荡. |
| 关 键 词： | 中心型拉格朗日格式 任意高精度格式 时空高精度 |
| 收稿时间： | 2012-09-11 |
| 修稿时间： | 2013-03-13 |
A 1D Conservative Lagrangian ADER Scheme |
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| CHENG Junbo,Eleuterio F. Toro. A 1D Conservative Lagrangian ADER Scheme[J]. Chinese Journal of Computational Physics, 2013, 30(4): 501-508 | |
| Authors: | CHENG Junbo Eleuterio F. Toro |
| Affiliation: | 1. Institute of Applied Physics and Computational Mathematics, Beijing 100094, China;2. Laboratory of Applied Mathematics, University of Trento, Trento, Italy |
| Abstract: | Based on Eulerian ADER scheme,we build a 1D,one-step,conservative,high-order accurate,Lagrangian ADER(LADER) scheme.Main procedures of r-th order LADER scheme include:Deducing integral form of the equations in Lagrangian framework from Euler equations,using WENO reconstruction method to reconstruct conserved variables and their spatial derivatives up to (r-1)-th order on interface of mesh with high-order accuracy,evaluating Godunov values of conserved variables and their space derivatives in Lagrangian framework,computing time material derivatives of conserved variables,approximating time-integral average of physical flux function with high-order accuracy at last.Simulation of smooth regions shows that LADER scheme achieves desired accuracy and examples of discontinuous regions show the scheme is essentially non-oscillatory near discontinuities. |
| Keywords: | centered Lagrangian scheme ADER scheme high-order accuracy in space and time |
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