二维高阶CIP数值方法及其应用

核聚变与等离子体物理 ›› 2012, Vol. 32 ›› Issue (2): 109-116.

二维高阶CIP数值方法及其应用

朱廷儒，彭晓东，王刚，赵小明，唐昌建

(1. 四川大学，成都 610064；2. 核工业西南物理研究院，成都 610041；3. 四川工商职业技术学院，成都 611837)

收稿日期:2011-09-26 修回日期:2012-03-05 出版日期:2012-06-15 发布日期:2011-06-14
作者简介:朱廷儒(1983-)，男，河南新乡人，硕士研究生，从事等离子体电子学与数值模拟研究。
基金资助:
国家磁约束核聚变研究专项资助项目(2009GB105002，2010GB106006)

Two dimensional high-order CIP numerical method and applications

ZHU Ting-ru, PENG Xiao-dong, WANG Gang, ZHAO Xiao-ming, TANG Chang-jian

(1. Sichuan University, Chengdu 610064; 2. Southwestern Institute of Physics, Chengdu 610041; 3. Sichuan Technology and Business College, Chengdu 611837)

Received:2011-09-26 Revised:2012-03-05 Online:2012-06-15 Published:2011-06-14

摘要/Abstract

摘要：

利用函数及其高阶导数值构造五次插值函数近似网格单元内的真实解，改进数值求解双曲类偏微分方程的CIP数值算法。基于之前的一维高阶CIP数值算法思想，不同于利用时间分裂技术，发展了二维高阶CIP数值算法。改进后的算法具有五阶数值精度和显示格式的优点。

关键词: CIP数值方法, 高阶插值, 磁流体

Abstract:

Employing a function and its derivatives to construct a fifth-order interpolation function to approximate to the real solution in a cell, we have improved the CIP (Constrained Interpolation Profile) numerical algorithm. A direct two-dimensional high-order CIP method differing from adopting a time-splitting technology has been developed on the basis of the previous one-dimensional case. The improved method is an explicit scheme with the fifth-order accuracy.

Key words: CIP numerical algorithm, High-order interpolation, MHD

中图分类号:

TL61+2.3

朱廷儒，彭晓东，王刚，赵小明，唐昌建. 二维高阶CIP数值方法及其应用[J]. 核聚变与等离子体物理, 2012, 32(2): 109-116.

ZHU Ting-ru, PENG Xiao-dong, WANG Gang, ZHAO Xiao-ming, TANG Chang-jian. Two dimensional high-order CIP numerical method and applications[J]. NUCLEAR FUSION AND PLASMA PHYSICS, 2012, 32(2): 109-116.

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