| 求解渗流问题的高精度差分格式 |
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| 引用本文： | 李金轩,罗细雅,徐卫东.求解渗流问题的高精度差分格式[J].煤田地质与勘探,2003,31(5):30-32. |
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| 作者姓名： | 李金轩 罗细雅 徐卫东 |
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| 作者单位： | 1. 东华理工学院,江西,抚州,344000
2. 江西省交通设计院,江西,南昌,330002 |
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| 摘 要： | 在求解渗流问题的传统差分格式中，只有Crank-Nicolson格式具有对时间t的二阶精度。本文在导数超收敛点概念的基础上，提出一种求解渗流问题的三阶精度差分格式，并将其与显式差分格式叠加形成组合差分格式以改善格式的稳定、收敛条件。算例计算结果表明，该组合格式具有精度高，稳定收敛限制宽松，易于编程等优点。
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| 关 键 词： | 渗流 差分格式 精度 稳定条件 收敛条件 |
| 文章编号： | 1001-1986(2003)05-0030-03 |
| 修稿时间： | 2003年2月13日 |
High accuracy difference scheme for seepage problem |
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| LI Jin xuan ,LUO Xi ya ,XU Wei dong.High accuracy difference scheme for seepage problem[J].Coal Geology & Exploration,2003,31(5):30-32. |
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| Authors: | LI Jin xuan LUO Xi ya XU Wei dong |
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| Institution: | LI Jin xuan 1,LUO Xi ya 2,XU Wei dong 1 |
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| Abstract: | Among the classical difference schemes for seepage,the Crank Nicolson scheme is only of 2 order accuracy on it.Based on the concept of ultraconvergence point of derivative,a new difference scheme,which is of 3 order accuracy in t,is propssed in this paper.For the purpose to improve the stable,convergence condition,the composite difference scheme based on linear superposition of 3 order accuracy scheme and explicit scheme is also proposed.Results of calculation example show that the advantages of the composite difference scheme are high accuracy,loose limitation of stability and convergence,easy programming and so on. |
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| Keywords: | seepage difference scheme accuracy stable condition convergence condition |
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