论文标题:一类非结构三角形网格有限体积方法及其收敛性
A Class of Finite Volume Method on Unstructured Triangular Meshes and Its Convergence
论文作者
论文导师 宋松和,论文学位 硕士,论文专业 计算数学
论文单位 国防科学技术大学,点击次数 2159,论文页数 57页File Size5282k
2004-10-01论文网 http://www.lw23.com/lunwen_26597/
Hyperbolic conservation laws; Finite volume method of unstructured meshes; TVD-type
用有限差分方法来数值求解双曲型守恒律方程已取得了很大的成就,特别是近年来TVD、ENO等有限差分格式的出现。有限差分方法要求计算区域比较规则,而且人们往往是对一维方程构造差分格式,再用分裂方法将其推广到多维。随着工程上问题的复杂化,计算区域也变得更加复杂,这对数值方法提出了新的挑战。目前对双曲型守恒律方程,非结构网格有限体积方法的研究成为计算流体力学领域中主要的研究方向之一,该方法对计算区域的形状没有限制。我们考虑双曲型守恒律方程,对二维非结构三角形网格有限体积方法做了如下工作: 本文中我们对二维标量双曲型守恒律方程,提出了一类满足极值原理的有限体积方法。其主要思想是以一阶单调格式作为基础格式,利用单调线性恢复函数在每个单元内进行线性恢复,使得格式既具有(弱)二阶精度,又保证数值在间断附近无震荡,此类格式是TVD型的。最后我们进行了收敛性的分析,数值结果表明此类格式具有较好的分辨率。
The finite difference methods, specially TVD and ENO schemes, for hyperbolic conservation laws are very successful. But the finite difference methods require that computational domain is regular, and usually people construct the difference scheme for one dimension and then extend it to two or three dimensions in a dimension by dimension fashion. Due to the engineering problem and computational domain become more complicated and more complicated, the finite volume method on unstructured meshes for hyperbolic conservation laws is playing an important role in computational fluid dynamics, this method has no restriction for computational domain. The following work has been done in the thesis:In the presend paper , we constract a class of finite volume method statisfying the maximum principle for two dimensions scalar hyperbolic conservation law. The key idea of the new method is based upon first order monotone scheme and upon linear reconstrution with monotone limiting in every mesh, the resulting method is TVD-type and has second order accuracy. Analysis of convergence has been given.
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