Algorithm 731: A moving-grid interface for systems of one-dimensional time-dependent partial differential equations
Algorithm 731: A moving-grid interface for systems of one-dimensional time-dependent partial differential equations
复制标题
算法 731：一维时变偏微分方程组的移动网格接口
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
P. Zegeling
中科院分区：
文献类型：
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作者：
J. Blom;P. Zegeling
在过去的十年中，已经开发了一些数值技术来解决一维时间相关偏微分方程（PDE）在空间和时间上具有陡峭梯度的解决方案。这些技术之一，移动网格方法的基础上的拉格朗日描述的PDE和平滑的均匀分布的原则，以定义在每个时间级别的网格位置，已被耦合的空间离散化方法，自动离散化的空间部分的用户定义的PDE以下的方法线的方法。我们提供了两个FORTRAN子程序，CWRESU和CWRESX，计算残差的微分代数方程（DAE）系统得到半离散，分别是PDE和移动网格方程组。这些例程组合在一个包络例程SKMRES中，该例程提供完整DAE系统的残差。为了求解这种刚性的非线性DAE系统，必须应用鲁棒且有效的时间积分器，例如，在DAE求解器SPRINT [Berzins和Furzeland 1985; 1986; Berzins等人1989]和DASSL [Brenan等人1989; Petzold 1983]中实现的BDF方法。一些数值例子来说明这个软件接口的简单和有效的使用。
In the last decade, several numerical techniques have been developed to solve time-dependent partial differential equations (PDEs) in one dimension having solutions with steep gradients in space and in time. One of these techniques, a moving-grid method based on a Lagrangian description of the PDE and a smoothed-equidistribution principle to define the grid positions at each time level, has been coupled with a spatial discretization method that automatically discreizes the spatial part of the user-defined PDE following the method of lines approach. We supply two FORTRAN subroutines, CWRESU and CWRESX, which compute the residuals of the differential algebraic equations (DAE) system obtained from semidiscretizing, respectively, the PDE and the set of moving-grid equations. These routines are combined in an enveloping routine SKMRES, which delivers the residuals of the complete DAE system. To solve this stiff, nonlinear DAE system, a robust and efficient time-integrator must be applied, for example, a BDF method such as implemented in the DAE solvers SPRINT [Berzins and Furzeland 1985; 1986; Berzins et al. 1989] and DASSL [Brenan et al. 1989; Petzold 1983]. Some numerical examples are shown to illustrate the simple and effective use of this software interface.