《应用数学与计算数学学报》2018年32卷2期：173-189
基于简化三维模型的浅溪混合流动扩散数值研究
NADOLIN K A
(俄罗斯南联邦大学数学、力学和计算机科学系, 罗斯托夫 344090, 俄罗斯)
摘要 考虑求解一个特殊初始边界值问题的数值方法. 在所提方法中，将Galerkin方法和有限差分方法进行了结合，并采用了双曲偏微分方程系统的特征线网格.所解决的偏微分方程是一个长而浅的河道中被动混合流动过程的数学模型，该模型是二维的，但是一个三维的过程. 采用显式的或者隐式的有限差分方法都可以完成计算过程，也可以采用并行计算实现其计算过程.
关键词 河床水流；被动流动；简化模型；数值模型；Galerkin方法；特征线网格；有限差分方法
Numerical study of the admixture in a very shallow stream
on the basis of the reduced 3D model
NADOLIN K A
(Department of Mathematics, Mechanics and Computer Science, Southern Federal University, Rostov-on-Don 344090, Russia)
Abstract：A numerical method for solving one special initial-boundary value problem is presented. The algorithm of this numerical method combines the Galerkin approach and the finite-difference scheme, which uses a grid of characteristic lines for a hyperbolic system of partial differential equations. The problem for partial differential equations, which is solved, is a mathematical model of the process of passive admixture transport in a long and very shallow channel flow. The model is actually two-dimensional, but takes into account the three-dimensionality of the process. The computational procedure is well adapted to the problem under consideration and is fairly simple to use for both explicit and implicit finite difference schemes. It is also promising for implementation on parallel computers.
Key words：river bed-stream flow; passive mass-transport; reduced model; numerical modeling; Galerkin method; characteristic-lines grid; finite difference scheme
全文链接：http://www.camc.shu.edu.cn/CN/abstract/abstract9416.shtml