New Grid Approach for Solution of Boundary Problems for Convection-Diffusion Equations

被引：0
|
作者：
Polyakov, Sergey V. [1 ,2 ]
Karamzin, Yuri N. [1 ]
Kudryashova, Tatiana A. [1 ,2 ]
Podryga, Viktoriia O. [1 ,2 ]
机构：
[1] Keldysh Inst Appl Math, 4 Miusskaya Sq, Moscow 125047, Russia
[2] Natl Res Nucl Univ MEPhI, 31 Kashirskoe Sh, Moscow 115409, Russia
来源：
NUMERICAL ANALYSIS AND ITS APPLICATIONS (NAA 2016) | 2017年 / 10187卷
关键词：
Convection-diffusion equation (CDE); Integral transformation; Finite-difference schemes; Non-monotonic sweep procedure;
D O I：
10.1007/978-3-319-57099-0_62
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
The numerical solution of boundary value problems is considered for multidimensional equations of convection-diffusion (CDE). These equations are used for many physical processes in solids, liquids and gases. A new approach to the spatial approximation for such equations is proposed. This approach is based on the integral transformation of second order differential operators. A linear version of CDE was selected to simplify analysis. For this variant, a new exponential finite difference scheme was offered, algorithms of its implementation were developed, and brief analysis of the stability and convergence was fulfilled.
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页码：550 / 558
页数：9
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