Finite volume implementation of the method of asymptotic partial domain decomposition for the heat equation on a thin structure

被引：0
作者：
G. Panasenko
M. -C. Viallon
机构：
[1] Université de Lyon,Institut Camille Jordan, UMR CNRS 5208, Faculté des Sciences et Techniques
来源：
Russian Journal of Mathematical Physics | 2015年 / 22卷
关键词：
Mathematical Physic; Asymptotic Expansion; Control Volume; Heat Equation; Finite Volume Method;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The unsteady heat equation is considered in thin structures. The asymptotic expansion of the solution constructed earlier is used to evaluate partial derivatives of the solution. The method of partial asymptotic domain decomposition is applied to the unsteady heat equation. It reduces the original 2D model to a hybrid dimension one, partially 2D, partially 1D with some special interface conditions between the 2D and 1D parts. The finite volume method is applied to numerically solve the hybrid dimension model. The error estimate is established. A numerical experiment confirms the theoretical error evaluation.
引用
收藏
页码：237 / 263
页数：26
相关论文
共 23 条
[1]  
Agmon S(1959)Estimates near the Boundary for Solutions of Elliptic Partial Differential Equations Satisfying General Boundary Conditions. I,II Comm. Pure Appl. Math. 12 623-723
[2]  
Douglis A(1982)On the Asymptotic Behaviour at Infinity of Solutions in Linear Elasticity Arch. Ration. Mech. Anal. 78 29-53
[3]  
Nirenberg L(1998)Method of Asymptotic Partial Decomposition of Domain Math. Models Methods Appl. Sci. 8 139-156
[4]  
Oleinik O A(2008)The Finite Volume Implementation of the Partial Asymptotic Domain Decomposition Appl. Anal. 87 1397-1424
[5]  
Yosifian G A(2013)Error Estimate in the Finite Volume Approximation of the Partial Asymptotic Domain Decomposition Math. Methods Appl. Sci. 36 1892-1917
[6]  
Panasenko G P(2005)A Finite Volume Method for the Laplace Equation on Almost Arbitrary Two-Dimensional Grids M2AN Math. Model. Numer. Anal. 39 1203-1249
[7]  
Panasenko G P(2007)FEM Implementation for the Asymptotic Partial Decomposition Appl. Anal. 86 519-536
[8]  
Viallon M-C(1992)Asymptotic Solutions of the Elasticity Theory System of Equations for Lattice and Skeletal Structures Math. Sb. 183 89-113
[9]  
Panasenko G P(2000)Method of Asymptotic Partial Decomposition of Rod Structures Internat. J. Comput., Civil Struct. Engrg. (Begel House Publ.) 1 57-70
[10]  
Viallon M-C(2000)Asymptotic Expansion of the Solution of Navier-Stokes Equation in Tube Structure and Partial Asymptotic Decomposition of the Domain Appl. Anal. Internat. J. 76 363-381
123