Symmetry groups and similarity solutions for the system of equations for a viscous compressible fluid

被引：14

作者：

Pandey, Manoj ^{[1
]}

Pandey, B. D. ^{[2
]}

Sharma, V. D. ^{[1
]}

机构：

[1] Indian Inst Technol, Dept Math, Bombay 400076, Maharashtra, India

[2] Ohio State Univ, Dept Math, Marion, OH 43302 USA

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2009年 / 215卷 / 02期

关键词：

Similarity solutions; Lie group analysis; Viscous compressible fluids; Exact solutions; LIE GROUP-ANALYSIS; SUBSTITUTION PRINCIPLES; STRONG SHOCKS; GAS;

D O I：

10.1016/j.amc.2009.05.070

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Here, using Lie group transformations, we consider the problem of finding similarity solutions to the system of partial differential equations (PDEs) governing one-dimensional unsteady motion of a compressible fluid in the presence of viscosity and thermal conduction, using the general form of the equation of state. The symmetry groups admitted by the governing system of PDEs are obtained, and the complete Lie algebra of infinitesimal symmetries is established. Indeed, with the use of the entailed similarity solution the problem is transformed to a system of ordinary differential equations(ODEs), which in general is nonlinear; in some cases, it is possible to solve these ODEs to determine some special exact solutions. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：681 / 685

页数：5

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