An Approximate Analytical Solution of Imploding Strong Shocks in a Non-Ideal Gas through Lie Group Analysis

• Published in: Chinese physics letters Vol. 27; no. 1; pp. 178 - 181
• Main Authors: Singh, L. P, Husain, Akmal, Singh, M
• Format: Journal Article
• Language: English
• Published: IOP Publishing 2010
• Subjects: Approximation; Differential equations; Group theory; Lie groups; Mathematical analysis; Partial differential equations; Similarity; Transformations; 偏微分方程系统; 变换方法; 完备李代数; 常微分方程系统; 群分析; 近似解析解; 非理想
• ISSN: 0256-307X; 1741-3540
• DOI: 10.1088/0256-307X/27/1/014702

The method of Lie group transformation is used to obtain an approximate analytical solution to the system of first-order quasilinear partial differential equations that govern a one-dimensional unsteady planer, cylindrically symmetric and spherically symmetric motion in a non-ideal gas, involving strong shock waves. Invariance groups admitted by the governing system of partial differential equations, which are indeed continuous group of transformations under which the system of partial differential equations remains invariant, are determined, and the complete Lie algebra of infinitesimal symmetries is established. The infinitesimal generators are used to construct the similarity variables. These similarity variables are used to reduce the governing system of partial differential equations into a system of ordinary differential equations.