Group‐invariant solutions and optimal systems for multidimensional hydrodynamics
| Autor: | J. Meyer‐ter‐Vehn, S.V. Coggeshall |
|---|---|
| Rok vydání: | 1992 |
| Předmět: |
Stochastic partial differential equation
Nonlinear system Method of characteristics Differential equation Collocation method Mathematical analysis Statistical and Nonlinear Physics Differential algebraic equation Mathematical Physics Separable partial differential equation Mathematics Numerical partial differential equations |
| Zdroj: | Journal of Mathematical Physics. 33:3585-3601 |
| ISSN: | 1089-7658 0022-2488 |
| DOI: | 10.1063/1.529907 |
| Popis: | The group properties of the three‐dimensional (3‐D), one‐temperature hydrodynamic equations, including nonlinear conduction and a thermal source, are presented. A subgroup corresponding to axisymmetric geometry is chosen, and the details of the construction of the one‐ and two‐dimensional optimal systems are shown. The two‐dimensional optimal system is used to generate 23 intrinsically different reductions of the 2‐D partial differential equations to ordinary differential equations. These ordinary differential equations can be solved to provide analytic solutions to the original partial differential equations. Two example analytic solutions are presented: a 2‐D axisymmetric flow with a P2 asymmetry and a 3‐D spiraling flow. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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