Self-adjoint formulation of spherically symmetric hydrodynamics
A useful extension of the self-dual formulation of one-dimensional gasdynamics to spherically symmetric compressible flow in N dimensions and to axisymmetric swirling flow is presented. A significant feature of this formulation is the fact that it is integrable in closed form. This makes it especially useful for the purpose of comparison with results from numerical calculations. The influence of the equation of state is discussed with respect to the symmetry \((T^*)\). The result corresponds to \textit{L. V. Ovsiannikov}'s analysis who pointed out the existence of such a transformation [Group analysis of differential equations (1982; Zbl 0485.58002)]. For self-similar problems the new formulation of the ordinary differential equations is very compact and leads to an algebraic general integral. This treatment of the Euler equations is suited for the investigation of conservation laws.
spherical symmetry self-similar solution
scientific article; zbMATH DE number 4012193