THE ONE-DIMENSIONAL UNSTEADY DIFFERENTIAL EQUATION OF THE MGD POTENTIAL FLOW AS A VARIATIONAL PROBLEM.
Abstract
A method is given which allows to determine an approximate closed solution of a certain non-linear second order differential equation. The method is suited for treating non-linear (propagation of a finite pressure jump) and nonseparable problems. A variational functional to the one-dimensional unsteady potential equation of the ideal MGD (magneto gas dynamics) was given for general values of mu, as a function of the local velocity of sound. This functional was expressed as a function of the velocity potential phi for the mu -values 3/2 and 2. The variation-integral was evaluated numerically by means of the Ritz method. A modified Kantorovitsch method can be applied in order to obtain higher accuracy since this method allows to determine a continuous function instead of discrete constants c sub mu nu. The numerical labor is rather less with this method. There are, however, no results on this method. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 10, 1966
- Accession Number
- AD0637724
Entities
People
- Franz Herrnegger
Organizations
- University of Innsbruck