The Treatment of the Sonic Line and of Shocks in a Finite Element Approach to Transonic Flow Computations.
Abstract
Even if one uses the same shape functions throughout in a finite element computation of transonic flow fields, one must, for reasons of stability, apply the weights differently in the subsonic and supersonic regions. In the present report this aspect is accepted without further discussion. It is necessary, in addition, to impose special conditions at the sonic line and at the line where one returns from supersonic to subsonic speeds. These conditions are first explored by means of a semidiscretization. (The differential operators are discretized with respect to the direction normal to the streamlines, but not with respect to the streamline direction.) The resulting system of ordinary differential equations has singular points, whose position is related to the transition from one regime to the other. These singularities are compatible with weak solutions of the problems. (Finite difference and finite element solutions are realizations of the concept of weak equality.) But from the physical point of view these singularities are not admissible, at least not in the transition from a subsonic to a supersonic speed. One thus obtains the requirements that at the sonic line the partial differential equation be satisfied in the strong sense.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1980
- Accession Number
- ADA087740
Entities
People
- Karl G. Guderley
Organizations
- University of Dayton