Considerations on existence and uniqueness in numerical inverse design
Abstract
The present paper is concerned with the design of configurations, such as airfoils, cascades of airfoils, and ducts. It is assumed that the gas is perfect and inviscid, while the flow is steady. A number of crucial questions arise in connection with the design, taking into account the existence of a solution to the problem as posed, the consistence of the design technique with the mathematical model of the flow, the asymptotic convergence for a numerical iterative technique, and the characteristics of the asymptotic results. The problem is considered for the case in which the flow is incompressible and irrotational, giving attention to thin airfoil theory and cascades of airfoils. Other cases discussed are related to compressible flow design, the numerical influence from boundaries, the numerical nonexistence of certain transonic flows, cascade design with lift and thickness distributions prescribed, and nonuniqueness.
- Publication:
-
Communications in Applied Numerical Methods
- Pub Date:
- February 1986
- Bibcode:
- 1986CANM....2...11M
- Keywords:
-
- Airfoils;
- Computational Fluid Dynamics;
- Existence Theorems;
- Incompressible Flow;
- Uniqueness Theorem;
- Cascade Flow;
- Compressible Flow;
- Inviscid Flow;
- Mathematical Models;
- Steady Flow;
- Transonic Flow;
- Fluid Mechanics and Heat Transfer