Applications of variational principles in computing rotational flows
Abstract
Ecer and Akay (1983) have developed a variational formulation of rotational flow for Euler equations. The present paper provides a summary of these developments. The considered variational formulation provides a transformation of a type considered by Clebsch (1859). In this transformation, a new set of variables replaces the more commonly used primitive variables u(i), rho and p. Here, u(i) denotes the velocity components, while rho is the density, and p the pressure. The employed transformation produces a natural uncoupling of the equations when written in a quasi-linear form. After obtaining the governing equations in terms of the 'Clebsch variables', a solution scheme developed for calculating steady flows is discussed. Attention is given to numerical solutions of Euler equations based on the derived variational principles, and a study of inviscid, separated flows is conducted.
- Publication:
-
IN: Advances in computational transonics (A86-20926 08-02). Swansea
- Pub Date:
- 1985
- Bibcode:
- 1985act..book..777E
- Keywords:
-
- Flow Characteristics;
- Inviscid Flow;
- Rotating Fluids;
- Separated Flow;
- Transonic Flow;
- Variational Principles;
- Channel Flow;
- Corner Flow;
- Differential Equations;
- Euler Equations Of Motion;
- Lagrange Multipliers;
- Steady Flow;
- Unsteady Flow;
- Fluid Mechanics and Heat Transfer