Variational finite-element method for three-dimensional, steady, compressible, viscous flows
A variational formulation is developed for three-dimensional steady, compressible, and viscous flows starting with the Hamilton's principle. The Clebsch transformation of the velocity vector and a set of governing equations in terms of Lagrangian multipliers and entropy are derived. It is shown that these equations are equivalent to the Navier-Stokes equations written in terms of the velocity vector, pressure, and density. The finite-element approximation and a relaxation scheme are employed to obtain the steady-state solution of these equations. This formulation provides a unified-solution scheme for potential, Euler, and Navier-Stokes equations. Developing channel flow is analyzed and compared with available theoretical results. Compressible viscous flow through a convergent channel is also investigated.
- Research Organization:
- Purdue Univ., Lafayette, IN (USA)
- OSTI ID:
- 6697933
- Country of Publication:
- United States
- Language:
- English
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