A VARIATIONAL FINITE ELEMENT METHOD FOR THREE-DIMENSIONAL, STEADY, COMPRESSIBLE, VISCOUS FLOWS
Abstract
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.
Degree
Ph.D.
Subject Area
Mechanical engineering
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