A variational finite element method for compressible NavierStokes flows
Abstract
A variational method is developed for analyzing threedimensional steady, compressible and viscous flowfield starting with the energy formulation. A Clebsch transformation of the velocity vector and a set of governing equations in terms of Lagrangian multipliers and entropy are derived. This mathematical model is equivalent to the classic full NavierStokes equations in terms of primitive variables. It provided a unified solution scheme for potential, Euler and NavierStokes flow equations if different levels of flow simplification are made. The isoparametric finite element approximation and a relaxation solution scheme are employed to obtain the solutions at steadystate in an uncoupled sequence. A computer code is developed and verified by comparing the computed solutions with the available theoretical results of developing entrance channel flow. A convergent channel flow problem is also investigated.
 Publication:

Recent Advances in Computational Fluid Dynamics
 Pub Date:
 1989
 Bibcode:
 1989racf.proc..263S
 Keywords:

 Compressible Flow;
 Computational Fluid Dynamics;
 Finite Element Method;
 NavierStokes Equation;
 Three Dimensional Flow;
 Variational Principles;
 Entropy;
 Euler Equations Of Motion;
 Lagrange Multipliers;
 Steady Flow;
 Viscous Flow;
 Fluid Mechanics and Heat Transfer