Investigation of solution of NavierStokes equations using a variational formulation
Abstract
Use of a variational form to obtain a numerical solution to the NavierStokes equations for viscous, incompressible flows is presented. A variational functional is defined in four variables for the incompressibility condition and a kinematic relationship in the vorticity transport equation. A Lagrangian is formulated and the variational functional is shown to satisfy specific boundary conditions which involve bilinear, fournoded isoparametric elements. The flow boundary conditions become natural boundary conditions and a fully coupled system is defined for solution of the equations. Examples are given of applications for turbulent flow in terms of twodimensional symmetric flow around a cylinder and flow through a stepped channel. Laminar flows with Re numbers 25, 73, and 229, and turbulent flows at an Re of 3025 were examined. Results for velocity profiles are provided, and it is shown that calculations of the length of the separation zone are in good agreement with dye tracer and laser anemometer measurements.
 Publication:

Numerical Methods in Laminar and Turbulent Flow
 Pub Date:
 1981
 Bibcode:
 1981nmlt.proc...91R
 Keywords:

 Incompressible Flow;
 NavierStokes Equation;
 Two Dimensional Flow;
 Variational Principles;
 Viscous Flow;
 Boundary Conditions;
 Boundary Value Problems;
 Channel Flow;
 Computational Fluid Dynamics;
 Cylindrical Bodies;
 Flow Deflection;
 Flow Velocity;
 Laminar Flow;
 Turbulent Flow;
 Velocity Distribution;
 Vorticity Transport Hypothesis;
 Fluid Mechanics and Heat Transfer