A treatment of wall boundaries for the finite element analysis of turbulent flows
Abstract
A method for connecting momentum equations with the universal law of the wall is developed using the finite element method for turbulent wall flows. This method is based on the rotation of the coordinates at every node near the wall inclined obliquely to the coordinate direction. By examining the weak form of momentum equations, the surface integral matching the universal law of the wall is induced. The discrete momentum equations are solved by the NewtonRaphson method. As the vector of the surface integral is a function of the velocity component parallel to the wall, the Jacobian coefficient matrix of the surface integral can be included in that of momentum equations. This method is applied to steady state problems and a good convergence is obtained. For timedependent problems, velocity is explicitly integrated with time.
 Publication:

IN: Numerical methods in laminar and turbulent flow; Proceedings of the Fourth International Conference
 Pub Date:
 1985
 Bibcode:
 1985nmlt.proc..418T
 Keywords:

 Computational Fluid Dynamics;
 Finite Element Method;
 Incompressible Flow;
 Turbulent Flow;
 Wall Flow;
 Boundary Value Problems;
 Continuity Equation;
 Convergence;
 Kinetic Equations;
 NewtonRaphson Method;
 Steady State;
 Time Dependence;
 Velocity Distribution;
 Fluid Mechanics and Heat Transfer