chapter  7
10 Pages

Convection-diffusion problems with no slip boundary conditions

Fig. 7.3. Separating velocity profile v(x ,y ) = (y^( 1 - y)^,0) for (3 > 1

In this chapter we examine model problems with these three kinds of degen­ erate boundary layers in their solutions. We show that a monotone numerical method based on a standard upwind finite difference operator and a piecewiseuniform fitted mesh is £-uniform for a typical problem from a wide problem class. We also show, through numerical experiments, that it is essential to use the correct expression for the width of the boundary layer in the construction of the mesh. Problems with these three kinds of degenerate parabolic boundary

Fig. 7.4. Turbulent velocity profile v(x,?/) = (y(3( 1 — y )13,0) for (3 < 1

layers are included in the following problem class, which also contains more gen­ eral degenerate parabolic boundary layers on the walls Tb and Tt corresponding to the velocity profiles \ (x ,y ) — (2 /^ (1 — 2/)^2 , 0 ).