Stokes Plots

Problem 1

G₊ = G_- = 0 , u_-1 = u_h = -U = -2

Zeroth-Order Approximations
h = 1.0
Full-Color Stream Function (Psi) with Flow Field.   Figure 2^.
Full-Color Vorticity (Phi) with Flow Field .

h = 1.2
Full-Color Stream Function (Psi) with Flow Field.   Figure 3^.
Full-Color Vorticity (Phi) with Flow Field.

h = 3.0
Full-Color Stream Function (Psi) with Flow Field.   Figure 4^*.
Full-Color Vorticity (Phi) with Flow Field.

For the above examples, the splitter plate along the negative x-axis has a thickness of 2 delta where delta = 0.002.

Problem 2

u_-1 = u_h = -U = 0 , psi_-1 = 0.5 , psi_h = -0.5

Zeroth-Order Approximations
h = 1.2
Full-Color Stream Function (Psi) with Flow Field .
Full-Color Vorticity (Phi) with Flow Field.

h = 3.0
Full-Color Stream Function (Psi) with Flow Field.   Figure 6^.
Full-Color Vorticity (Phi) with Flow Field .
Zeroth-Order vs. First-Order Approximations
h = 3.0
Zeroth-Order Stream Function (Psi) level curves with Flow Field.   Figure 6^.
First-Order Stream Function (Psi) level curves with Flow Field.   Figure 7^*.

For the above examples, the splitter plate along the negative x-axis again has a thickness of 2 delta where delta = 0.002.

Wide Splitter Plate

Top Boundary Value of Phi: Vorticity (Phi) along y = h.

First-Order Approximation

h = 3.0

For the above examples, the splitter plate along the negative x-axis has a thickness of 2 delta where delta = 0.02.

Reference

^Figure numbering on this page refers to J. D. Fehribach & A. M. J. Davis, Stokes flow around an asymmetric channel divider; a computational appproach using MATLAB, Journal of Engineering Mathematics* 39 (2001) 207-220.

All plots presented here were created using MATLAB and PDEToolbox.

JDF (E-Mail: bach@wpi.edu)
Last Updated: Friday, 4 January 2002
Copyright 2000, 2002, Joseph D. Fehribach