2.58 One of the problems in fluid dynamics is determining pressure in narrow and non-narrow regions through which fluid flows. It is a function of several parameters, including boundary conditions on mass and momentum flux. Stay and Barocas (Int’l J. for Numerical Methods in Fluids, 2003) demonstrated a localized reduction technique called “stitching” for solving such hydrodynamic problems. They compared peak pressure in a region calculated using the coupled Stokes-Raynolds model with the analytic solution. The difference between the analytic solution and the peak pressure calculated with the coupled Stokes-Raynolds model (i.e., error in pressure)
and the CPU solution time for the coupled Stokes-Raynolds model are recorded in table below for different stitch lengths. Note that error measures the solution error or accuracy of solution by the coupled Stokes-Raynolds method and the CPU time indicates efficiency of the coupled Stokes-Raynolds method.

a Make a scatterplot of error in pressure versus stitch length. Comment on the trend observed.
b Make a scatterplot of CPU time versus stitch length. Comment on the trend observed.
c Put the information from both the scatterplots together to comment on the efficiency and accuracy of the coupled Stokes-Raynolds method.

Transcribed Image Text:

Stitch Length (cm) Error in CPU time Pressure (sec) 0.1 0.01 140 0.2 0.11 130 0.3 0.15 118 0.4 0.17 102 0.5 0.20 105 0.6 0.24 100 0.7 0.25 85 0.8 0.25 85 0.9 0.24 81 1.0 0.21 73 1.1 0.20 65 1.2 1.3 1.4 221 0.18 55 0.18 58 0.15 50