Simulating Incompressible Fluid Flow with the Navier-Stokes Equation

Overview

Objectives/Goals The objective was to determine how accurite my fluid simulator was. Methods/Materials The simulation method was a staggered grid finite difference approximation of the two dimensional incompressible Navier Stokes Equations. To test the method's accuracy I simulated fluid flow around circles of varying size. I programed the whole program in java from scratch. Results The simulation produced results that looked like water in general but did not agree with past experiments numerically. The frequency did decrease with cylinder size as expected but it was almost exactly ten times more than it should be. Also, the frequency decreased about half as much, proportionally, as expected for the higher diameters. All the simulations converged to a stable frequency after less than ten vortices. Conclusions/Discussion This experiment showed definitively that my simulator was too inaccurate for anything but possibly computer graphics. However, he cause of the inaccuracy is still uncertain. A question for future exploration is wether the error approches zero as the grid resolution approches infinity and the time step approches zero. If so, than the approximation method needs to be improved and possibly greater computing power must be used. If not, than there is probably a bug in the program or something fundamentally wrong with the math.

Competition history

• CSEF 2011 Mathematics & Software · Entry S1424

Resources

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