Numerical Simulation of Viscous Incompressible Fluid Flows 



APPLICATIONS 



The surge of water under a sluice gate is an example of a complicated non- 

 linear fluid flow. Figure 3 shows the marker particle configuration obtained in 

 a MAC calculation of such a flow. Fluid falls under the influence of gravity and 

 jets under the gate into a stagnate pool. A surge wave is formed moving to the 

 left. A velocity vector plot, Fig. 4, shows a large eddy at the back of the wave. 

 Each line segment in Fig. 4 characterizes the velocity magnitude and direction 

 for a single computing cell. 





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 !:.H5S5L=3H£!HiHH: 



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Fig, 3 - Marker particle configuration of a sluice gate calculation 



It is evident from the velocity plot that some difficulty is developing along 

 the bottom of the flow region. The irregular appearance of the velocities indi- 

 cates a computational instability. Although many stable sluice gate problems 

 have been calculated and have given excellent agreement with experimental data, 

 we have purposely chosen a bad example to illustrate an instability. 



There are, in fact, two instabilities in this calculation. One is behind the 

 sluice gate and the other is under the surge wave. A decrease in St by a factor 

 of 20 eliminates the instability under the wave, but produces no significant 

 changes behind the gate. A decrease in ox (and 5y which is equal to Sx) elim- 

 inates the latter instability also. The instability under the surge wave is due to 

 a violation of the condition in Eq. (28), and the other instability to a violation of 

 the condition in Eq. (29). With sufficiently small space and time increments, or 

 a sufficiently large value of v, the sluice gate calculation is stable. 



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