An Approach to the Mechanics of Fluids

by Frank C. Fung - 1st published in June, 2008.

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Section VIII - Time Depenedent { Finite Elements }

Summary for the Section :

• In this Section , we shall look at non-stationary { finite elements } .

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An { Unsteady Flow } Situation :

• In { unsteady flow } , the { velocity vectors } may simply vary with { time } .

  When we previously developed the { finite elements } using { Flow Nets } :

  • we constructed the { Stream-Lines } , based on the { Velocity Vectors } , and

  • we constructed the { planes orthogonal to the Stream-Lines } ;

    to arrive at the { 8 nodal-points } for our { Six-Face Object } as the { finite elements } .

• Our contention here is simply that the { finite elements } may move with the variations in { Stream-Lines } .
  • And this may be advantages in certian types of situations .

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Moving-Down the { Stream-Tube } :

• We bring-back , at this point , the { Flow Net } diagram for the { Dam } :

  

  Our contention here is simply that a { finite element } may change :

  • its { size and shape } , as well as its { positon and orientation } , in { time } ;

    as per the example in the diagram above , where :

    • the { finite element } marked in { orange-color } moved , in { time } :
      • from { position #1 } ,
      • to { position #2 } ,
      • to { position #3 } ,
      • to { position #4 } .

  We simply have a { move-on-the-fly } situation which may be advantages .

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go to the next section : Section IX - { [ 18 ] on [ 18 ] } for the { Six-Face Object }

go to the last section : Section VII - A { Steady Flow } Situation

return to the Mechanics of Fluids HomePage

original dated 2008-6-03