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description.tm
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<TeXmacs|1.0.7.18>
<style|generic>
<\body>
Solve Navier-Stokes equation
<\eqnarray*>
<tformat|<table|<row|<cell|<choice|<tformat|<table|<row|<cell|>|<cell|<frac|d
ee|d t>=-u*<frac|d ee|d x>-v <frac|d ee|d y>\<noplus\>+Re*\<Delta\>
<around*|(|ee|)>>>|<row|<cell|>|<cell|ee=\<Delta\><around*|(|ps|)>>>|<row|<cell|>|<cell|<frac|d
ps|d y>=u<rsub|>\<nocomma\>,<frac|d ps|d x>=-v>>>>>>|<cell|>|<cell|>>>>
</eqnarray*>
with border conditions:
<\eqnarray*>
<tformat|<table|<row|<cell|\<downarrow\>O
y>|<cell|B3>|<cell|\<rightarrow\>O x>>|<row|<cell| input
B4>|<cell|>|<cell|B6 output>>|<row|<cell|>|<cell|B1>|<cell|>>>>
</eqnarray*>
\ B4 is steam input. It weak near edges (coasts) and strong near center
\ so it use parabola equation for speed <math|V=(u(y),0) >where<math|
u(y)=C*y*(H-y)>. For ps used :
<\equation*>
\ ps<around*|(|y|)>=<big|int><rsub|0><rsup|y>u(s) d s=<frac|C H
y<rsup|2>|2>-<frac|C H y<rsup|3>|3>+const
</equation*>
\
B6 is same like B4
\ B1 and B3 we use <math|u=<frac|d ps|d y>,v=-<frac|d ps|d x>
\<Rightarrow\>ps=v*x+c=c1*x+c=u0*x+c> (u0 is const for init)
for <math|ee> in all borders Bi \ used deffinition of function of vorticity
\
<\equation*>
ee=<frac|d u|d y>-<frac|d v|d x>
</equation*>
</body>
<\initial>
<\collection>
<associate|language|american>
</collection>
</initial>