Problem Statement
DE for 2-D, steady convection diffusion is
DE:
BCs:
q(x,0) = q(0,y) = 0
data: q(1,1)
= 1, s = 0 The Galerkin weak statement definition
GWSN
=
when implemented as GWSh via the
linear FE basis leads to {WS}e = (u,[ ],[ ],0,’B201L’,q) +(v,[ ],[ ],0,’B202L’,q) +(1/Pe,[ ],[ ],-1,’B211L’,q) +(1/Pe,[ ],[ ],-1,’B212L’,q) +(1/Pe,[ ],[ ],-1,’B221L’,q)
+(1/Pe,[ ],[ ],-1,’B222L’,q) The TWSh augmentation to GWSh generates the “b-term,” and the steady state theory determines the form to be
TWSh
Recall the Peclet number Pe is the product of
Prandtl(Pr) and Reynolds(Re) number, which for practical engineering
problems is large. Implementation of the TWS “b-term”
adds the following to the GWSh {WS}e
template syntax +(h2Pe/12,[ ],[ ],-1,'B211L',q) +(h2Pe/12,[ ],[ ],-1,'B212L',q) +(h2Pe/12,[ ],[ ],-1,'B221L',q)
+(h2Pe/12,[ ],[ ],-1,'B222L',q) where ‘h’ represents the length of the element for the uniform mesh.
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