Page 204 - Fundamentals of The Finite Element Method for Heat and Fluid Flow
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CONVECTION HEAT TRANSFER
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0.8 1 Standard Galerkin
Characteristic Galerkin
Exact solution
0.6
Function 0.4
0.2
0
0 0.2 0.4 0.6 0.8 1
Horizontal distance
(a) Pe = 1.0
1
0.8 Standard Galerkin
Characteristic Galerkin
Exact solution
0.6
Function 0.4
0.2
0
0 0.2 0.4 0.6 0.8 1
Horizontal distance
(b) Pe = 1.5
Figure 7.11 Spatial variation of a function, φ, in one-dimensional space for different
element Peclet numbers
without the source term is
∂φ ∂φ ∂φ ∂ ∂φ ∂ ∂φ
+ u 1 + u 2 = k + k (7.105)
∂t ∂x 1 ∂x 2 ∂x 1 ∂x 1 ∂x 1 ∂x 2
The convection velocity components u 1 and u 2 are assumed to be constant in deriving
this equation. Applying the characteristic Galerkin procedure to the above equation, we
