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Adaptive Hp-Finite Element Methods in Wind Engineering*

The computational wind engineering problems like flow around cylinders, bridges, and high buildings is highly
computer intensive. For these unsteady computations adaptive finite element may reduce the computer
time and storage space required. Also computation can be transformed to a desired accuracy. In this work
p-adaptive finite element is first implemented to a circular cylinder. The flow around the circular cylinder
with Reynolds number of 1000 is considered for computation. The computed results are in good agreement with
other reported results. Instead of taking 2.5 times the initial unknowns if the whole region is refined, only
1.33 times the initial unknowns are considered by adaptive procedure. The order of the polynomial considered
varied from 2nd to 4th. The Navier-Stokes equations are solved by finite element method. Unequal order
interpolation is used for velocity and pressure.

Figure 1. Finite Element Grid for the Computational Wind Region
(Number of Elements: 3,195; Number of Nodes: 3,279)

Figure 2. The Distribution of the Relative Errors of the Vorticity
(Highest Order of the Interpolation Polynomial: 2; Highest Error: 19.35%)

Figure 3(a). The Distribution of the Different Orders of Polynomial
(Highest Order of the Interpolation Polynomial: 3)
**(Number of Elements with 2 and 3-Order Polynomial: 2940 and 339)**

Figure 3(b). The Distribution of the Relative Errors of the Vorticity
(Highest Error: 10.08%)

Figure 4(a). The Distribution of the Different Orders of Polynomial
(Highest Order of the Interpolation Polynomial: 4)
**(Number of Elements with 2, 3, and 4-Order Polynomial: 2917, 330, and 32)**

Figure 4(b). The Distribution of the Relative Errors of the Vorticity
(Highest Error: 10.06%)

Figure 5. The Distribution of the Pressure Around the Cylinder

Figure 6. The Distribution of the Velocity of the Wind Around the Cylinder

Figure 7. Coefficient of the Draft Force

**Updated on June 4th 2000**