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Applied Computational Fluid Dynamics Techniques - Wiley Episode 1 Part 10

Tham khảo tài liệu 'applied computational fluid dynamics techniques - wiley episode 1 part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | INCOMPRESSIBLE FLOW SOLVERS 215 Time Time d Figure 11.2. Continued The run was repeated with a number of timestepping schemes. The lift of the cylinder as a function of time for the original explicit-advection projection scheme the 2 3 5-step explicitadvection projection scheme as well as the implicit-advection Cranck-Nicholson Ớ 0.50 scheme with different timesteps is displayed in Figure 11.2 d . For the implicit timestepping scheme the pseudo-steady-state system given by 11.38 and 11.39 was solved using a local Courant number of C 4.0 implicit advection and SGS relaxation. Typically 10-20 SGS iterations per timestep were required for convergence. Observe that for the schemes that employ a reasonable timestep and in particular all the explicit-advection multistep schemes the results are almost identical. Not surprisingly as the timestep is increased the implicit schemes remain stable but the solution deteriorates. Recall that for At 0.4 a particle in the free stream crosses the cylinder in 2.5 timesteps . The timings recorded are summarized in Table 11.2. Note that the timestep for the explicit-advection schemes is approximate. 216 APPLIED COMPUTATIONAL FLUID DYNAMICS TECHNIQUES Table 11.2. von Karman vortex street Scheme At ntime CPU s Speedup Ex 1 0.1 0.002 9961 12 929 1.00 Ex 2 0.4 0.008 2490 4194 3.08 Ex 3 0.6 0.012 1660 3296 3.92 Ex 5 0.8 0.016 1245 3201 4.03 Ex 5 1.2 0.025 830 1546 8.36 Ex 5 1.6 0.033 623 1114 11.60 Ex 5 1.8 0.037 554 995 12.99 ImSGS 5 0.1 200 3189 4.05 ImSGS 5 0.2 100 1612 8.02 ImSGS 5 0.4 50 962 13.43 11.9.2. NACA0012WING This classic example considers a NACA0012 wing at a 5 angle of attack. The aim of this test is to gauge the performance of the different schemes presented as well as the projective pressure increment predictor for a steady inviscid Euler case. Figures 11.3 a and b show the surface mesh employed as well as the surface pressures obtained. The mesh consisted of 68 000 points and 368 000 elements. With C denoting the Courant