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 . 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 scheme with different timesteps is displayed in Figure d . For the implicit timestepping scheme the pseudo-steady-state system given by and was solved using a local Courant number of C 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 a particle in the free stream crosses the cylinder in timesteps . The timings recorded are summarized in Table . Note that the timestep for the explicit-advection schemes is approximate. 216 APPLIED COMPUTATIONAL FLUID DYNAMICS TECHNIQUES Table . von Karman vortex street Scheme At ntime CPU s Speedup Ex 1 9961 12 929 Ex 2 2490 4194 Ex 3 1660 3296 Ex 5 1245 3201 Ex 5 830 1546 Ex 5 623 1114 Ex 5 554 995 ImSGS 5 200 3189 ImSGS 5 100 1612 ImSGS 5 50 962 . 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 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
