By Prof. Dr. Mohamed Hafez, Prof. Dr. Koji Morinishi, Prof. Dr. Jacques Periaux (auth.)
This quantity includes new developments of Computational Fluid Dynamics (CFD) for the twenty first Century. It involves 24 papers provided at a symposium honoring Prof. Nobuyuki Satofuka at the get together of his sixtieth birthday, Kyoto, July 15-17, 2000. The contributing authors are from Japan in addition to from the overseas group in Asia, Europe and North the United States. the themes coated during this quantity are Cartesian scheme, gridless scheme, excessive order and new schemes, optimization ideas, parallel computation, incompressible and compressible flows, multi-phase flows and solid/fluid interactions, magneto-hydrodynamics, and circulation visualization suggestions. they're particularly necessary to the more youthful iteration of scientists and engineers within the field.
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Additional info for Computational Fluid Dynamics for the 21st Century: Proceedings of a Symposium Honoring Prof.Satofuka on the Occasion of his 60th Birthday, Kyoto, Japan, July 15–17, 2000
The convergence rate of the explicit solver is intolerably slow at this low Mach number flow condition, whereas the convergence rate of the implicit one is quite satisfactory. Using the implicit solver, the residual is reduced six orders of magnitude in about 1,200 steps, while the residual of the explicit solver is only reduced about two orders of magnitude in 8,000 steps. Consequently, the implicit solver is more than oue order of magnitude efficient compared with the explicit counterpart. 25 0 is one of the weH known test cases for CFD code validation.
X Figure 2: Computational domain of flow around a circular cylinder Figure 3: Generated hierarchical Cartesian grid The cornputational Cartesian grid is generated by using the hierarchical grid system shown in Figure 3. The figure shows the 5-1evel hierarchical Cartesian grid system. It is 22 necessary to specify the physical values on the boundary of each hierarchical Cartesian grids. First, the values on Gib shown in Figure 4 are updated by the values on F in . Then, the values on F eb can be determined by using the second order interpolation technique.
_ ... - - .. :... _ . _. (b) Vorticity = 40) Figure 5 shows the steady state solutions of the pressure and vorticity. The flow characteristics (Cd, vortex length L, and press ure difference PE = p(1f) - p(O)) are compared with the other DNS results[9,1O] in Table 1. l:3 r:Fl 4-< 0 a 0 Z I N ~ PE Cd ! = 40) 0 -1 10 -2 10 -3 10 -4 10 -5 10 -6 10 0 5000 10000 15000 20000 Number of Time Steps Figure 6: Time history of streamwise velocity 24 good agreement with the other results. In order to validate the velocity on the vertual boundary points, the time history of streamwise velocity component is shown in Figure 6.