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By Prof. Dr. Mohamed Hafez, Prof. Dr. Koji Morinishi, Prof. Dr. Jacques Periaux (auth.)

This quantity comprises new tendencies of Computational Fluid Dynamics (CFD) for the twenty first Century. It involves 24 papers provided at a symposium honoring Prof. Nobuyuki Satofuka at the social gathering of his sixtieth birthday, Kyoto, July 15-17, 2000. The contributing authors are from Japan in addition to from the overseas neighborhood in Asia, Europe and North the USA. the themes lined during this quantity are Cartesian scheme, gridless scheme, excessive order and new schemes, optimization innovations, parallel computation, incompressible and compressible flows, multi-phase flows and solid/fluid interactions, magneto-hydrodynamics, and stream visualization options. they're in particular valuable to the more youthful iteration of scientists and engineers within the field.

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Additional resources 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

Example text

1) above, adua11y verifies 'iM 2': Mo, 'i11, E V, which the llsual definition for the order of error of interpolation, with resped to the size of the mesh, which is, in this case I/AI. 2 Optimising the mesh in order to interpolate irregular fllnctions USllal interpolation processes can be very precise for regular enough fundions. For instance, let T N be a Delaunay mesh of H with N nodes, and 7r N be the PI classical finite element interpolation. We have Problems arise when interpolating less regular fund ions with such processes : n, Typica11y, in dimension d = 2 ou 3, a fundion in H 2 (H) is continuolls on while a fundion H I (H) may have a discontinuity along a sllrface of dimension d - 1 (a line for d = 2 and a plane for d = 3).

5) n=l N s is the total virtual boundary points in the cell. 2 Governing Equations The incompressible Navier-Stokes equations can be written in the nondimensional form by OUi ~=O, OUi OUi 'ut" + Uj-;:;-uXj op = -~ UXi UX·1. 1 0 2 Ui + -Re ~2 + Gi, UXi (6) (7) Equation (6) denotes the continuity equation and Equation (7) the moment um equations. The velocity and the pressure are expressed by Ui and p, respectively and Re is Reynolds number defined by Re = U Ljv where v is the kinematic viscosity.

0. 4. Subiteration is introduced to the present solver at every physical time step in ~r to keep its time accuracy. Figure 16 shows the unstructured grid used, which are ~rated with the simple Delaunay triangulation. The total number of points is 993. initial shock position and pressure contours obtained at the nondimensional time of ll"e also drawn in the figure. 5) at the nondimensional time is compared with the exact solution in Figure 17. in the position and strength of the propagating shock wave are correctly predicted .

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