By Milton D. Van Dyke, Milton Van Dyke

Concepts for treating normal and singular perturbations are illustrated by means of software to difficulties of fluid movement. specifically, the strategy of matched asymptotic expansions is utilized to the aerodynamics of airfoils and wings, and to viscous movement at low and high Reynolds numbers. different themes contain the tools of strained coordinates and of a number of scales, and the development of sequence.

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A. Wolf-Gladrow, Lattice-Gas Cellular Automata and Lattice Boltzmann Models, Vol. 1725 of Lecture Notes in Mathematics, Springer, Berlin, 2000. 3. S. Succi, The Lattice Boltzmann Equation – For Fluid Dynamics and Beyond, Claren don Press, 2001. 4. L. Oliker, J. C. A. Canning, J. Shalf, S. Ethier, Scientiﬁc computations on modern parallel vector systems, in: Proceedings of SC2004, CD-ROM, 2004. 5. T. Pohl, F. Deserno, N. Th¨ urey, U. R¨ ude, P. Lammers, G. Wellein, T. Zeiser, Per formance evaluation of parallel large-scale lattice Boltzmann applications on three supercomputing architectures, in: Proceedings of SC2004, CD-ROM, 2004.

R¨ ude, P. Lammers, G. Wellein, T. Zeiser, Per formance evaluation of parallel large-scale lattice Boltzmann applications on three supercomputing architectures, in: Proceedings of SC2004, CD-ROM, 2004. 6. F. Massaioli, G. Amati, Achieving high performance in a LBM code using OpenMP, in: EWOMP’02, Roma, Italy, 2002. 7. G. Wellein, T. Zeiser, S. Donath, G. Hager, On the single processor performance of simple lattice Boltzmann kernels, Computers & Fluids. 8. T. Pohl, M. Kowarschik, J. Wilke, K. Iglberger, U.

These Cartesian grids can be treated with eﬃcient approximations leading to fast methods with low memory usage. Overlapping grids have been used successfully for the numerical solution of a variety of problems involving inviscid and viscous ﬂows, see the references in [2,3] for example. S. Department of Energy by the University of California, Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48. ∗ 22 Ω interpolation unused ghost point ∂Ω physical boundary i2 = N2 bc(2,2) G1 i2 = 0 G2 i1 = 0 i1 = N1 bc(1,1) bc(1,2) bc(2,1) Figure 1.