By Z. J. Wang
This ebook includes vital contributions by means of world-renowned specialists on adaptive high-order equipment in computational fluid dynamics (CFD). It covers numerous familiar, and nonetheless intensively researched tools, together with the discontinuous Galerkin, residual distribution, finite quantity, differential quadrature, spectral quantity, spectral distinction, PNPM, and correction method through reconstruction tools. the focus is functions in aerospace engineering, however the e-book must also be priceless in lots of different engineering disciplines together with mechanical, chemical and electric engineering. for the reason that lots of those equipment are nonetheless evolving, the ebook may be a very good reference for researchers and graduate scholars to achieve an realizing of the state-of-the-art and closing demanding situations in high-order CFD equipment.
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Extra info for Adaptive High-Order Methods in Computational Fluid Dynamics
For practical aerodynamic flows, the question remains whether a coarse space is necessary for a scalable preconditioner. 6 In numerical simulations with up to 128 processors, Venkatakrishnan shows that the presence of the coarse grid gives some improvement in the performance of the preconditioner in terms of number of iterations, though this does not necessarily translate into faster solution time. Gropp et al. 43 We note that this observation is consistent with the theoretical result for the time-dependent convectiondiffusion problems, where a coarse space is not necessary if the time step is sufficiently small.
Meth. Fluids. 60(8), 847–865, (2009). 23. F. Bassi, N. Franchina, A. Ghidoni, and S. Rebay, Spectral p-multigrid discontinuous Galerkin solution of the Navier-Stokes equations, Int. J. Numer. Meth. Fluids. (2010). accepted. 24. P. Tesini. An h-multigrid approach for high-order discontinuous Galerkin methods. PhD thesis, Universit` a degli studi di Bergamo, Dipartimento di Ingegneria Industriale, Viale Marconi 5, 24044 Dalmine (BG), Italy, (2008). 01˙Chapter-1 November 23, 2010 11:58 World Scientific Review Volume - 9in x 6in CHAPTER 2 MASSIVELY PARALLEL SOLUTION TECHNIQUES FOR HIGHER-ORDER FINITE-ELEMENT DISCRETIZATIONS IN CFD Laslo T.
Thus, the local solver may replaced with an iteration of an efficient serial preconditioner, such as an ILU factorization or a multigrid cycle. The performance of the Schwarz method will, in general, depend upon the strength of the local solver. 41,42 In particular, this allowed for different number of iterations to be used in each subdomain ensuring that each local problem was solved with sufficient accuracy. 10 As discussed previously, the case of generous overlap ensures that the preconditioner is optimal.