By Z. J. Wang
This e-book comprises very important contributions by means of world-renowned specialists on adaptive high-order tools in computational fluid dynamics (CFD). It covers numerous commonplace, and nonetheless intensively researched equipment, together with the discontinuous Galerkin, residual distribution, finite quantity, differential quadrature, spectral quantity, spectral distinction, PNPM, and correction strategy through reconstruction equipment. the main target is functions in aerospace engineering, however the ebook also needs to be invaluable in lots of different engineering disciplines together with mechanical, chemical and electric engineering. given that a lot of those equipment are nonetheless evolving, the booklet might be a good reference for researchers and graduate scholars to realize an figuring out of the state-of-the-art and ultimate demanding situations in high-order CFD equipment.
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Extra resources for Adaptive High-Order Methods in Computational Fluid Dynamics
Thus, for a fixed number of elements on each subdomain, a scalable algorithm may be viewed as being optimal on a macro scale. A scalable algorithm is truly optimal if the rate convergence is also independent of the number of elements on each subdomain. For unsteady simulations, explicit methods have been touted as being highly parallelizable, as inter-processor communication is required only in updating ghosted data from neighbouring processors, while residual evaluations are trivially parallelized.
In particular, an efficient preconditioner for elliptic problems requires a means of controlling the lowest frequency error modes which extend throughout the domain. While elliptic problems are characterized by Green’s functions that extend throughout the entire domain, convection-dominated problems have a hyperbolic behaviour where the errors propagate along characteristics in the flow. Thus, for convection-dominated problems, the resulting discretization is strongly coupled along the characteristics with little dissipation of errors present especially across characteristics.
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.
Adaptive High-Order Methods in Computational Fluid Dynamics by Z. J. Wang