This book provides state-of-art information on high-accuracy scientific computing and its future prospects, as applicable to the broad areas of fluid mechanics and combustion, and across all speed regimes. Beginning with the concepts of space-time discretization and dispersion relation in numerical computing, the foundations are laid for the efficient solution of the Navier-Stokes equations, with special reference to prominent approaches such as LES, DES and DNS. The basis of high-accuracy computing is rooted in the concept of stability, dispersion and phase errors, which require the comprehensive analysis of discrete computing by rigorously applying error dynamics. In this context, high-order finite-difference and finite-volume methods are presented. Naturally, the coverage also includes fundamental notions of high-performance computing and advanced concepts on parallel computing, including their implementation in prospective hexascale computers. Moreover, the book seeks to raisethe bar beyond the pedagogical use of high-accuracy computing by addressing more complex physical scenarios, including turbulent combustion. Tools like proper orthogonal decomposition (POD), proper generalized decomposition (PGD), singular value decomposition (SVD), recursive POD, and high-order SVD in multi-parameter spaces are presented. Special attention is paid to bivariate and multivariate datasets in connection with various canonical flow and heat transfer cases. The book mainly addresses the needs of researchers and doctoral students in mechanical engineering, aerospace engineering, and all applied disciplines including applied mathematics, offering these readers a unique resource.

About the Author

Sergio Pirozzoli is professor of Fluid Dynamics at Sapienza University of Rome, Italy. His research interests focus on the numerical simulation of incompressible and compressible turbulent flows, having carried out the first DNS of shock/boundary layer interactions in 2004. His expertise includes the development of energy-conserving discretizations for the compressible Navier-Stokes equations. He has been involved as leader of research units in several research projects funded by the European Union focusing of the understanding of unsteady effects in turbulent and transitional SBLI.

Tapan K. Sengupta is head of the High Performance Computing Laboratory at IIT Kanpur, India. His research interests focus on developing high accuracy computing methods to aid in bridging the gap between theoretical and computational fluid dynamics and heat transfer. He has published over 100 papers in international refereed journals covering diversetopics such as transition and turbulence, unsteady aerodynamics, flow control, CFD and numerical methods, mixed convection and compressible flows.

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