The main aim of this course is to acquaint the participants with present state of art of high accuracy scientific computing and its future prospects, as applicable to the broad areas of fluid mechanics and thermal analysis, across all speed regimes. Beginning with the concepts of space-time discretization and dispersion relation in numerical computing, the foundation will be laid for the solution of Navier-Stokes equation and its solution strategies for RANS (Reynolds-averaged Navier-Stokes), LES, DES (detached eddy simulation) and DNS using classical discretization techniques. Also, newer, approaches to cope with geometrical complexity like immersed boundary methods will be used not only for high accuracy computing, emplyoing high performance computing, but also for futuristic exascale computing. Basics of high accuracy computing is rooted to the concept of stability, dispersion and phase errors, which require global spectral analysis (GSA) of discrete computing by rigorously following error dynamics. In this context we present high-order methods from finite difference, finite volume and finite element (including spectral element). We will specifically discuss compact schemes, which promise very high accuracy computing for DNS/LES of incompressible and compressible flows. Naturally, discussion would involve high performance computing (HPC) with various concepts of parallel computing. With the added help of multi-dimensional filtering, results have been produced for turbulence starting from receptivity stage without any modeling from first principle. This will be one case that will be discussed for simulating transitional and turbulent flows. Another interesting case is the simulation of wall bounded turbulence for both incompressible and compressible flows, which will be described in all essential details. With growth of available computer power, DNS has recently got to the stage of simulating high Reynolds number flows, where comparison with experiments is a distinct possibility. It is now even conceivable to solve for even higher values of Reynolds number. We plan to discuss about complex fluid-structure interaction problems involving moving bodies and heat transfer. This course aims to raise the bar above the pedagogical usage of high- accuracy computing in addressing more complex physical scenarios, like discussing turbulent combustion. This will span from modeling level to investigation of complex combustion instabilities in gas turbines, which may also incorporate acoustically coupled causes. The participants would also gain insights into the industry practices in the areas of turbomachines via the usage of hybrid-RANS, LES modeling. Such advanced industrial simulations using LES also require innovative hybrid turbulence models. The pre- and post-processing of LES data is another challenge that is faced in present day industrial practices. Obtained results of Navier-Stokes equation in time-accurate manner constitute huge data bases, whose analysis poses significant challenges already to researchers. In the near future one would aim at peta and exascale computing. To visualize and analyze such big data arising from models in industrial scale simulations, LES and DNS of canonical problems one needs to familiarize oneself with various pre- and post-processing tools. We specifically present tools like proper orthogonal decomposition (POD), proper generalized decomposition (PGD), singular value decomposition (SVD), recursive POD, high order SVD in multi-parameter spaces. Special attention would be paid to bivariate and multivariate data sets in the course, with respect to various canonical flow and heat transfer cases. The course is mainly addressed to doctoral students in mechanical, aerospace engineering and all applied disciplines including applied mathematics. We believe that the covered materials would also significantly benefit post-doctoral fellows and young professional working in related fields. The course will be offered with enough scope of interaction between the lecturers and the participants. As we expect that some of the participants would be already involved in similar activities, an afternoon would be set aside for participants to discuss their specific problems orally via informal and/ or poster presentations.