Executive Summary : | Turbulent flows are ubiquitously observed in nature (clouds/oceans/tornados/cyclones,etc) and applications of engineering relevance (flow over wind turbine or tidal turbine farm or flow over vehicles/turbomachinery components/chemically reacting flows, etc.). Modelling or resolving turbulent flows is highly challenging due to the wide range of Spatio-temporal scales involved. To accurately predict the turbulent flows, it is essential to carry out high-fidelity eddy resolving simulations in which the tightly coupled partial differential equations (Navier-Stokes equations) are directly solved. Such simulations are possible with the advent of high-performance computing, and with a substantial leap in the number of floating-point operations per second (FLOPS) reaching from petascale to exascale. Of late, efforts are made to accelerate the CFD solvers on many-core graphical processing units (GPUs) to exploit the benefits offered by these highly scalable hardware architectures. On this hardware, simulations carried out using low precision: (a) are remarkably faster (around 1.5-2 times) than those with high precision and (b) can accommodate larger grid points (atleast twice the grid points) as the memory requirements are significantly lower than that of high precision. Nevertheless, additional errors accumulate in mean and turbulent statistics when the simulations are carried out with low-precision in contrast to the high-precision. The proposed project intends to accelerate such CFD applications by modelling the sub-precision inaccuracies which accumulate during the time-accurate unsteady CFD simulations. Typically, the mid to higher frequencies in the energy spectra are much more susceptible to amplitude/phase-related errors due to precision. Mathematical models will be developed to quantify these inaccuracies. Concepts from stability analysis will be used to model the growth and the non-linear saturation of the errors due to precision. Subsequently, the accumulated errors will be systematically corrected using suitable strategies. The performance of these models, in terms of speed up vs accuracy, will be evaluated on both the canonical turbulent flows and test cases of industrial relevance. |