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This paper explores the suitability of upcoming novel computing technologies, particularly adiabatic annealing based quantum computers, to solve fluid dynamics problems that form a critical component of several science and engineering applications. For our experiments, we start with a well-studied one-dimensional simple flow problem, and provide a framework to convert such problems in continuum to a form amenable for deployment on such quantum annealers. Since the DWave annealer returns multiple states sampling the energy landscape of the problem, we explore multiple solution selection strategies to approximate the solution of the problem. We analyze the continuum solutions obtained both qualitatively and quantitatively as well as their sensitivities to the particular solution selection scheme.

For a particular choice of the smoothing kernel, it is shown that the system of partial differential equations governing the vortex-blob method corresponds to the averaged Euler equations. These latter equations have recently been derived by averaging the Euler equations over Lagrangian fluctuations of length scale $\a$, and the same system is also encountered in the description of inviscid and incompressible flow of second-grade polymeric (non-Newtonian) fluids. While previous studies of this system have noted the suppression of nonlinear interaction between modes smaller than $\a$, we show that the modification of the nonlinear advection term also acts to enhance the inverse-cascade of energy in two-dimensional turbulence and thereby affects scales of motion larger than $\a$ as well. This latter effect is reminiscent of the drag-reduction that occurs in a turbulent flow when a dilute polymer is added.