These offer a natural framework for fundamentally new phenomena, in particular possibility of dissipation in quantum mechanics, solitons, vortices and chaos. The introduction of dissipation in the Navier - Stokes sense transform the differential equations from hyperbolic to parabolic type, with nonlinear and dispersive terms. This paper extends the QFD formalism to include dissipation in the form of Navier - Stokes term in classical fluid dynamics. The QFD formalism is utilized advantageously for solving the time dependent Schrödinger equation for scattering problems. The QFD approach leads to two conservation laws, for ''mass'' and ''momentum'', similar to those in fluid-dynamics for a compressible fluid as a set of nonlinear partial differential equations. This chapter describes results of a recent investigation aiming to assess the potential of quantum computing and suitably designed algorithms for future computational fluid dynamics applications. Einstein expected the complete theory to have nonlinearity and admit solutions with ``particle'' nature, similar to solitons in contemporary terminology. The approach is partly motivated by Einstein's questioning of the completeness of the quantum theory. It is an interpretation of quantum mechanics with the goal to find classically identifiable dynamical variables at the sub-particle level. Recently, quantum computing has been proven to outperform a classical computer on. When the number of grid cells grows, massive computing resources are needed correspondingly. In FVM, space is discretized to many grid cells. The finite volume method (FVM) is an important one. The Quantum Fluid Dynamics (QFD) representation has its foundations in the works of Madelung, De Broglie and Bohm. Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical methods to solve fluid flows.
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