In studying fluid dynamics it is useful to employ two different perspectives of a fluid flowing through a domain D. The Eulerian point of view is to consider a fixed point x ∈ D, and observe the fluid flowing past. The Lagrangian point of view is to consider a fixed but arbitrary volume of fluid, called a parcel of fluid, and follow the parcel as it travels with the flow. One would think that o...

A brief description of the Smoothed Particle Hydrodynamics method is presented together with some test calculations and astrophysical examples of accretion phenomena.

This paper describes the extension of a recently developed numerical solver for the Landau-Lifshitz Navier-Stokes (LLNS) equations to binary mixtures in three dimensions. The LLNS equations incorporate thermal fluctuations into macroscopic hydrodynamics by using white-noise fluxes. These stochastic PDEs are more complicated in three dimensions due to the tensorial form of the correlations for t...

In the nanochannel flow behavior with respect to expand their applications in modern systems is of utmost importance. According to the results obtained in this study, the condition of nonslip on the wall of the nanochannel is not acceptable because in the nano dimensions, slip depends on different parameters including surface roughness. In this study, keeping the side area roughness, deformatio...

This summary contains two sections. In Section 1, the background and the motivation for the work in this thesis is discussed. In Section 2, the papers I{VI are summarized and the results are reviewed.

We propose a kinetic model of a fluid in which five macroscopic fields, the mass, energy, and three components of momentum, are conserved. The dynamics is constructed using the methods of statistical dynamics, and results in a discrete-time Markov chain for random fields on a lattice, followed by projection onto the information manifold. In the continuum limit we obtain a non-linear coupled par...

3+1-dimensional free inviscid fluid dynamics is shown to satisfy the criteria for exact integrability, i.e. having an infinite set of independent, conserved quantities in involution, with the Hamiltonian being one of them. With (density dependent) interaction present, distinct infinite serieses of conserved quantities in involution are discovered. Clebsch parametrization of the velocity field i...

We present a conformal theory of a dissipationless relativistic fluid in 2 space-time dimensions. The theory carries with it a representation of the algebra of 2-D area-preserving diffeomorphisms in the target space of the complex scalar potentials. A complete canonical description is given, and the central charge of the current algebra is calculated. The passage to the quantum theory is discus...

T opological fluid dynamics is a young mathematical discipline that studies topological features of flows with complicated trajectories and their applications to fluid motions, and develops group-theoretic and geometric points of view on various problems of hydrodynamical origin. It is situated at a crossroads of several disciplines, including Lie groups, knot theory, partial differential equat...