Analysis of Carleman Linearization of Lattice Boltzmann

We explore the Carleman linearization of the collision term of the lattice Boltzmann formulation, as a first step towards formulating a quantum lattice Boltzmann algorithm. Specifically, we deal with the case of a single, incompressible fluid with the Bhatnagar Gross and Krook equilibrium function. Under this assumption, the error in the velocities is proportional to the square of the Mach number. Then, we showcase the Carleman linearization technique for the system under study. We compute an upper bound to the number of variables as a function of the order of the Carleman linearization. We study both collision and streaming steps of the lattice Boltzmann formulation under Carleman linearization. We analytically show why linearizing the collision step sacrifices the exactness of streaming in lattice Boltzmann, while also contributing to the blow up in the number of Carleman variables in the classical algorithm. The error arising from Carleman linearization has been shown analytically and numerically to improve exponentially with the Carleman linearization order. This bodes well for the development of a corresponding quantum computing algorithm based on the Lattice Boltzmann equation.

Application of Direct Numerical Simulation to Determine the Correlation Describing Friction Losses during the Transverse Flow of Fluid in Hexagonal Array Pin Bundles

This paper presents the results of a numerical simulation to determine the hydraulic resistance for a transverse flow through the bundle of hexagonal rods. The calculations were carried out using the precision CFD code CONV-3D, intended for direct numerical simulation of the flow of an incompressible fluid (DNS-approximation) in the parts of fast reactors cooled by liquid metal. The obtained dependencies of the pressure drop and the coefficient of anisotropy of friction on the Reynolds number can be used in the thermal-hydraulic codes that require modeling of the flow in similar structures and, in particular, in the inter-wrapper space of the reactor core.

STUDY OF SELF-SUPERPOSABLE FLUID MOTIONS IN CONFOCAL PARABOLOIDAL DUCTS

In this paper, studies have been made on some self-superposable motion of incompressible fluid is confocal Paraboloidal ducts. The boundary conditions have been neglected therefore the solutions contain a set of constants. Pressure distribution and the nature of vorticity are discussed. Tendency of irrotationality of the fluid flow is also determined. The aim of the paper is to introduce a method for solving the basic equations of fluid dynamics in confocal paraboloidal coordinates by using the property of self superposability.

Introductory Incompressible Fluid Mechanics

This introduction to the mathematics of incompressible fluid mechanics and its applications keeps prerequisites to a minimum – only a background knowledge in multivariable calculus and differential equations is required. Part One covers inviscid fluid mechanics, guiding readers from the very basics of how to represent fluid flows through to the incompressible Euler equations and many real-world applications. Part Two covers viscous fluid mechanics, from the stress/rate of strain relation to deriving the incompressible Navier-Stokes equations, through to Beltrami flows, the Reynolds number, Stokes flows, lubrication theory and boundary layers. Also included is a self-contained guide on the global existence of solutions to the incompressible Navier-Stokes equations. Students can test their understanding on 100 progressively structured exercises and look beyond the scope of the text with carefully selected mini-projects. Based on the authors' extensive teaching experience, this is a valuable resource for undergraduate and graduate students across mathematics, science, and engineering.