Pressure (density) and velocity boundary conditions inside a flow domain are studied for 2-D and 3-D lattice Boltzmann BGK models (LBGK) and a new method to specify these conditions are proposed. These conditions are constructed in consistency of the wall boundary condition based on an idea of bounceback of non-equilibrium distribution. When these conditions are used together with the improved incompressible LBGK model by Zou et al., the simulation results recover the analytical solution of the plane Poiseuille flow driven by pressure (density) difference with machine accuracy. Since the half-way wall bounceback boundary condition is very easy to implement and was shown theoretically to give second-order accuracy for the 2-D Poiseuille flow with forcing, it is used with pressure (density) inlet/outlet conditions proposed in this paper and in Chen et al. to study the 2-D Poiseuille flow and the 3-D square duct flow. The numerical results are approximately second-order accurate. The magnitude of the error of the half-way wall bounceback is comparable with that using some other published boundary conditions. Besides, the bounceback condition has a much better stability behavior than that of other boundary conditions.

https://arxiv.org/pdf/comp-gas/9611001.pdf

On pressure and velocity flow boundary conditions and bounceback for the lattice Boltzmann BGK model

Some Preliminary Thoughts * Part I: Inviscid Hypersonic Flow * Hypersonic Shock and Expansion-Wave Relations * Local Surface Inclination Methods * Hypersonic Inviscid Flowfields: Approximate Methods * Hypersonic Inviscid Flowfields: Exact Methods * Part II: Viscous Hypersonic Flow * Viscous Flow: Basic Aspects, Boundary Layer Results, and Aerodynamic Heating * Hypersonic Viscous Interactions * Computational Fluid Dynamic Solutions of Hypersonic Viscous Flows * Part III: High-Temperature Gas Dynamics * High-Temperature Gas Dynamics: Some Introductory Considerations * Some Aspects of the Thermodynamics of Chemically Reacting Gases (Classical Physical Chemistry) * Elements of Statistical Thermodynamics * Elements of Kinetic Theory * Chemical Vibrational Nonequilibrium * Inviscid High-Temperature Equilibrium Flows * Inviscid High-Temperature Nonequilibrium Flows * Kinetic Theory Revisited: Transport Properties in High-Temperature Gases * Viscous High-Temperature Flows * Introduction to Radiative Gas Dynamics.

Hypersonic and high temperature gas dynamics

Pressure ~density! and velocity boundary conditions are studied for 2-D and 3-D lattice Boltzmann BGK models ~LBGK! and a new method to specify these conditions is proposed. These conditions are constructed in consistency with the wall boundary condition, based on the idea of bounceback of the non-equilibrium distribution. When these conditions are used together with the incompressible LBGK model @J. Stat. Phys. 81 ,3 5 ~1995!# the simulation results recover the analytical solution of the plane Poiseuille flow driven by a pressure ~density! difference. The half-way wall bounceback boundary condition is also used with the pressure ~density! inlet/outlet conditions proposed in this paper and in Phys. Fluids 8, 2527 ~1996! to study 2-D Poiseuille flow and 3-D square duct flow. The numerical results are approximately second-order accurate. The magnitude of the error of the half-way wall bounceback boundary condition is comparable with that of other published boundary conditions and it has better stability behavior. © 1997 American Institute of Physics. @S1070-6631~97!03406-5#

http://phelafel.technion.ac.il/~drorden/project/ZouHe.pdf

On pressure and velocity boundary conditions for the lattice Boltzmann BGK model

■ Abstract Fluid flow at the microscale exhibits unique phenomena that can be leveraged to fabricate devices and components capable of performing functions useful for biological studies. The physics of importance to microfluidics are reviewed. Common methods of fabricating microfluidic devices and systems are described. Components, including valves, mixers, and pumps, capable of controlling fluid flow by utilizing the physics of the microscale are presented. Techniques for sensing flow characteristics are described and examples of devices and systems that perform bioanalysis are presented. The focus of this review is microscale phenomena and the use of the physics of the scale to create devices and systems that provide functionality useful to the life sciences.

https://www.researchgate.net/profile/Glennys_Mensing/publication/11260597_Physics_and_applications_of_microfluidics_in_biology/links/5437f5160cf2027cbb206767.pdf

Physics and applications of microfluidics in biology.

Microrobots have the potential to revolutionize many aspects of medicine. These untethered, wirelessly controlled and powered devices will make existing therapeutic and diagnostic procedures less invasive and will enable new procedures never before possible. The aim of this review is threefold: first, to provide a comprehensive survey of the technological state of the art in medical microrobots; second, to explore the potential impact of medical microrobots and inspire future research in this field; and third, to provide a collection of valuable information and engineering tools for the design of medical microrobots.

/pdf/microrobots-for-minimally-invasive-medicine-cvnrt37y65.pdf

Microrobots for Minimally Invasive Medicine

1 Preliminary Concepts 2 Fundamental Equations of Compressible Viscous Flow 3 Solutions of the Newtonian Viscous-Flow Equations 4 Laminar Boundary Layers 5 The Stability of Laminar Flows 6 Incompressible Turbulent Mean Flow 7 Compressible Boundary Layer Flow Appendices A Transport Properties of Various Newtonian Fluids B Equations of Motion of Incompressible Newtonian Fluids in Cylindrical and Spherical Coordinates C A Runge-Kutta Subroutine for N Simultaneous Differential Equations Bibliography Index

Frank M. White

Papers

Viscous Fluid Flow