A finite difference lattice Boltzmann method based on the Bhatnagar–Gross–Krook-type modeled Boltzmann equation is proposed. Themethod relies on a different lattice equilibriumparticle distribution function and the use of a splitting method to solve the modeled lattice Boltzmann equation. The splitting technique permits the boundary conditions for the lattice Boltzmann equation to be set as con...

This paper investigates different high order finite difference schemes and their accuracy for Burgers equation and Navier-Stokes equations. On a coarse grid, theoretical and numerical analysis indicate that a higher order difference scheme does not necessarily obtain more accurate solutions than a lower order scheme in the regions of high gradient variation (2nd order derivative). On a coarse g...

This note details the derivation of the generalized advective-diffusive equation system for the 2D space-time incompressible Navier-Stokes governing equations, in conservation form.

A gas-kinetic model with multiple translational temperature for the continuum and near continuum flow simulations is proposed. The main purpose for this work is to derive the generalized Navier-Stokes equations with multiple temperature. It is well recognized that for increasingly rarefied flowfields, the predictions from continuum formulation, such as the Navier-Stokes equations lose accuracy....

We describe a method to compute veriied enclosures for solutions of the stationary Navier-Stokes equation in two-dimensional bounded domains. In order to obtain error bounds for numerical approximations , we use the theorem of Newton{Kantorovich. Therefore, we compute approximations for the stream function of the ow and upper bounds of the defect in H ?2 (); we determine an upper bound for the ...

The Burgers’ equation first appeared in the paper by Bateman [3], who mentioned two of the essentially steady solutions. Due to extensive works of Burgers [4] involving the Burgers’ equation especially as a mathematical model for the turbulence, it is known as Burgers’ equation. The equation is used as a model in fields as wide as heat conduction [5], gas dynamics [13], shock waves [4], longitu...

The validity of the compressible Reynolds equation to predict the local pressure in a gas-lubricated, textured parallel slider bearing is investigated. The local bearing pressure is numerically simulated using the Reynolds equation and the Navier-Stokes equations for different texture geometries and operating conditions. The respective results are compared and the simplifying assumptions inhere...

Quantum mechanics has been argued to be a coarse-graining of some underlying deterministic theory. Here we support this view by establishing a map between certain solutions of the Schroedinger equation, and the corresponding solutions of the irrotational Navier–Stokes equation for viscous fluid flow. As a physical model for the fluid itself we propose the quantum probability fluid. It turns out...