Discretization of the velocity space in solution of the Boltzmann equation

We point out an equivalence between the discrete velocity method of solving the Boltzmann equation, of which the lattice Boltzmann equation method is a special example, and the approximations to the Boltzmann equation by a Hermite polynomial expansion. Discretizing the Boltzmann equation with a BGK collision term at the velocities that correspond to the nodes of a Hermite quadrature is shown to be equivalent to truncating the Hermite expansion of the distribution function to the corresponding order. The truncated part of the distribution has no contribution to the moments of low orders and is negligible at small Mach numbers. Higher order approximations to the Boltzmann equation can be achieved by using more velocities in the quadrature

Lattice Boltzmann Simulation of Non-Ideal Fluids

A lattice Boltzmann scheme able to model the hydrodynamics of phase separation and two-phase flow is described. Thermodynamic consistency is ensured by introducing a non-ideal pressure tensor directly into the collision operator. We also show how an external chemical potential can be used to supplement standard boundary conditions in order to investigate the effect of wetting on phase separation and fluid flow in confined geometries. The approach has the additional advantage of reducing many of the unphysical discretisation problems common to previous lattice Boltzmann methods.Comment: 11 pages, revtex, 4 Postscript figures, uuencode

An Euler Solver Based on Locally Adaptive Discrete Velocities

A new discrete-velocity model is presented to solve the three-dimensional Euler equations. The velocities in the model are of an adaptive nature---both the origin of the discrete-velocity space and the magnitudes of the discrete-velocities are dependent on the local flow--- and are used in a finite volume context. The numerical implementation of the model follows the near-equilibrium flow method of Nadiga and Pullin [1] and results in a scheme which is second order in space (in the smooth regions and between first and second order at discontinuities) and second order in time. (The three-dimensional code is included.) For one choice of the scaling between the magnitude of the discrete-velocities and the local internal energy of the flow, the method reduces to a flux-splitting scheme based on characteristics. As a preliminary exercise, the result of the Sod shock-tube simulation is compared to the exact solution.Comment: 17 pages including 2 figures and CMFortran code listing. All in one postscript file (adv.ps) compressed and uuencoded (adv.uu). Name mail file `adv.uu'. Edit so that `#!/bin/csh -f' is the first line of adv.uu On a unix machine say `csh adv.uu'. On a non-unix machine: uudecode adv.uu; uncompress adv.tar.Z; tar -xvf adv.ta

Lattice Boltzmann Thermohydrodynamics

We introduce a lattice Boltzmann computational scheme capable of modeling thermohydrodynamic flows of monatomic gases. The parallel nature of this approach provides a numerically efficient alternative to traditional methods of computational fluid dynamics. The scheme uses a small number of discrete velocity states and a linear, single-time-relaxation collision operator. Numerical simulations in two dimensions agree well with exact solutions for adiabatic sound propagation and Couette flow with heat transfer.Comment: 11 pages, Physical Review E: Rapid Communications, in pres

Wastewater Sample Site Selection to Estimate Geographically Resolved Community Prevalence of COVID-19: A Sampling Protocol Perspective

Wastewater monitoring for virus infections within communities can complement conventional clinical surveillance. Currently, most SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) clinical testing is voluntary and inconsistently available, except for a few occupational and educational settings, and therefore likely underrepresents actual population prevalence. Randomized testing on a regular basis to estimate accurate population-level infection rates is prohibitively costly and is hampered by a range of limitations and barriers associated with participation in clinical research. In comparison, community-level fecal monitoring can be performed through wastewater surveillance to effectively surveil communities. However, epidemiologically defined protocols for wastewater sample site selection are lacking. Herein, we describe methods for developing a geographically resolved population-level wastewater sampling approach in Jefferson County, Kentucky, and present preliminary results. Utilizing this site selection protocol, samples (n = 237) were collected from 17 wastewater catchment areas, September 8 to October 30, 2020 from one to four times per week in each area and compared to concurrent clinical data aggregated to wastewater catchment areas and county level. SARS-CoV-2 RNA was consistently present in wastewater during the studied period, and varied by area. Data obtained using the site selection protocol showed variation in geographically resolved wastewater SARS-CoV-2 RNA concentration compared to clinical rates. These findings highlight the importance of neighborhood-equivalent spatial scales and provide a promising approach for viral epidemic surveillance, thus better guiding spatially targeted public health mitigation strategies

Generalized drift-diffusion model for miniband superlattices

A drift-diffusion model of miniband transport in strongly coupled superlattices is derived from the single-miniband Boltzmann-Poisson transport equation with a BGK (Bhatnagar-Gross-Krook) collision term. We use a consistent Chapman-Enskog method to analyze the hyperbolic limit, at which collision and electric field terms dominate the other terms in the Boltzmann equation. The reduced equation is of the drift-diffusion type, but it includes additional terms, and diffusion and drift do not obey the Einstein relation except in the limit of high temperatures.Comment: 4 pages, 3 figures, double-column revtex. To appear as RC in PR