Natural neighbour co-ordinates (Sibson co-ordinates) is a well-known interpolation scheme for multivariate data tting and smoothing. The numerical implementation of natural neighbour co-ordinates in a Galerkin method is known as the natural element method (NEM). In the natural element method, natural neighbour co-ordinates are used to construct the trial and test functions. Recent studies on NE...

Direct methods for solving the generalized Boltzmann equation are advanced by simulating flow past threedimensional immersed bodies in diatomic nitrogen in rotational-translational non-equilibrium. The simulations are performed by solving the entire domain with the generalized Boltzmann equation using a solver based upon the conservative discrete ordinates method of Tcheremissine. Coarse and re...

A concise and accurate solution to the problem of plane Couette flow for a binary mixture of rigid-sphere gases described by the linearized Boltzmann equation and general (specular-diffuse) Maxwell boundary conditions for each of the two species of gas particles is developed. An analytical version of the discrete-ordinates method is used to establish the velocity, heat-flow, and shearstress pro...

A recently developed analytical version of the discrete-ordinates method is used to establish a concise and particularly accurate solution to the problem of Couette #ow of a binary gas mixture in a plane channel. The model kinetic equations used to describe the #ow are based on the BGK theory of the linearized Boltzmann equation, and, in addition to the complete distribution functions for the t...

The P-1 radiation model is spatially decomposed to solve the radiative transport equation on parallel computers. Mathematical libraries developed by third parties are employed to solve the linear systems that result during the solution procedure. Multigrid preconditioning accelerated the convergence of iterative methods. The parallel performance did not depend strongly on the radiative properti...

An analytical variation of the discrete-ordinates method is used to establish a concise and accurate solution to the temperature-jump problem for a binary gas mixture. The analysis is based on Boltzmann equations of the BGK type subject to Maxwell's boundary conditions with arbitrary accommodation coe$cients. The results include the complete temperature and density "elds for speci"ed mass, dens...

The ADO (analytical discrete ordinates) method, a pre-processing procedure, and the break-point analysis developed for azimuthally symmetric problems in a previous work are generalized and used to solve a radiative-transfer problem defined by a finite, plane–parallel, multi-layer medium subject to Fresnel boundary and interface conditions and uniform illumination in the form of obliquely incide...

in this paper, the effects of baffle on thermal characteristics of combined convection-radiation heat transfer in laminar flow adjacent to an inclined backward facing step (bfs) in a horizontal duct are investigated. a baffle is mounted on the top wall of channel downstream side of step. in this study, the fluid is treated as a gray, absorbing, emitting and scattering medium; therefore, in the ...