A second order control-volume finite-element least-squares strategy for simulating diffusion in strongly anisotropic media

An unstructured mesh �nite volume discretisation method for simulating di�usion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume �nite-element method and it retains the local continuity of the ux at the control volume faces. A least squares function recon- struction technique together with a new ux decomposition strategy is used to obtain an accurate ux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it signi�cantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes, and appears independent of the mesh quality.

Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions

In this paper, a space fractional di®usion equation (SFDE) with non- homogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Analytic solutions of the SFDE are derived. Finally, some numerical results are given to demonstrate that the MTT is a computationally e±cient and accurate method for solving SFDE.

Quantification of motor vehicle emission factors from on road measurements

Assessment and prediction of the impact of vehicular traffic emissions on air quality and exposure levels requires knowledge of vehicle emission factors. The aim of this study was quantification of emission factors from an on road, over twelve months measurement program conducted at two sites in Brisbane: 1) freeway type (free flowing traffic at about 100 km/h, fleet dominated by small passenger cars - Tora St); and 2) urban busy road with stop/start traffic mode, fleet comprising a significant fraction of heavy duty vehicles - Ipswich Rd. A physical model linking concentrations measured at the road for specific meteorological conditions with motor vehicle emission factors was applied for data analyses. The focus of the study was on submicrometer particles; however the measurements also included supermicrometer particles, PM2.5, carbon monoxide, sulfur dioxide, oxides of nitrogen. The results of the study are summarised in this paper. In particular, the emission factors for submicrometer particles were 6.08 x 1013 and 5.15 x 1013 particles per vehicle-1 km-1 for Tora St and Ipswich Rd respectively and for supermicrometer particles for Tora St, 1.48 x 109 particles per vehicle-1 km-1. Emission factors of diesel vehicles at both sites were about an order of magnitude higher than emissions from gasoline powered vehicles. For submicrometer particles and gasoline vehicles the emission factors were 6.08 x 1013 and 4.34 x 1013 particles per vehicle-1 km-1 for Tora St and Ipswich Rd, respectively, and for diesel vehicles were 5.35 x 1014 and 2.03 x 1014 particles per vehicle-1 km-1 for Tora St and Ipswich Rd, respectively. For supermicrometer particles at Tora St the emission factors were 2.59 x 109 and 1.53 x 1012 particles per vehicle-1 km-1, for gasoline and diesel vehicles, respectively.