Finite element and finite difference discretizations for evolutionary convection-diffusion-reaction equations in two and three dimensions are studied which give solutions without or with small underand overshoots. The studied methods include a linear and a nonlinear FEM-FCT scheme, simple upwinding, an ENO scheme of order 3, and a fifth order WENO scheme. Both finite element methods are combine...

This study considers environmental impacts and the power production potential of a number of coastally attached tidal lagoons, proposed along the North Wales coast, UK. Initially, the impoundment shape, turbine and sluice gate locations were modified according to the regional bathymetric data. A refined 0-Dimensional approach was implemented to optimise the lagoon operation, based on given turb...

An accurate representation of linking processes between one-dimensional (1-D) and two-dimensional (2-D) models is of particular importance for many floodmodelling projects. This paper provides a comparison of 1-D/2-D linking methods used to simulate a hypothetical embankment failure. Comparisons were made by implementing 1-D/2-D linked models using two different 1-D/ 2-D linking methods, namely...

In this paper, we consider linear stability issues for one-dimensional hyperbolic conservation laws using a class of conservative high order upwind-biased finite difference schemes, which is a prototype for the weighted essentially non-oscillatory (WENO) schemes, for initial-boundary value problems (IBVP). The inflow boundary is treated by the so-called inverse Lax-Wendroff (ILW) or simplified ...

Two conjectures of Su and Wang (2008) concerning binomial coefficients are proved. For n ≥ k ≥ 0 and b > a > 0, we show that the finite sequence Cj = ( n+ja k+jb ) is a Pólya frequency sequence. For n ≥ k ≥ 0 and a > b > 0, we show that there exists an integer m ≥ 0 such that the infinite sequence ( n+ja k+jb ) , j = 0, 1, . . ., is log-concave for 0 ≤ j ≤ m and log-convex for j ≥ m. The proof ...