An efficient finite difference scheme for three-dimensional, non-equilibrium flows using operator splitting

An efficient finite difference scheme is presented for the inviscid terms of the three-dimensional, compressible flow equations for chemical non-equilibrium gases. This scheme represents an extension and an improvement of one proposed by the author, and includes operator splitting.

A finite difference scheme for inviscid flows with non-eequilibrium chemistry and internal energy

A finite difference scheme is presented for the inviscid terms of the equations of compressible fluid dynamics with general non-equilibrium chemistry and internal energy.

An efficient Riemann solver for unsteady flows with non-ideal gases

A Riemann solver is presented for the Euler equations of gas dynamics with real gases. This represents a more efficient version of an algorithm originally presented by the author.

Similarity solutions for multicomponent flows

A one-dimensional shock-reflection test problem in the case of slab, cylindrical or spherical symmetry is discussed for multi-component flows. The differential equations for a similarity solution are derived and then solved numerically in conjunction with the Rankine-Hugoniot shock relations.

Real gas flows in a duct

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a real gas in a single spatial coordinate. This include flow in a duct of variable cross-section as well as flow with cylindrical or spherical symmetry, and can prove useful when testing codes for the two-dimensional equations governing compressible flow of a real gas. The scheme is applied with success to a problem involving the interaction of converging and diverging cylindrical shocks for four equations of state and to a problem involving the reflection of a converging shock.

Cylindrically symmetric flows in a Lagrangian frame

An approximate Riemann solver, in a Lagrangian frame of reference, is presented for the compressible flow equations with cylindrical and spherical symmetry, including flow in a duct of variable cross section. The scheme is applied to a cylindrically symmetric problem involving the interaction of shocks.

Flux difference splitting for open channel flows

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow-water equations in open channels, together with an extension to two-dimensional flows. A linearized problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearized problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second-order scheme which avoids non-physical, spurious oscillations. The scheme is applied to a one-dimensional dam-break problem, and to a problem of flow in a river whose geometry induces a region of supercritical flow. The scheme is also applied to a two-dimensional dam-break problem. The numerical results are compared with the exact solution, or other numerical results, where available.

A numerical scheme for two-dimensional, open channel flows with non-rectangular geometries

An algorithm based on flux difference splitting is presented for the solution of two-dimensional, open channel flows. A transformation maps a non-rectangular, physical domain into a rectangular one. The governing equations are then the shallow water equations, including terms of slope and friction, in a generalized coordinate system. A regular mesh on a rectangular computational domain can then be employed. The resulting scheme has good jump capturing properties and the advantage of using boundary/body-fitted meshes. The scheme is applied to a problem of flow in a river whose geometry induces a region of supercritical flow.

Riemann solvers with primitive parameter vectors for two-dimensional compressible flows of a real gas

An analysis of averaging procedures is presented for an approximate Riemann solver for the equations governing the compressible flow of a real gas. This study extends earlier work for the Euler equations with ideal gases.

Discounted cash flow: accounting for uncertainty

Valuation is the process of estimating price. The methods used to determine value attempt to model the thought processes of the market and thus estimate price by reference to observed historic data. This can be done using either an explicit model, that models the worth calculation of the most likely bidder, or an implicit model, that that uses historic data suitably adjusted as a short cut to determine value by reference to previous similar sales. The former is generally referred to as the Discounted Cash Flow (DCF) model and the latter as the capitalisation (or All Risk Yield) model. However, regardless of the technique used, the valuation will be affected by uncertainties. Uncertainty in the comparable data available; uncertainty in the current and future market conditions and uncertainty in the specific inputs for the subject property. These input uncertainties will translate into an uncertainty with the output figure, the estimate of price. In a previous paper, we have considered the way in which uncertainty is allowed for in the capitalisation model in the UK. In this paper, we extend the analysis to look at the way in which uncertainty can be incorporated into the explicit DCF model. This is done by recognising that the input variables are uncertain and will have a probability distribution pertaining to each of them. Thus buy utilising a probability-based valuation model (using Crystal Ball) it is possible to incorporate uncertainty into the analysis and address the shortcomings of the current model. Although the capitalisation model is discussed, the paper concentrates upon the application of Crystal Ball to the Discounted Cash Flow approach.

Real estate capital flows and transitional economies

reign real estate capital was a major source of financing domestic property market office construction in Central Europe after the fall of the Berlin Wall in 1989. During the 1990s, over 800 office buildings were either newly constructed or refurbished in Budapest, Prague and Warsaw. The primary focus of this analysis is explaining the spatial construction and redevelopment patterns of the post-1989 office buildings in these cities. Secondarily, we analyze the correlation of foreign direct investment flows to annual construction of office buildings. We seek to explain the location of new or refurbished office buildings in the central business district (CBD) or in non-CBD locations in terms of the effect of time, size of property and other variables, and test whether there is a positive correlation relationship of foreign direct investment flows and new office construction or refurbishment. Integrating relevant foreign direct investment (FDI), economic geography and property theories in the research, the authors attempt to bridge existing gaps in the literature.