The Numerical Simulation of Radiative Shocks I: The elimination of numerical shock instabilities using a localized oscillation filter

We address a numerical instability that arises in the directionally split computation of hydrodynamic flows when shock fronts are parallel to a grid plane. Transverse oscillations in pressure, density and temperature are produced that are exacerbated by thermal instability when cooling is present, forming post--shock `stripes'. These are orthogonal to the classic post--shock 'ringing' fluctuations. The resulting post--shock `striping' substantially modifies the flow. We discuss three different methods to resolve this problem. These include (1) a method based on artificial viscosity; (2) grid--jittering and (3) a new localized oscillation filter that acts on specific grid cells in the shock front. These methods are tested using a radiative wall shock problem with an embedded shear layer. The artificial viscosity method is unsatisfactory since, while it does reduce post--shock ringing, it does not eliminate the stripes and the excessive shock broadening renders the calculation of cooling inaccurate, resulting in an incorrect shock location. Grid--jittering effectively counteracts striping. However, elsewhere on the grid, the shear layer is unphysically diffused and this is highlighted in an extreme case. The oscillation filter method removes stripes and permits other high velocity gradient regions of the flow to evolve in a physically acceptable manner. It also has the advantage of only acting on a small fraction of the cells in a two or three dimensional simulation and does not significantly impair performance.Comment: 20 pages, 6 figures, revised version submitted to ApJ Supplement Serie

"Computing Densities and Expectations in Stochastic Recursive Economies: Generalized Look-Ahead Techniques"

We propose a generalized look-ahead estimator for computing densities and expectations in economic models. We provide conditions under which the estimator converges globally with probability one, and exhibit the asymptotic distribution of the error. Our estimator is more efficient than other Monte Carlo based approaches. Numerical experiments indicate that the estimator can provide large increases in accuracy and speed relative to traditional methods. Particular applications we consider are the stochastic growth model and an income fluctuation problem.

The Explicit Simplified Interface Method for compressible multicomponent flows

This paper concerns the numerical approximation of the Euler equations for multicomponent flows. A numerical method is proposed to reduce spurious oscillations that classically occur around material interfaces. It is based on the "Explicit Simplified Interface Method" (ESIM), previously developed in the linear case of acoustics with stationary interfaces (2001, J. Comput. Phys. 168, pp.~227-248). This technique amounts to a higher order extension of the "Ghost Fluid Method" introduced in Euler multicomponent flows (1999, J. Comput. Phys. 152, pp. 457-492). The ESIM is coupled to sophisticated shock-capturing schemes for time-marching, and to level-sets for tracking material interfaces. Jump conditions satisfied by the exact solution and by its spatial derivative are incorporated in numerical schemes, ensuring a subcell resolution of material interfaces inside the meshing. Numerical experiments show the efficiency of the method for rich-structured flows.Comment: to be published in SIAM Journal of Scientific Computing (2005

Prediction of the aerodynamic performance of re-usable single stage to orbit vehicles

Re-usable single stage to orbit launch vehicles promise to reduce the cost of access to space, but their success will be particularly reliant on accurate modelling of their aero-thermodynamic characteristics. Non-equilibrium effects due to the rarefaction of the gas in the atmosphere are important at the very high altitudes at which lifting R-SSTO configurations will experience their greatest thermal load during re-entry. Current limitations in modelling the behaviour of the gas and hence in capturing these effects have a strong impact on the accuracy with which the thermal and aerodynamic loading on the surface of the vehicle can be predicted during this design-critical flight regime. The problem is most apparent in the presence of strong shock interactions, and this is likely to exacerbate the problem of aerodynamic characterisation of re-usable single stage to orbit vehicles, especially given design pressures towards increased geometric complexity compared to historical spacecraft designs, and hence the complexity of the shock structures that the vehicle will produce in high-speed flight. The development of this class of vehicles will thus very likely be paced by the development of the specialised modelling tools that will be required to account fully for the properties of the gas at the high speeds and altitudes that are characteristic of their re-entry into the atmosphere of the earth

Global Food Price Shock and the Poor in Egypt and Ukraine

The global food price shock of 2006-2008 has particularly affected poorer strata of populations in several developing countries. In Egypt and some other countries it has put food subsidy schemes to the test. This paper develops two comparable computable general equilibrium models for Egypt and Ukraine which are used to simulate direct and indirect impacts of the food price surge and various policy options on the performance of the main macroeconomic indicators as well as on poverty outcomes. The results illustrate the limited ability of realistic policy responses to mitigate negative social consequences of an external price shock. Food import tariff cuts are a partial remedy faring better than other analysed options. Furthermore, the Egyptian system of food subsidies needs substantial reforms limiting the related fiscal burden and improving the targeting of the poor population.food subsidy, agriculture, price shock, poverty, Ukraine, Egypt

A linearized Euler analysis of unsteady flows in turbomachinery

A method for calculating unsteady flows in cascades is presented. The model, which is based on the linearized unsteady Euler equations, accounts for blade loading shock motion, wake motion, and blade geometry. The mean flow through the cascade is determined by solving the full nonlinear Euler equations. Assuming the unsteadiness in the flow is small, then the Euler equations are linearized about the mean flow to obtain a set of linear variable coefficient equations which describe the small amplitude, harmonic motion of the flow. These equations are discretized on a computational grid via a finite volume operator and solved directly subject to an appropriate set of linearized boundary conditions. The steady flow, which is calculated prior to the unsteady flow, is found via a Newton iteration procedure. An important feature of the analysis is the use of shock fitting to model steady and unsteady shocks. Use of the Euler equations with the unsteady Rankine-Hugoniot shock jump conditions correctly models the generation of steady and unsteady entropy and vorticity at shocks. In particular, the low frequency shock displacement is correctly predicted. Results of this method are presented for a variety of test cases. Predicted unsteady transonic flows in channels are compared to full nonlinear Euler solutions obtained using time-accurate, time-marching methods. The agreement between the two methods is excellent for small to moderate levels of flow unsteadiness. The method is also used to predict unsteady flows in cascades due to blade motion (flutter problem) and incoming disturbances (gust response problem)

The Large Scale Energy Landscapes of Randomly Pinned Objects

We discuss the large scale effective potential for elastic objects (manifolds) in the presence of a random pinning potential, from the point of view of the Functional Renormalisation Group (FRG) and of the replica method. Both approaches suggest that the energy landscape at large scales is a succession of parabolic wells of random depth, matching on singular points where the effective force is discontinuous. These parabolas are themselves subdivided into smaller parabolas, corresponding to the motion of smaller length scales, in a hierarchical manner. Consequences for the dynamics of these pinned objects are underlined.Comment: 14 pages, two postcript figures attache