American Journal of Applied Mathematics and Statistics

In this paper, viscous fluid flow over an unconventional diamond-shaped obstacle in a confined channel is simulated in low to moderate Reynolds numbers. The diamond-shaped obstacle is altered geometrically in order to represent different blockage coefficients based on the channel height and different aspect ratios based on the length to height ratios of the obstacle. An in-house finite difference Navier-Stokes solver using staggered grid arrangement and Chorin’s projection method is developed for the simulation of the laminar viscous flow. The numerical solver is validated against numerical results that are presented in the literature for the flow over rectangular cylinders and good agreement is observed. Grid resolution has been studied within a mesh convergence test and as a result, suitable grid dimension is achieved. A series of simulations have been carried out for each set of geometry and configuration in order to find the critical Reynolds number for each case in which the vortex shedding will occur. Therefore, simulations are divided into two groups of steady and unsteady flows. In the case of unsteady flow, non-dimensional Strouhal Number (St) is investigated and results prove the dependency of St on the blockage coefficient and aspect ratio. It is shown that the Strouhal number will increase with the rise of blockage ratio and the local maximum of St will occur at lower Re for geometries with lower aspect ratios (bluff bodies) than geometries with higher aspect ratios, i.e. with more streamlined bodies.

American Journal of Applied Mathematics and Statistics. 2013, 1(1), 11-20. DOI: 10.12691/ajams-1-1-3
Pub. Date: March 07, 2013

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Robust Goodness of Fit Test Based on the Forward Search

by Abbas Mahdavi

Original Research

The most frequency used goodness of fit tests are based on measuring the distance between the theoretical distribution function and the empirical distribution function (EDF), but presence of outliers influences these tests strongly. In this study, we propose a simple robust method for goodness of fit test by using the “Forward Search” (FS) method. The FS method is a powerful general method for identifying outliers and their effects on the hypothesized model. The performance and the ability of the procedure to capture the structure of data, even in the presence of outliers, are illustrated by some simulation studies and real data examples.

American Journal of Applied Mathematics and Statistics. 2013, 1(1), 6-10. DOI: 10.12691/ajams-1-1-2
Pub. Date: March 07, 2013

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New Methods for Comparing the Forecasts Accuracy

by Bratu (Simionescu) Mihaela

Original Research

The main purpose of this research is to show the diversity of statistical methods that could be used to assess and compare forecasts accuracy. Some of the statistical approaches were not used before in literature to evaluate the forecasts accuracy. The different methods applied to compare the accuracy of the USA inflation forecasts on the horizon 1976-2012 started from the predictions provided by Survey of Professional Forecasters (SPF), Congressional Budget Office (CBO), Blue Chips (BC), and Administration, determining different results. According to U1 Theil’s statistic, non-parametric tests and a new indicator proposed by us (RRSSE- ratio of radicals of sum of squared errors), the best forecasts were provided by Administration and the less accurate by SPF. The Spearman’s and Kendall’s coefficients of correlation and the ranks method gavea hierarchy of institutions performance regarding the accuracy that starts with BC and finished with SPF. The logistic regression computed by the author and the relative distance to the maximal performance method considered CBO as the best institution. Some methods of improving the forecasts accuracy were applied, getting more accurate predictions for the combined forecasts of BC and CBO using optimal scheme of combination. The smoothed predicted values based on Hodrick-Prescott filter outperformed all the initial predictions and the combined ones.

American Journal of Applied Mathematics and Statistics. 2013, 1(1), 1-5. DOI: 10.12691/ajams-1-1-1
Pub. Date: March 07, 2013

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