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Computational experiments on the weighted linear discontinuous method
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This thesis is based on numerical results reported by Szilard and Pomramng' related to an anomalous third order behavior obtained as they approximated solutions to the angular flux in the neutron transport equation by means of a modified linear disrontinuous method that includes a spatially linear representation of such flux. The anomaly consists in that analytical predictions suggested this method to have only second order. The main objective of this thesis is then provide an explanation for this anomalous behavior. The " Quasi-lEgh Order" effect seems to provide a reasonable explanation for such phenomenon. The essence of this effect is the observation that if an error involves both second-order and third order terms, but the coefficient of the second order term is much smaller in magnitude than the third order until very fine meshes indeed are reached. This effect may be difficult to observe directly, because the coefficients can be sensitive functions of the physical and numerical characteristics of the particular problem. In particular, the material thickness and the secondary scattering ratio are found to be two of those physical parameters that have an important impact in the values of these coefficients for one region problems. It was also observed that for two material problems that share a material interface, the " Quasi-lEgh Order" effect can be seen at such interfaces. However, for these "w of problems the predicted second order behavior was observed under source and boundary conditions. To provide with the evidence that supports the hypothesis mentioned above we made use of LOCFES-G, which is a slightly modified version of previously existing code LOCFES. LOCFES is intended to provide computational estimates of the asymptotic order of accuracy for any spatial approximation in one-dirnensional plane-parallel geometry that falls within the broad class of so-called " closed linear one-cefl functional" methods. The " Quasi-lEgh Order Hypothesis" is confirmed directly in the sense that for an appropriate combination of material thickness and secondary g ratio LOCFES-G estimates the order as three for coarse meshes but as two for finer meshes, with an intermediate transition region. If one accepts this evidence as establishing the quasi-high order hypothesis, then this the original predictions of Szilard and Pomraning.
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Includes bibliographical references.
Rodriguez, Gabriel (1994). Computational experiments on the weighted linear discontinuous method. Master's thesis, Texas A&M University. Available electronically from
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