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• W2016124412 abstract "Split numerical methods have been commonly used in computational physics for many years due to their speed, simplicity, and the accessibility of shock capturing methods in one-dimension. For a variety of reasons, it has been challenging to determine just how accurate operator split methods are, especially in the presence of curved wave features. One of these difficulties has been the lack of multidimensional shock capturing methods. Another is the difficulty of mathematical analysis of dis-continuous flow phenomena. Also, computational studies have been limited due to a lack of multidimensional model problems with analytic solutions that probe the nonlinear features of the flow equations. However, a new genuinely unsplit numerical method has been invented. With the advent of the Space-Time Conservation Element/Solution Element (CE/SE) method, it has become possible to attain high accuracy in multidimensional flows, even in the presence of curved shocks. Examples presented here provide some new evidence of the errors committed in the use of operator split techniques, even those employing �unsplit� corrections. In these problems, the CE/SE method is able to maintain the original cylindrical symmetry of the problem and track the main features of the flow, while the operator split methods fail to maintain symmetry and position the shocks incorrectly, particularly near the focal point of the incomi" @default.
• W2016124412 created "2016-06-24" @default.
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• W2016124412 date "1998-10-23" @default.
• W2016124412 modified "2023-09-24" @default.
• W2016124412 title "High accuracy capture of curved shock fronts using the method of space-time conservation element and solution elemen" @default.
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