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• W2078136370 abstract "Nonoscillatory advection schemes contain switches, so that the derivative of the numerical solution at any time step with respect to that at the previous time step may be discontinuous. In consequence, sensitivities calculated using the adjoint of the numerical scheme may be discontinuous or ambiguous. This discontinuity is not a property of the continuous advection equation; it is an artefact of the numerical schemes used to solve it. The problem is demonstrated in some simple one-dimensional test cases. We derive a result showing that there is no possibility of smoothing the switches in nonoscillatory advection schemes to remove the discontinuities while retaining an obvious and desirable scaling property. We discuss some alternative approaches to deriving the adjoint schemes needed for sensitivity calculations." @default.
• W2078136370 created "2016-06-24" @default.
• W2078136370 creator A5033149529 @default.
• W2078136370 creator A5072359304 @default.
• W2078136370 date "2001-08-01" @default.
• W2078136370 modified "2023-09-23" @default.
• W2078136370 title "Adjoints of Nonoscillatory Advection Schemes" @default.
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• W2078136370 doi "https://doi.org/10.1006/jcph.2001.6799" @default.
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