An Explanation to the Phenomenon of Coupled First Order Shift of Conservative Quantities during the Interaction of Captured Discontinuities
Dupont, Todd F.
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High resolution capturing schemes generally speaking can take advantage of the piece-wise smooth property of the weak solutions of conservation laws and achieve high order accuracy wherever the solution is smooth. Thus In 1D, the positions of smeared discontinuities may supposedly be recovered before they interact with each other using the subcell resolution methods (Harten ). An interesting phenomenon is that after their interaction, the recovered positions of smeared discontinuities degenerate to first order. We study this phenomena in an ideal model and give an explanation.