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A Shock Tracking Technique Based on Conservation in One Space Dimension

by M. De-kang

(Report number 1992-12)

Abstract
In this paper, which is a continuation of [20], [21], [22] and [24], we present a shock tracking technique in one space dimension. The main feature of the technique is that it uses the conservativity of the hyperbolic conservation laws rather than the Hugoniot condition to track discontinuities. Roughly speaking, the technique is as follows: The computation of a numerical solution on each side of a discontinuity uses information only from the same side. This can be done by employing extrapolated data on the same side. From the viewpoint of shock capturing the overall scheme is not conservative therefore, conservation errors that indicate how far the numerical solution is away from being conserved are formed on every time level. These conservation errors are used to locate the discontinuity positions within the grid cells. Numerical analysis of the conservation and of the relation between the conservation errors and discontinuity positions are presented. Handling of interactions of discontinuities is developed. Finally, numerical examples are presented to show the efficiency of the technique.

Keywords: shocking tracking, conservation errors, stacking technique, clean-up step

@Techreport{D92_22,
  author = {M. De-kang},
  title = {A Shock Tracking Technique Based on Conservation in One Space Dimension},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1992-12},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1992/1992-12.pdf },
  year = {1992}
}

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