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Shock tracking based on high resolution wave propagation methods

by R. J. LeVeque and K. M. Shyue

(Report number 1992-01)

Abstract
We present a simple approach to shock tracking in conjunction with conservative high resolution shock-capturing methods in one space dimension. An underlying uniform grid is used with additional grid interfaces introduced at appropriate points for tracked shocks. Conservative high resolution methods based on the large time step wave propagation approach are used on the resulting nonuniform grid. This method is stable even if some of the small cells created by the tracked interface are orders of magnitude smaller than the regular cells used to determine the time step. A fractional step method is used to handle source terms. Several calculations are presented to demonstrate the effectiveness of the method, including an unstable detonation wave calculation where mesh refinement in the reaction zone is required in addition to shock tracking. Extension of these ideas to two space dimensions is briefly discussed.

Keywords: shock tracking, finite volume methods, high resolution methods, mesh refinement.

@Techreport{LS92_11,
  author = {R. J. LeVeque and K. M. Shyue},
  title = {Shock tracking based on high resolution wave propagation methods},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1992-01},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1992/1992-01.pdf },
  year = {1992}
}

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