Abstract
High-order centered finite difference approximations of hyperbolic conservation laws are considered. Different ways of adding artificial viscosity to obtain sharp shock resolution are proposed. For the Riemann problem simple explicit formulas for obtaining stationary one- and two-point shocks are presented. This can be done for any order of accuracy. It is shown that the addition of artificial viscosity is equivalent to ensuring the Laxk-shock condition. Numerical experiments verify the theoretical results.
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This work has been sponsored by NASA under Contract No. NAS 2-13721.
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Gustafsson, B., Olsson, P. High-order centered difference methods with sharp shock resolution. J Sci Comput 11, 229–260 (1996). https://doi.org/10.1007/BF02088817
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DOI: https://doi.org/10.1007/BF02088817