An investigation of the internal structure of shock profiles for shock capturing schemes
2007 (English)In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, Vol. 201, no 1, 8-29 p.Article in journal (Refereed) Published
The theoretical understanding of discrete shock transitions obtained by shock capturing schemes is very incomplete. Previous experimental studies indicate that discrete shock transitions obtained by shock capturing schemes can be modeled by continuous functions, so called continuum shock profiles. However, the previous papers have focused on linear methods. We have experimentally studied the trajectories of discrete shock profiles in phase space for a range of different high resolution shock capturing schemes, including Riemann solver based flux limiter methods, high resolution central schemes and ENO type methods. In some cases, no continuum profiles exists. However, in these cases the point values in the shock transitions remain bounded and appear to converge toward a stable limit cycle. The possibility of such behavior was anticipated in Bultelle, Grassin and Serre, 1998, but no specific examples, or other evidence, of this behavior have previously been given. In other cases, our results indicate that continuum shock profiles exist, but are very complicated. We also study phase space orbits with regard to post shock oscillations.
Place, publisher, year, edition, pages
2007. Vol. 201, no 1, 8-29 p.
hyperbolic conservation law, shock capturing, shock profile, discrete shock, internal structure, flux limiter method, high resolution central scheme, ENO method
IdentifiersURN: urn:nbn:se:kth:diva-37193DOI: 10.1016/j.cam.2006.01.036ISI: 000244405000003ScopusID: 2-s2.0-33846163199OAI: oai:DiVA.org:kth-37193DiVA: diva2:432511