Després, Bruno; Lagoutière, Frédéric Contact discontinuity capturing schemes for linear advection and compressible gas dynamics. (English) Zbl 0999.76091 J. Sci. Comput. 16, No. 4, 479-524 (2001). Summary: We present a non-diffusive contact discontinuity capturing scheme for linear advection and compressible Euler system. In the case of advection, this scheme is equivalent to Ultra-Bee limiter. We prove for the Ultra-Bee scheme a property of exact advection for a large set of piecewise constant functions. We prove that the numerical error is uniformly bounded in time for such prepared (i.e., piecewise constant) initial data, and state a conjecture of non-diffusion at infinite time, based on some local over-compressivity of the scheme, for general initial data. Finally, we generalize the scheme to compressible gas dynamics, and present some numerical results. Cited in 5 ReviewsCited in 59 Documents MSC: 76M20 Finite difference methods applied to problems in fluid mechanics 76N15 Gas dynamics (general theory) 76R99 Diffusion and convection 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs Keywords:error estimate; TVD limiter; non-diffusive contact discontinuity capturing scheme; linear advection; compressible Euler system; Ultra-Bee limiter; local over-compressivity Software:HE-E1GODF PDFBibTeX XMLCite \textit{B. Després} and \textit{F. Lagoutière}, J. Sci. Comput. 16, No. 4, 479--524 (2001; Zbl 0999.76091) Full Text: DOI