×

Contact discontinuity capturing schemes for linear advection and compressible gas dynamics. (English) Zbl 0999.76091

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.

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

Software:

HE-E1GODF
PDFBibTeX XMLCite
Full Text: DOI