Abstract
We present a non-diffusive and contact discontinuity capturing scheme for linear advection and compressible Euler system. In the case of advection, this scheme is equivalent to the Ultra-Bee limiter of [24], [29]. 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. We generalize the scheme to compressible gas dynamics and present some numerical results.
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Després, B., Lagoutière, F. Contact Discontinuity Capturing Schemes for Linear Advection and Compressible Gas Dynamics. Journal of Scientific Computing 16, 479–524 (2001). https://doi.org/10.1023/A:1013298408777
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DOI: https://doi.org/10.1023/A:1013298408777