Title: Improving the quantification of overshooting shock-capturing oscillations

Authors: Fan Zhang

Addresses: Centre for Mathematical Plasma-Astrophysics, Department of Mathematics, KU Leuven, Leuven 3001, Belgium; Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029, Blindern, 0315 Oslo, Norway; Rosseland Centre for Solar Physics, University of Oslo, P.O. Box 1029, Blindern, 0315 Oslo, Norway

Abstract: An approach for quantitatively evaluating overshooting oscillations is designed to characterise the performance of shock-capturing schemes. Specifically, following our previous work focused on cases with only discontinuities, now we account for the concurrent presences of discontinuities and smooth waves, each with a complete set of supported modes on a given discretisation. The linear advection equation is taken as the model equation, and a standardised measurement is given for overshooting oscillations produced by shock-capturing schemes. Thereby, we can quantitatively reveal the shock-capturing robustness of, for example, weighted essentially non-oscillatory schemes, by comparing and analysing the resulting overshoots. In particular, we are able to find out the ranges of wavenumbers in which the numerical schemes are especially prone to produce overshooting oscillations. While lower dissipation is usually anticipated for high-order schemes, we provide a simple measurement for evaluating the shock-capturing robustness, which was not trivial due to the nonlinearity of shock-capturing computations.

Keywords: shock-capturing; overshooting oscillation; quantitative measurement; high-order scheme; finite-difference method.

DOI: 10.1504/PCFD.2024.138236

Progress in Computational Fluid Dynamics, An International Journal, 2024 Vol.24 No.3, pp.135 - 142

Received: 07 Jul 2023
Accepted: 15 Oct 2023
Published online: 30 Apr 2024 *

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