Abstract:
We considered the central-difference NT-scheme (Nessyahu-Tadmor scheme) with the
second-order MUSCL reconstruction of flows. We studied the accuracy of the NT-scheme in calculations of shock waves propagating with a variable velocity. We showed
that this scheme has approximately the first order of the local convergence in the
domains of the influence of shock waves and the same order of integral convergence on
the intervals, one of the boundaries of which is in the region of the influence of shock
wave. As a result, the local accuracy of the NT-scheme is significantly reduced in these
areas. Test calculations are presented that demonstrate these properties of the NT-scheme.
Keywords:
NT scheme, MUSCL reconstruction, WENO scheme, combined scheme,
shock wave, accuracy of finite-difference scheme.
Citation:
O. A. Kovyrkina, V. V. Ostapenko, “On accuracy of MUSCL type scheme when calculating discontinuous solutions”, Mat. Model., 33:1 (2021), 105–121; Math. Models Comput. Simul., 13:5 (2021), 810–819
This publication is cited in the following 4 articles:
Olyana A. Kovyrkina, Vladimir V. Ostapenko, “On the accuracy of shock-capturing schemes when calculating Cauchy problems with periodic discontinuous initial data”, Russian Journal of Numerical Analysis and Mathematical Modelling, 39:2 (2024), 97
V. V. Ostapenko, E. I. Polunina, N. A. Khandeeva, “On the Accuracy of Calculating Invariants in Centered Rarefaction Waves and in Their Influence Area”, Dokl. Math., 2024
V. V. Ostapenko, E. I. Polunina, N. A. Khandeeva, “On the accuracy of calculating invariants in centered rarefaction waves and in their influence area”, Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, 518:1 (2024), 65
Shaoshuai Chu, Olyana A. Kovyrkina, Alexander Kurganov, Vladimir V. Ostapenko, “Experimental convergence rate study for three shock‐capturing schemes and development of highly accurate combined schemes”, Numerical Methods Partial, 39:6 (2023), 4317
Citation in format AMSBIB
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