Geodesic
On accuracy of MUSCL type scheme when calculating discontinuous solutions
Matematičeskoe modelirovanie, Tome 33 (2021) no. 1, pp. 105-121

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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, WENO scheme, combined scheme, shock wave, accuracy of finite-difference scheme.
Mots-clés : MUSCL reconstruction 
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     author = {O. A. Kovyrkina and V. V. Ostapenko},
     title = {On accuracy of {MUSCL}  type scheme when calculating discontinuous solutions},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {105--121},
     publisher = {mathdoc},
     volume = {33},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2021_33_1_a7/}
}
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O. A. Kovyrkina; V. V. Ostapenko. On accuracy of MUSCL  type scheme when calculating discontinuous solutions. Matematičeskoe modelirovanie, Tome 33 (2021) no. 1, pp. 105-121. http://geodesic.mathdoc.fr/item/MM_2021_33_1_a7/