Geodesic
Accuracy of MUSCL-type schemes in shock wave calculations
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 492 (2020), pp. 43-48.

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The central-difference Nessyahu–Tadmor (NT) scheme is considered, which is built using second-order MUSCL reconstruction of fluxes. The accuracy of the NT scheme is studied as applied to calculating shock waves propagating with a variable velocity. It is shown that this scheme has the first order of integral convergence on intervals with one of the boundaries lying in the region of influence of the 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 flux reconstruction, shock wave, accuracy of finite-difference scheme. 
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     author = {O. A. Kovyrkina and V. V. Ostapenko},
     title = {Accuracy of {MUSCL-type} schemes in shock wave calculations},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {43--48},
     publisher = {mathdoc},
     volume = {492},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_492_a8/}
}
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O. A. Kovyrkina; V. V. Ostapenko. Accuracy of MUSCL-type schemes in shock wave calculations. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 492 (2020), pp. 43-48. http://geodesic.mathdoc.fr/item/DANMA_2020_492_a8/

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