TY - JOUR

T1 - On the Construction of Combined Finite-Difference Schemes of High Accuracy

AU - Kovyrkina, O. A.

AU - Ostapenko, V. V.

N1 - Publisher Copyright: © 2018, Pleiades Publishing, Ltd.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - A method is proposed for constructing combined shock-capturing finite-difference schemes that localize shock fronts with high accuracy and preserve the high order of convergence in all domains where the computed weak solution is smooth. A particular combined scheme is considered in which a nonmonotone compact scheme with a third-order weak approximation is used as a basis one, while the internal scheme is the second-order accurate (for smooth solutions) monotone CABARET. The advantages of the new scheme are demonstrated using test computations.

AB - A method is proposed for constructing combined shock-capturing finite-difference schemes that localize shock fronts with high accuracy and preserve the high order of convergence in all domains where the computed weak solution is smooth. A particular combined scheme is considered in which a nonmonotone compact scheme with a third-order weak approximation is used as a basis one, while the internal scheme is the second-order accurate (for smooth solutions) monotone CABARET. The advantages of the new scheme are demonstrated using test computations.

UR - http://www.scopus.com/inward/record.url?scp=85044305759&partnerID=8YFLogxK

U2 - 10.1134/S1064562418010246

DO - 10.1134/S1064562418010246

M3 - Article

AN - SCOPUS:85044305759

VL - 97

SP - 77

EP - 81

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 1

ER -