Minimal dissipation hybrid bicompact schemes for hyperbolic equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 6, pp. 958-972
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New monotonicity-preserving hybrid schemes are proposed for multidimensional hyperbolic equations. They are convex combinations of high-order accurate central bicompact schemes and upwind schemes of first-order accuracy in time and space. The weighting coefficients in these combinations depend on the local difference between the solutions produced by the high- and low-order accurate schemes at the current space-time point. The bicompact schemes are third-order accurate in time, while having the fourth order of accuracy and the first difference order in space. At every time level, they can be solved by marching in each spatial variable without using spatial splitting. The upwind schemes have minimal dissipation among all monotone schemes constructed on a minimum space-time stencil. The hybrid schemes constructed has been successfully tested as applied to a number of two-dimensional gas dynamics benchmark problems.
@article{ZVMMF_2016_56_6_a3,
author = {M. D. Bragin and B. V. Rogov},
title = {Minimal dissipation hybrid bicompact schemes for hyperbolic equations},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {958--972},
publisher = {mathdoc},
volume = {56},
number = {6},
year = {2016},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_6_a3/}
}
TY - JOUR AU - M. D. Bragin AU - B. V. Rogov TI - Minimal dissipation hybrid bicompact schemes for hyperbolic equations JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2016 SP - 958 EP - 972 VL - 56 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_6_a3/ LA - ru ID - ZVMMF_2016_56_6_a3 ER -
%0 Journal Article %A M. D. Bragin %A B. V. Rogov %T Minimal dissipation hybrid bicompact schemes for hyperbolic equations %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2016 %P 958-972 %V 56 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_6_a3/ %G ru %F ZVMMF_2016_56_6_a3
M. D. Bragin; B. V. Rogov. Minimal dissipation hybrid bicompact schemes for hyperbolic equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 6, pp. 958-972. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_6_a3/