Geodesic
Implicit-explicit bicompact schemes for hyperbolic systems of conservation laws
Matematičeskoe modelirovanie, Tome 34 (2022) no. 6, pp. 3-21

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High-order bicompact schemes for hyperbolic systems of conservation laws are considered. The goal is to achieve a significant speed-up for these schemes. Implicit-explicit Runge-Kutta methods are proposed for time discretization, instead of the previously used diagonally implicit methods. The global Lax-Friedrichs-Rusanov flux splitting is a premise for the implicit-explicit approximation. It is shown that implicit-explicit bicompact schemes are stable for any ratio of steps in time and space. The high accuracy of the new implicit-explicit schemes and the substantial speed-up are demonstrated on multidimensional gas dynamics problems.
Keywords: compact schemes, bicompact schemes, implicit-explicit Runge-Kutta methods, high-order schemes, hyperbolic systems of equations. 
@article{MM_2022_34_6_a0,
     author = {M. D. Bragin},
     title = {Implicit-explicit bicompact schemes for hyperbolic systems of conservation laws},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--21},
     publisher = {mathdoc},
     volume = {34},
     number = {6},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2022_34_6_a0/}
}
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M. D. Bragin. Implicit-explicit bicompact schemes for hyperbolic systems of conservation laws. Matematičeskoe modelirovanie, Tome 34 (2022) no. 6, pp. 3-21. http://geodesic.mathdoc.fr/item/MM_2022_34_6_a0/