Geodesic
Application of WENO-schemes for modelling shockwave processes
Matematičeskoe modelirovanie, Tome 36 (2024) no. 2, pp. 25-40

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The present paper is concerned with the analysis of WENO-schemes for the solution of one-dimensional Euler equations with a Mie–Grüneisen type equation of state. The least dissipative and oscillatory modifications of WENO-schemes in characteristic variables with a monotonicity-preserving (MP) limiter are presented. A modified scheme, MP-WENO-SM, is developed, demonstrating the smallest amplitude of oscillations in the solution of the test problems with discontinuous initial data.
Keywords: WENO, computational fluid dynamics, equations of state, shock waves in metals. 
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     author = {F. A. Belolutskiy and V. V. Shepelev and S. V. Fortova},
     title = {Application of {WENO-schemes} for modelling shockwave processes},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {25--40},
     publisher = {mathdoc},
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     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2024_36_2_a1/}
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F. A. Belolutskiy; V. V. Shepelev; S. V. Fortova. Application of WENO-schemes for modelling shockwave processes. Matematičeskoe modelirovanie, Tome 36 (2024) no. 2, pp. 25-40. http://geodesic.mathdoc.fr/item/MM_2024_36_2_a1/