Geodesic
Modeling of shock waves interaction on dynamically adapting grids
Matematičeskoe modelirovanie, Tome 19 (2007) no. 11, pp. 83-95

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The further development of a method of dynamic adaptation for gas dynamics problems describing repeated interaction of shock waves, rarefaction waves and contact boundaries is considered in the present paper. On an example of a test Woodward–Colella problem the efficiency of an offered method for problems of gas dynamics with explicit front tracking of shock waves and contact boundaries is shown. For a problem decision the elementary diffusing type adaptation is used. The choice of adaptation coefficient is reasonable to receive in each of subareas of the decision quasiuniform grid. The interaction of breaks among themselves is given from a Riemann solver. The application of a method of dynamic adaptation has allowed to receive the decision on 420 cells practically coincident with results of WENO5m method on 12800 cells. 
@article{MM_2007_19_11_a9,
     author = {P. V. Breslavskiy and V. I. Mazhukin},
     title = {Modeling of shock waves interaction on dynamically adapting grids},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {83--95},
     publisher = {mathdoc},
     volume = {19},
     number = {11},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2007_19_11_a9/}
}
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P. V. Breslavskiy; V. I. Mazhukin. Modeling of shock waves interaction on dynamically adapting grids. Matematičeskoe modelirovanie, Tome 19 (2007) no. 11, pp. 83-95. http://geodesic.mathdoc.fr/item/MM_2007_19_11_a9/