Geodesic
Numerical simulation of the dynamics of non-uniform compressible media based on the CIP-CUP method on dynamically adaptive Soroban grids
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 2, pp. 55-71

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We compare the efficiency of the CIP-CUP method on a stationary uniform staggered grid and the modifications of this method on a non-staggered dynamically adaptive Soroban grid and a non-staggered stationary uniform grid in their use for computing problems of wave propagation in uniform (liquid) and non-uniform (with the presence of gas–gas and gas–liquid contact boundaries) media. We show that as compared with the initial version of the CIP-CUP method on a stationary uniform staggered grid, its modification on a Soroban grid allows one to conduct computations with similar or even higher accuracy and to apply significantly smaller number of grid vertices. The modification of the CIP-CUP method on a stationary uniform non-staggered grid is least efficient. Moreover, it can lead to non-monotonic solutions.
Keywords: shock waves, non-uniform medium, CIP-CUP method, adaptive Soroban grids. 
@article{UZKU_2014_156_2_a5,
     author = {A. A. Aganin and T. S. Guseva},
     title = {Numerical simulation of the dynamics of non-uniform compressible media based on the {CIP-CUP} method on dynamically adaptive {Soroban} grids},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {55--71},
     publisher = {mathdoc},
     volume = {156},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2014_156_2_a5/}
}
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A. A. Aganin; T. S. Guseva. Numerical simulation of the dynamics of non-uniform compressible media based on the CIP-CUP method on dynamically adaptive Soroban grids. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 2, pp. 55-71. http://geodesic.mathdoc.fr/item/UZKU_2014_156_2_a5/