Geodesic
The second order approximation TVD scheme on moving adaptive grids for hyperbolic systems
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 3 (2000) no. 2, pp. 109-121

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The second order approximation finite difference scheme for moving adaptive grids which is the generalization of the well-known Harten scheme is presented. The conditions sufficient to ensure that the scheme is the TVD are obtained. The numerical tests of the scheme for the system of equation of shallow water when solutions contain shocks and rarefaction waves are conducted. 
@article{SJVM_2000_3_2_a2,
     author = {V. B. Barakhnin and N. V. Borodkin},
     title = {The second order approximation {TVD} scheme on moving adaptive grids for hyperbolic systems},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {109--121},
     publisher = {mathdoc},
     volume = {3},
     number = {2},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2000_3_2_a2/}
}
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V. B. Barakhnin; N. V. Borodkin. The second order approximation TVD scheme on moving adaptive grids for hyperbolic systems. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 3 (2000) no. 2, pp. 109-121. http://geodesic.mathdoc.fr/item/SJVM_2000_3_2_a2/