Geodesic
Computation of two-dimensional flows using multilevel meshes
Numerical methods and programming, Tome 14 (2013) no. 4, pp. 451-460.

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For two-dimensional problems of perfect gas dynamics, a special form of equations consisting of conservation laws for directed invariants is proposed. Based on these equations, a number of schemes for computing gas flows using multilevel meshes are developed. These schemes use the time-multilevel refinement for the rate of change in the invariants which allows one to substantially reduce computational cost. An additional advantage of these schemes is the fact that an appropriate choice of the directions of the invariants allows one to prevent the distortions of the solution dependent on the orientation of coordinate axes.
Keywords: AMR (Automated Mesh Refinement); irregular grids; Riemann invariants; AMR (Automated Mesh Refinement). 
@article{VMP_2013_14_4_a3,
     author = {D. A. Gubaidullin and P. P. Osipov},
     title = {Computation of two-dimensional flows using multilevel meshes},
     journal = {Numerical methods and programming},
     pages = {451--460},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2013_14_4_a3/}
}
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D. A. Gubaidullin; P. P. Osipov. Computation of two-dimensional flows using multilevel meshes. Numerical methods and programming, Tome 14 (2013) no. 4, pp. 451-460. http://geodesic.mathdoc.fr/item/VMP_2013_14_4_a3/