Geodesic
Finite-difference method for the Navier–Stokes equations in a variable domain with curved boundaries
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 3, pp. 491-504

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A semi-implicit finite-difference scheme is proposed for solving the nonlinear viscous compressible Navier–Stokes equations. Coordinate transformations are constructed that yield a uniform mesh in the computational plane even though the physical domain under consideration is time-varying and curvilinear. The finite-difference scheme was tested using model examples. 
@article{ZVMMF_2008_48_3_a9,
     author = {A. B. Usov},
     title = {Finite-difference method for the {Navier{\textendash}Stokes} equations in a~variable domain with curved boundaries},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {491--504},
     publisher = {mathdoc},
     volume = {48},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_3_a9/}
}
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A. B. Usov. Finite-difference method for the Navier–Stokes equations in a variable domain with curved boundaries. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 3, pp. 491-504. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_3_a9/