Geodesic
Cartesian grids methods for numerical solution of Navier--Stokes equations in domains with curvilinear boundaries
Matematičeskoe modelirovanie, Tome 17 (2005) no. 8, pp. 15-30

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In this article the questions for numerical solution of Navier–Stokes equations for incompressible fluid in domains with curvilinear boundary are considered. A brief overview for contemporary approaches for solving problems on Cartesian grids is given. A modification of ghost-cell immersed boundary method with implicit extrapolation procedure for boundary condition approximation on curvilinear boundary is introduced. Numerical solution of test problems for flow in symmetric channel with smooth expansion is carried out. Obtained results are validated by comparison with high precision results, taken as “exact”. 
@article{MM_2005_17_8_a2,
     author = {V. V. Vinnikov and D. L. Reviznikov},
     title = {Cartesian grids methods for numerical solution of {Navier--Stokes} equations in domains with curvilinear boundaries},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {15--30},
     publisher = {mathdoc},
     volume = {17},
     number = {8},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2005_17_8_a2/}
}
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V. V. Vinnikov; D. L. Reviznikov. Cartesian grids methods for numerical solution of Navier--Stokes equations in domains with curvilinear boundaries. Matematičeskoe modelirovanie, Tome 17 (2005) no. 8, pp. 15-30. http://geodesic.mathdoc.fr/item/MM_2005_17_8_a2/