Geodesic
Nonlinear correction of Cabaret scheme
Matematičeskoe modelirovanie, Tome 10 (1998) no. 12, pp. 107-123.

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The paper presents a conservative algorithm of nonlinear correction for new three layer second order Cabaret scheme with a space split time derivative, which possesses enhanced dispersion and diffusion properties. The properties of the new algorithm are illustrated through sets of computational runs, where the algorithm is demonstrated to provide monotonicity of evolving solution with big space variations profiles. After comparison with positive nonlinear second order TVD and UNO schemes it is concluded that the new method enables to obtain sufficiently more accurate solution. The new method is used for solution of hyperbolic equations system following from two-phase filtration of immiscible fluids problem in the Backley–Laverett model. 
@article{MM_1998_10_12_a4,
     author = {V. M. Goloviznin and S. A. Karabasov},
     title = {Nonlinear correction of {Cabaret} scheme},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {107--123},
     publisher = {mathdoc},
     volume = {10},
     number = {12},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1998_10_12_a4/}
}
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V. M. Goloviznin; S. A. Karabasov. Nonlinear correction of Cabaret scheme. Matematičeskoe modelirovanie, Tome 10 (1998) no. 12, pp. 107-123. http://geodesic.mathdoc.fr/item/MM_1998_10_12_a4/